add september notes & hw2 code / pdf

8 files changed, 566 insertions, 0 deletions

diff --git a/homeworks/hw-2.org b/homeworks/hw-2.org
new file mode 100644
index 0000000..c570b65
--- /dev/null
+++ b/homeworks/hw-2.org
@@ -0,0 +1,179 @@
+#+TITLE: HW 02
+#+AUTHOR: Elizabeth Hunt
+#+STARTUP: entitiespretty fold inlineimages
+#+LATEX_HEADER: \notindent \notag  \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry}
+#+LATEX: \setlength\parindent{0pt}
+#+OPTIONS: toc:nil
+
+* Question One
+Computing $\epsilon_{\text{mac}}$ for single precision numbers
+
+#+BEGIN_SRC lisp :session t :results table 
+  (load "../cl/lizfcm.asd")
+  (ql:quickload :lizfcm)
+
+  (let ((domain-values (lizfcm.approx:compute-maceps 1.0
+                                                     (lambda (x) x))))
+    (lizfcm.utils:table (:headers '("a" "h" "err")
+                         :domain-order (a h err)
+                         :domain-values domain-values)))
+#+END_SRC
+
+(with many rows truncated)
+
+|   a |             h |           err |
+| 1.0 |           0.5 |           0.5 |
+| 1.0 |          0.25 |          0.25 |
+| 1.0 |         0.125 |         0.125 |
+| 1.0 |        0.0625 |        0.0625 |
+| 1.0 | 1.9073486e-06 | 1.9073486e-06 |
+| 1.0 |  9.536743e-07 |  9.536743e-07 |
+| 1.0 | 4.7683716e-07 | 4.7683716e-07 |
+| 1.0 | 2.3841858e-07 | 2.3841858e-07 |
+| 1.0 | 1.1920929e-07 | 1.1920929e-07 |
+| 1.0 | 5.9604645e-08 |           0.0 |
+
+$\epsilon_{\text{mac}}$ \approx 5.9604 \cdot 10^{-8}
+
+* Question Two
+Computing $\epsilon_{\text{mac}}$ for double precision numbers:
+
+#+BEGIN_SRC lisp :session t :results table
+  (let ((domain-values (lizfcm.approx:compute-maceps 1.0d0
+                                                     (lambda (x) x))))
+    (lizfcm.utils:table (:headers '("a" "h" "err")
+                         :domain-order (a h err)
+                         :domain-values domain-values)))
+#+END_SRC
+
+(with many rows truncated)
+|     a |                      h |                    err |
+| 1.0d0 |                  0.5d0 |                  0.5d0 |
+| 1.0d0 |                 0.25d0 |                 0.25d0 |
+| 1.0d0 |                0.125d0 |                0.125d0 |
+| 1.0d0 |               0.0625d0 |               0.0625d0 |
+| 1.0d0 |              0.03125d0 |              0.03125d0 |
+| 1.0d0 |             0.015625d0 |             0.015625d0 |
+| 1.0d0 |            0.0078125d0 |            0.0078125d0 |
+| 1.0d0 |           0.00390625d0 |           0.00390625d0 |
+| 1.0d0 |          0.001953125d0 |          0.001953125d0 |
+| 1.0d0 |  7.105427357601002d-15 |  7.105427357601002d-15 |
+| 1.0d0 |  3.552713678800501d-15 |  3.552713678800501d-15 |
+| 1.0d0 | 1.7763568394002505d-15 | 1.7763568394002505d-15 |
+| 1.0d0 |  8.881784197001252d-16 |  8.881784197001252d-16 |
+| 1.0d0 |  4.440892098500626d-16 |  4.440892098500626d-16 |
+| 1.0d0 |  2.220446049250313d-16 |  2.220446049250313d-16 |
+| 1.0d0 | 1.1102230246251565d-16 |                  0.0d0 |
+
+Thus, $\epsilon_{\text{mac}}$ \approx 1.1102 \cdot 10^{-16}
+
+* Question Three - |v|_2
+#+BEGIN_SRC lisp :session t
+  (let ((vs '((1 1) (2 3) (4 5) (-1 2)))
+        (2-norm (lizfcm.vector:p-norm 2)))
+    (lizfcm.utils:table (:headers '("x" "y" "2norm")
+                         :domain-order (x y)
+                         :domain-values vs)
+      (funcall 2-norm (list x y))))
+#+END_SRC
+
+
+|  x | y |     2norm |
+|  1 | 1 | 1.4142135 |
+|  2 | 3 | 3.6055512 |
+|  4 | 5 | 6.4031243 |
+| -1 | 2 |  2.236068 |
+
+* Question Four - |v|_1
+#+BEGIN_SRC lisp :session t
+  (let ((vs '((1 1) (2 3) (4 5) (-1 2)))
+        (1-norm (lizfcm.vector:p-norm 1)))
+    (lizfcm.utils:table (:headers '("x" "y" "1norm")
+                         :domain-order (x y)
+                         :domain-values vs)
+      (funcall 1-norm (list x y))))
+#+END_SRC
+
+
+|  x | y | 1norm |
+|  1 | 1 |     2 |
+|  2 | 3 |     5 |
+|  4 | 5 |     9 |
+| -1 | 2 |     3 |
+
+* Question Five - |v|_{\infty}
+#+BEGIN_SRC lisp :session t
+  (let ((vs '((1 1) (2 3) (4 5) (-1 2))))
+    (lizfcm.utils:table (:headers '("x" "y" "max-norm")
+                         :domain-order (x y)
+                         :domain-values vs)
+      (lizfcm.vector:max-norm (list x y))))
+#+END_SRC
+
+
+|  x | y | infty-norm |
+|  1 | 1 |          1 |
+|  2 | 3 |          3 |
+|  4 | 5 |          5 |
+| -1 | 2 |          2 |
+
+* Question Six - ||v - u|| via |v|_{2}
+#+BEGIN_SRC lisp :session t
+  (let* ((vs '((1 1) (2 3) (4 5) (-1 2)))
+         (vs2 '((7 9) (2 2) (8 -1) (4 4)))
+         (2-norm (lizfcm.vector:p-norm 2)))
+    (lizfcm.utils:table (:headers '("v1" "v2" "2-norm-d")
+                         :domain-order (v1 v2)
+                         :domain-values (mapcar (lambda (v1 v2)
+                                                  (list v1 v2))
+                                                vs
+                                                vs2))
+      (lizfcm.vector:distance v1 v2 2-norm)))
+#+END_SRC
+
+
+| v1     | v2     |    2-norm |
+| (1 1)  | (7 9)  |      10.0 |
+| (2 3)  | (2 2)  |       1.0 |
+| (4 5)  | (8 -1) | 7.2111025 |
+| (-1 2) | (4 4)  | 5.3851647 |
+
+* Question Seven - ||v - u|| via |v|_{1}
+#+BEGIN_SRC lisp :session t
+  (let* ((vs '((1 1) (2 3) (4 5) (-1 2)))
+         (vs2 '((7 9) (2 2) (8 -1) (4 4)))
+         (1-norm (lizfcm.vector:p-norm 1)))
+    (lizfcm.utils:table (:headers '("v1" "v2" "1-norm-d")
+                         :domain-order (v1 v2)
+                         :domain-values (mapcar (lambda (v1 v2)
+                                                  (list v1 v2))
+                                                vs
+                                                vs2))
+      (lizfcm.vector:distance v1 v2 1-norm)))
+#+END_SRC
+
+
+| v1     | v2     | 1-norm-d |
+| (1 1)  | (7 9)  |       14 |
+| (2 3)  | (2 2)  |        1 |
+| (4 5)  | (8 -1) |       10 |
+| (-1 2) | (4 4)  |        7 |
+
+* Question Eight - ||v - u|| via |v|_{\infty}
+#+BEGIN_SRC lisp :session t
+  (let* ((vs '((1 1) (2 3) (4 5) (-1 2)))
+         (vs2 '((7 9) (2 2) (8 -1) (4 4))))
+    (lizfcm.utils:table (:headers '("v1" "v2" "max-norm-d")
+                         :domain-order (v1 v2)
+                         :domain-values (mapcar (lambda (v1 v2)
+                                                  (list v1 v2))
+                                                vs
+                                                vs2))
+      (lizfcm.vector:distance v1 v2 'lizfcm.vector:max-norm)))
+#+END_SRC
+
+| v1     | v2     | max-norm-d |
+| (1 1)  | (7 9)  |         -6 |
+| (2 3)  | (2 2)  |          1 |
+| (4 5)  | (8 -1) |          6 |
+| (-1 2) | (4 4)  |         -2 |
diff --git a/homeworks/hw-2.pdf b/homeworks/hw-2.pdf
new file mode 100644
index 0000000..fed1f44
--- /dev/null
+++ b/homeworks/hw-2.pdf
diff --git a/homeworks/hw-2.tex b/homeworks/hw-2.tex
new file mode 100644
index 0000000..5155448
--- /dev/null
+++ b/homeworks/hw-2.tex
@@ -0,0 +1,243 @@
+% Created 2023-09-25 Mon 09:52
+% Intended LaTeX compiler: pdflatex
+\documentclass[11pt]{article}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{graphicx}
+\usepackage{longtable}
+\usepackage{wrapfig}
+\usepackage{rotating}
+\usepackage[normalem]{ulem}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{capt-of}
+\usepackage{hyperref}
+\notindent \notag  \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry}
+\author{Elizabeth Hunt}
+\date{\today}
+\title{HW 02}
+\hypersetup{
+ pdfauthor={Elizabeth Hunt},
+ pdftitle={HW 02},
+ pdfkeywords={},
+ pdfsubject={},
+ pdfcreator={Emacs 28.2 (Org mode 9.7-pre)}, 
+ pdflang={English}}
+\begin{document}
+
+\maketitle
+\setlength\parindent{0pt}
+
+\section{Question One}
+\label{sec:orga203815}
+Computing \(\epsilon_{\text{mac}}\) for single precision numbers
+
+\begin{verbatim}
+(load "../cl/lizfcm.asd")
+(ql:quickload :lizfcm)
+
+(let ((domain-values (lizfcm.approx:compute-maceps 1.0
+                                                   (lambda (x) x))))
+  (lizfcm.utils:table (:headers '("a" "h" "err")
+                       :domain-order (a h err)
+                       :domain-values domain-values)))
+\end{verbatim}
+
+(with many rows truncated)
+
+\begin{center}
+\begin{tabular}{rrr}
+a & h & err\\[0pt]
+1.0 & 0.5 & 0.5\\[0pt]
+1.0 & 0.25 & 0.25\\[0pt]
+1.0 & 0.125 & 0.125\\[0pt]
+1.0 & 0.0625 & 0.0625\\[0pt]
+1.0 & 1.9073486e-06 & 1.9073486e-06\\[0pt]
+1.0 & 9.536743e-07 & 9.536743e-07\\[0pt]
+1.0 & 4.7683716e-07 & 4.7683716e-07\\[0pt]
+1.0 & 2.3841858e-07 & 2.3841858e-07\\[0pt]
+1.0 & 1.1920929e-07 & 1.1920929e-07\\[0pt]
+1.0 & 5.9604645e-08 & 0.0\\[0pt]
+\end{tabular}
+\end{center}
+
+\(\epsilon_{\text{mac}}\) \(\approx\) 5.9604 \(\cdot\) 10\textsuperscript{-8}
+
+\section{Question Two}
+\label{sec:orgdd79be1}
+Computing \(\epsilon_{\text{mac}}\) for double precision numbers:
+
+\begin{verbatim}
+(let ((domain-values (lizfcm.approx:compute-maceps 1.0d0
+                                                   (lambda (x) x))))
+  (lizfcm.utils:table (:headers '("a" "h" "err")
+                       :domain-order (a h err)
+                       :domain-values domain-values)))
+\end{verbatim}
+
+(with many rows truncated)
+\begin{center}
+\begin{tabular}{rrr}
+a & h & err\\[0pt]
+1.0d0 & 0.5d0 & 0.5d0\\[0pt]
+1.0d0 & 0.25d0 & 0.25d0\\[0pt]
+1.0d0 & 0.125d0 & 0.125d0\\[0pt]
+1.0d0 & 0.0625d0 & 0.0625d0\\[0pt]
+1.0d0 & 0.03125d0 & 0.03125d0\\[0pt]
+1.0d0 & 0.015625d0 & 0.015625d0\\[0pt]
+1.0d0 & 0.0078125d0 & 0.0078125d0\\[0pt]
+1.0d0 & 0.00390625d0 & 0.00390625d0\\[0pt]
+1.0d0 & 0.001953125d0 & 0.001953125d0\\[0pt]
+1.0d0 & 7.105427357601002d-15 & 7.105427357601002d-15\\[0pt]
+1.0d0 & 3.552713678800501d-15 & 3.552713678800501d-15\\[0pt]
+1.0d0 & 1.7763568394002505d-15 & 1.7763568394002505d-15\\[0pt]
+1.0d0 & 8.881784197001252d-16 & 8.881784197001252d-16\\[0pt]
+1.0d0 & 4.440892098500626d-16 & 4.440892098500626d-16\\[0pt]
+1.0d0 & 2.220446049250313d-16 & 2.220446049250313d-16\\[0pt]
+1.0d0 & 1.1102230246251565d-16 & 0.0d0\\[0pt]
+\end{tabular}
+\end{center}
+
+Thus, \(\epsilon_{\text{mac}}\) \(\approx\) 1.1102 \(\cdot\) 10\textsuperscript{-16}
+
+\section{Question Three - |v|\textsubscript{2}}
+\label{sec:org04608d9}
+\begin{verbatim}
+(let ((vs '((1 1) (2 3) (4 5) (-1 2)))
+      (2-norm (lizfcm.vector:p-norm 2)))
+  (lizfcm.utils:table (:headers '("x" "y" "2norm")
+                       :domain-order (x y)
+                       :domain-values vs)
+    (funcall 2-norm (list x y))))
+\end{verbatim}
+
+
+\begin{center}
+\begin{tabular}{rrr}
+x & y & 2norm\\[0pt]
+1 & 1 & 1.4142135\\[0pt]
+2 & 3 & 3.6055512\\[0pt]
+4 & 5 & 6.4031243\\[0pt]
+-1 & 2 & 2.236068\\[0pt]
+\end{tabular}
+\end{center}
+
+\section{Question Four - |v|\textsubscript{1}}
+\label{sec:orgfb57f3a}
+\begin{verbatim}
+(let ((vs '((1 1) (2 3) (4 5) (-1 2)))
+      (1-norm (lizfcm.vector:p-norm 1)))
+  (lizfcm.utils:table (:headers '("x" "y" "1norm")
+                       :domain-order (x y)
+                       :domain-values vs)
+    (funcall 1-norm (list x y))))
+\end{verbatim}
+
+
+\begin{center}
+\begin{tabular}{rrr}
+x & y & 1norm\\[0pt]
+1 & 1 & 2\\[0pt]
+2 & 3 & 5\\[0pt]
+4 & 5 & 9\\[0pt]
+-1 & 2 & 3\\[0pt]
+\end{tabular}
+\end{center}
+
+\section{Question Five - |v|\textsubscript{\(\infty\)}}
+\label{sec:org7bbdf04}
+\begin{verbatim}
+(let ((vs '((1 1) (2 3) (4 5) (-1 2))))
+  (lizfcm.utils:table (:headers '("x" "y" "max-norm")
+                       :domain-order (x y)
+                       :domain-values vs)
+    (lizfcm.vector:max-norm (list x y))))
+\end{verbatim}
+
+
+\begin{center}
+\begin{tabular}{rrr}
+x & y & infty-norm\\[0pt]
+1 & 1 & 1\\[0pt]
+2 & 3 & 3\\[0pt]
+4 & 5 & 5\\[0pt]
+-1 & 2 & 2\\[0pt]
+\end{tabular}
+\end{center}
+
+\section{Question Six - ||v - u|| via |v|\textsubscript{2}}
+\label{sec:orge36996c}
+\begin{verbatim}
+(let* ((vs '((1 1) (2 3) (4 5) (-1 2)))
+       (vs2 '((7 9) (2 2) (8 -1) (4 4)))
+       (2-norm (lizfcm.vector:p-norm 2)))
+  (lizfcm.utils:table (:headers '("v1" "v2" "2-norm-d")
+                       :domain-order (v1 v2)
+                       :domain-values (mapcar (lambda (v1 v2)
+                                                (list v1 v2))
+                                              vs
+                                              vs2))
+    (lizfcm.vector:distance v1 v2 2-norm)))
+\end{verbatim}
+
+
+\begin{center}
+\begin{tabular}{llr}
+v1 & v2 & 2-norm\\[0pt]
+(1 1) & (7 9) & 10.0\\[0pt]
+(2 3) & (2 2) & 1.0\\[0pt]
+(4 5) & (8 -1) & 7.2111025\\[0pt]
+(-1 2) & (4 4) & 5.3851647\\[0pt]
+\end{tabular}
+\end{center}
+
+\section{Question Seven - ||v - u|| via |v|\textsubscript{1}}
+\label{sec:orgd1577f0}
+\begin{verbatim}
+(let* ((vs '((1 1) (2 3) (4 5) (-1 2)))
+       (vs2 '((7 9) (2 2) (8 -1) (4 4)))
+       (1-norm (lizfcm.vector:p-norm 1)))
+  (lizfcm.utils:table (:headers '("v1" "v2" "1-norm-d")
+                       :domain-order (v1 v2)
+                       :domain-values (mapcar (lambda (v1 v2)
+                                                (list v1 v2))
+                                              vs
+                                              vs2))
+    (lizfcm.vector:distance v1 v2 1-norm)))
+\end{verbatim}
+
+
+\begin{center}
+\begin{tabular}{llr}
+v1 & v2 & 1-norm-d\\[0pt]
+(1 1) & (7 9) & 14\\[0pt]
+(2 3) & (2 2) & 1\\[0pt]
+(4 5) & (8 -1) & 10\\[0pt]
+(-1 2) & (4 4) & 7\\[0pt]
+\end{tabular}
+\end{center}
+
+\section{Question Eight - ||v - u|| via |v|\textsubscript{\(\infty\)}}
+\label{sec:org2661676}
+\begin{verbatim}
+(let* ((vs '((1 1) (2 3) (4 5) (-1 2)))
+       (vs2 '((7 9) (2 2) (8 -1) (4 4))))
+  (lizfcm.utils:table (:headers '("v1" "v2" "max-norm-d")
+                       :domain-order (v1 v2)
+                       :domain-values (mapcar (lambda (v1 v2)
+                                                (list v1 v2))
+                                              vs
+                                              vs2))
+    (lizfcm.vector:distance v1 v2 'lizfcm.vector:max-norm)))
+\end{verbatim}
+
+\begin{center}
+\begin{tabular}{llr}
+v1 & v2 & max-norm-d\\[0pt]
+(1 1) & (7 9) & -6\\[0pt]
+(2 3) & (2 2) & 1\\[0pt]
+(4 5) & (8 -1) & 6\\[0pt]
+(-1 2) & (4 4) & -2\\[0pt]
+\end{tabular}
+\end{center}
+\end{document}
\ No newline at end of file
diff --git a/homeworks/virtualization/hw1.pdf b/homeworks/virtualization/hw1.pdf
new file mode 100644
index 0000000..00d84a4
--- /dev/null
+++ b/homeworks/virtualization/hw1.pdf
diff --git a/homeworks/virtualization/img/htop.png b/homeworks/virtualization/img/htop.png
new file mode 100644
index 0000000..880befa
--- /dev/null
+++ b/homeworks/virtualization/img/htop.png
diff --git a/homeworks/virtualization/img/no_virtualization.png b/homeworks/virtualization/img/no_virtualization.png
new file mode 100644
index 0000000..2322456
--- /dev/null
+++ b/homeworks/virtualization/img/no_virtualization.png
diff --git a/homeworks/virtualization/virtual_machines.md b/homeworks/virtualization/virtual_machines.md
new file mode 100644
index 0000000..c6d3e12
--- /dev/null
+++ b/homeworks/virtualization/virtual_machines.md
@@ -0,0 +1,41 @@
+* Elizabeth Hunt (A02364151), MATH 4610
+
+## Virtual Machines
+
+**Question 1**
+
+Run the Linux OS as a virtual machine, or run the application in a containerized Linux environment (which
+is the same abstraction).
+
+**Question 2**
+
+A native system virtual machine has dedicated hardware to run the hypervisor, while a hosted system 
+virtual machine runs a hypervisor as a process in the operating system.
+
+**Question 3**
+
+A virtual machine hosts an entire operating system and requires users to perform configuration if they
+want to run an application, whereas a Virtual Appliance is built to provide an easy plug-and-play virtual 
+machine image built to run some specific software stack.
+
+**Question 4**
+
+In a large application sense, containerizing services into their own virtual machines allows for easier
+replication, scaling, and networking. Instead of running several smaller servers, one large server can
+host several applications in parallel. This provides a good seperation of concern. And, if one service 
+goes down, the whole system does not go down with it.
+
+Locally, it can help in development when targeting another operating system. Virtual machines can be
+used to verify builds without installing a whole other operating system.
+
+**Question 5**
+
+A virtual machine monitor is just another term for a hypervisor, so, see question 2.
+
+**Question 6**
+
+The three components of a virtual machine are:
+
+1. The host
+2. The virtualization layer
+3. The guest
diff --git a/homeworks/virtualization/virtualization.md b/homeworks/virtualization/virtualization.md
new file mode 100644
index 0000000..4d03637
--- /dev/null
+++ b/homeworks/virtualization/virtualization.md
@@ -0,0 +1,103 @@
+## Virtualization
+
+**Question 1** 
+
+I use an Apple Silicon Mac which is based on the ARM architecture - so it's necessary to use 
+[Multipass](https://multipass.run/), as native virtualization is _not available to us_.
+
+![No Virtualization Strings](./img/no_virtualization.png)
+
+**Question 2**
+
+One of the downsides of running a virtual machine, as opposed to a hosted virtual instance, is that local
+resources are used. On a laptop especially, this increases power draw, draining the battery. Additionally,
+the security of mind provided by "faster disaster recovery", as discussed in the article, is not as 
+necessary for consumer applications on personal machines as servers. Finally, virtual machines are 
+inherently slower in compute due to general overhead.
+
+**Question 3** 
+
+![htop resources](./img/htop.png)
+
+**Question 4** 
+
+In a large application sense, containerizing services into their own virtual machines allows for easier
+replication, scaling, and networking. Instead of running several smaller servers, one large server can
+host several applications in parallel.
+
+Locally, it can help in development when targeting another operating system. Virtual machines can be
+used to verify builds without installing a whole other operating system.
+
+**Question 5**
+
+A native system virtual machine has dedicated hardware to run the hypervisor, while a hosted system 
+virtual machine runs a hypervisor as a process in the operating system.
+
+**Question 6**
+
+1. Easier networking between "servers"
+2. Efficient resource use
+
+**Question 7**
+
+A Virtual Appliance is built to provide an easy plug-and-play virtual machine image built to run some 
+specific software stack.
+
+**Question 8** 
+
+A Virtual Appliance would be desirable to eliminate maintenance and configuration overhead when running an
+application. In my own experience, I've used a form of virtual appliances - "Docker Containers", to easily
+spin up multiple versions of small services at work.
+
+**Question 9** What are 2 benefits of Virtualization?
+
+See question 6.
+
+**Question 10** 
+
+See question 4.
+
+**Question 11** 
+
+See question 8.
+
+**Question 12**  What are the three main types of virtualization?
+
+1. Full virtualization
+2. Para virtualization
+3. OS-level virtualization
+
+**Question 13** What you should know about virtualization?
+
+How to create a virtual machine, and maintain it.
+
+**Question 14** What is the weakness of virtualization?
+
+Inherent overhead in all system operations.
+
+**Question 15** What are the six areas of virtualization?
+
+Source: [HiTechNectar](https://www.hitechnectar.com/blogs/virtualization-types)
+
+1. Application - run individual applications in a seperate environment than a host OS
+2. Data - abstract exact location and formatting information away from retrieval of data
+3. Desktop - hosts a desktop environment virtually on another machine (reminds me of mainframes).
+4. Network - physical networking tools are abstracted into software resources
+5. Server - division of a server into multiple guest operating systems
+6. Storage - abstraction over multiple storage arrays into a single pool
+
+**Question 16** What is the biggest challenge in virtualization?
+
+Resource distribution is a big one; it's difficult to keep track of several resources on a host machine 
+and ensure a Virtual Machine accesses them correctly.
+
+**Question 17** What is the risk of using virtualization?
+
+The biggest risk of using virtualization is sandbox escape vulnerabilities. Although mostly research and
+proof-of-concept, highly skilled engineers can theoretically craft exploits to escape the sandbox of the
+VM and directly mess with the host operating system.
+
+**Question 18**
+
+When (question 17) is trusted; sandboxing. Virtualization should supply no access to resources within the
+host operating system.