diff --git a/Gemfile b/Gemfile
old mode 100755
new mode 100644
index e3aacc5..6616c58
--- a/Gemfile
+++ b/Gemfile
@@ -20,14 +20,14 @@ group :jekyll_plugins do
   gem "jekyll-twitter-plugin"
   gem 'jekyll-relative-links'
   gem 'jekyll-seo-tag'
-  gem 'jekyll-toc'
+  gem 'jekyll-toc', '>= 0.15.0'
   gem 'jekyll-gist'
   gem 'jekyll-paginate'
   gem 'jekyll-sitemap'
 end
 
 gem "kramdown-math-katex"
-gem "jemoji"
+gem "jemoji", ">= 0.13.0"
 
 # Windows and JRuby does not include zoneinfo files, so bundle the tzinfo-data gem
 # and associated library.
diff --git a/Gemfile.lock b/Gemfile.lock
index 3b85fca..0fe5db1 100644
--- a/Gemfile.lock
+++ b/Gemfile.lock
@@ -1,31 +1,31 @@
 GEM
   remote: https://rubygems.org/
   specs:
-    activesupport (6.1.7.5)
+    activesupport (6.0.6.1)
       concurrent-ruby (~> 1.0, >= 1.0.2)
       i18n (>= 0.7, < 2)
       minitest (~> 5.1)
       tzinfo (~> 1.1)
       zeitwerk (~> 2.2, >= 2.2.2)
-    addressable (2.8.0)
-      public_suffix (>= 2.0.2, < 5.0)
+    addressable (2.8.7)
+      public_suffix (>= 2.0.2, < 7.0)
     colorator (1.1.0)
-    concurrent-ruby (1.1.7)
-    em-websocket (0.5.1)
+    concurrent-ruby (1.3.5)
+    em-websocket (0.5.3)
       eventmachine (>= 0.12.9)
-      http_parser.rb (~> 0.6.0)
+      http_parser.rb (~> 0)
     eventmachine (1.2.7)
     execjs (2.7.0)
     faraday (0.17.3)
       multipart-post (>= 1.2, < 3)
-    ffi (1.13.1)
+    ffi (1.17.2)
     forwardable-extended (2.6.0)
-    gemoji (3.0.1)
-    html-pipeline (2.14.0)
+    gemoji (4.1.0)
+    html-pipeline (2.14.3)
       activesupport (>= 2)
       nokogiri (>= 1.4)
-    http_parser.rb (0.6.0)
-    i18n (1.8.5)
+    http_parser.rb (0.8.0)
+    i18n (1.14.7)
       concurrent-ruby (~> 1.0)
     jekyll (4.1.1)
       addressable (~> 2.4)
@@ -57,44 +57,44 @@ GEM
       jekyll (>= 3.5, < 5.0)
       jekyll-sass-converter (>= 1.0, <= 3.0.0, != 2.0.0)
       rubyzip (>= 1.3.0, < 3.0)
-    jekyll-sass-converter (2.1.0)
+    jekyll-sass-converter (2.2.0)
       sassc (> 2.0.1, < 3.0)
     jekyll-seo-tag (2.6.1)
       jekyll (>= 3.3, < 5.0)
     jekyll-sitemap (1.4.0)
       jekyll (>= 3.7, < 5.0)
-    jekyll-toc (0.14.0)
-      jekyll (>= 3.8)
-      nokogiri (~> 1.10)
+    jekyll-toc (0.19.0)
+      jekyll (>= 3.9)
+      nokogiri (~> 1.12)
     jekyll-twitter-plugin (2.1.0)
     jekyll-watch (2.2.1)
       listen (~> 3.0)
-    jemoji (0.12.0)
-      gemoji (~> 3.0)
+    jemoji (0.13.0)
+      gemoji (>= 3, < 5)
       html-pipeline (~> 2.2)
       jekyll (>= 3.0, < 5.0)
     katex (0.6.0)
       execjs (~> 2.7)
-    kramdown (2.3.1)
-      rexml
+    kramdown (2.5.1)
+      rexml (>= 3.3.9)
     kramdown-math-katex (1.0.1)
       katex (~> 0.4)
       kramdown (~> 2.0)
     kramdown-parser-gfm (1.1.0)
       kramdown (~> 2.0)
-    liquid (4.0.3)
-    listen (3.2.1)
+    liquid (4.0.4)
+    listen (3.9.0)
       rb-fsevent (~> 0.10, >= 0.10.3)
       rb-inotify (~> 0.9, >= 0.9.10)
     mercenary (0.4.0)
-    mini_portile2 (2.8.8)
+    mini_portile2 (2.8.9)
     minima (2.5.1)
       jekyll (>= 3.5, < 5.0)
       jekyll-feed (~> 0.9)
       jekyll-seo-tag (~> 2.1)
-    minitest (5.14.2)
+    minitest (5.25.5)
     multipart-post (2.1.1)
-    nokogiri (1.18.3)
+    nokogiri (1.15.7)
       mini_portile2 (~> 2.8.2)
       racc (~> 1.4)
     octicons (11.0.0)
@@ -104,13 +104,13 @@ GEM
       sawyer (~> 0.8.0, >= 0.5.3)
     pathutil (0.16.2)
       forwardable-extended (~> 2.6)
-    public_suffix (4.0.6)
+    public_suffix (5.1.1)
     racc (1.8.1)
-    rb-fsevent (0.10.4)
-    rb-inotify (0.10.1)
+    rb-fsevent (0.11.2)
+    rb-inotify (0.11.1)
       ffi (~> 1.0)
-    rexml (3.3.9)
-    rouge (3.23.0)
+    rexml (3.4.1)
+    rouge (3.30.0)
     rubyzip (2.3.0)
     safe_yaml (1.0.5)
     sassc (2.4.0)
@@ -121,13 +121,13 @@ GEM
     terminal-table (1.8.0)
       unicode-display_width (~> 1.1, >= 1.1.1)
     thread_safe (0.3.6)
-    tzinfo (1.2.10)
+    tzinfo (1.2.11)
       thread_safe (~> 0.1)
     tzinfo-data (1.2020.1)
       tzinfo (>= 1.0.0)
-    unicode-display_width (1.7.0)
+    unicode-display_width (1.8.0)
     wdm (0.1.1)
-    zeitwerk (2.4.0)
+    zeitwerk (2.6.18)
 
 PLATFORMS
   ruby
@@ -143,9 +143,9 @@ DEPENDENCIES
   jekyll-remote-theme
   jekyll-seo-tag
   jekyll-sitemap
-  jekyll-toc
+  jekyll-toc (>= 0.15.0)
   jekyll-twitter-plugin
-  jemoji
+  jemoji (>= 0.13.0)
   kramdown-math-katex
   minima
   tzinfo (~> 1.2)