Manipulating Array

[,1][.2]
y `= [,1] 1 5
[,2] 2 6

2 * y + 1
y `= [,1] 3 11
[,2] 5 13

y %*% Y
y `= [,1] 11 35
[,2] 14 46

outer(x[,1], x[,1])
[,1] [,2] [,3] [,4] [,5]
[1,] 1 5 9 13 17
[2,] 2 6 10 14 18
[3,] 3 7 11 15 19
[4,] 4 8 12 16 20

rbind(x[1,], x[1,])
rbindは縦に結合
[,1] [,2] [,3] [,4] [,5]
[1,] 1 5 9 13 17
[2,] 1 5 9 13 17

cbind(x[1,], x[1,])

L = list(name = ‘John’, age=55, no.children=2, children.ages = c(15, 18))
names(L) name age no.children children.ages
L[[2]] 55
L$name John
L[‘name’] John
L$children.ages[2]
L[[4]][2]

names(R) = c(“NAME”, “AGE”, “SALARY”)

if-Else

a = 10; b = 5; c = 1
if (a < b){
	d = 1
} else if (a == b){
	d = 2
} else {
	d = 3
}
print(d)

R for loop

total = function(n){
    sum = 0
    for(i in 1:100){
    sum = sum + i
    }
    
    print(sum)
    return(sum)
}
total(100)

total = function(n){
    sum = 5050
    num = n
    repeat {
      sum = sum - num
      num = num - 1
      if(sum == 0)break
    }
    return(sum)
}

total = function(){
    sum = 0
    a = 1
    b = 10
    
    while (a

R command

ls() – list variable names in workspace memory
save.image(file=”R_workspace”) – saving variables to a file
save(new.var, legal.var.name, file = “R_workspace”) – save specified variables
load(“R_workspace”) – load variables saved in a file
system(“ls -al”) – executes a command in the shell, for example ls -al

scalar
numeric, integer, logical

ordered factor

current.season = factor("summer", levels = c("summer", "fall", "winter", "spring"), ordered = TRUE)

x = c(4,3,3,4,3,1)
outcome: 433431
length(x)
outcome: length = 6
y = vector(mode=”logical”, length=4)
outocome: y= FALSE FALSE FALSE FALSE
z = vector(length=3, mode==”numeric”)
outcome: z = 0 0 0

q = rep(3.2, times = 10)
q = 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2
w = seq(0, 1 by=0.1)
w – 0.0 0.1 0.2 … 0.9 1.0
w = seq(0, 1, length.out 11)

w <= 0.5 0.0 0.1 0.2 0.3 0.4 0.5 any(w <= 0.5) TRUE all(w <= 0.5) FALSE which(w <= 0.5) 1 2 3 4 5 6

List of DataSet

> data(iris)
> head(iris)
  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa
> levels(iris$Species)
[1] "setosa"     "versicolor" "virginica" 

> install.packages("ggplot2")

R: statistics, bio-statistics, social sciences
Matlab: engineering, applied math
python: web development, scripting

Running R – interactively

source("foo.R")
R CMD BATCH foo.R
Rscript foo.R

R Help documentation
>help {utils}
R Documentation
Documentation
Description
help is the primary interface to the help systems.
Usage
help(topic, package = NULL, lib.loc = NULL,
verbose = getOption(“verbose”),
try.all.packages = getOption(“help.try.all.packages”),
help_type = getOption(“help_type”))….

Security background

confidentiality, integrity, availability

The security of a system, application, or protocol is always relative to:
– a set of desired properties
– an adversary with specific capabilities

Control systems
sensor, system, actuator, controller

Open – loop
Desired output response -> controller -> actuator -> process -> output

closed – loop
Desired output response -> error -> controller -> actuator -> process -> output

Networking

BAN, LAN, MAN and WAN

Ring Topology, star, extended star

OSI Model
Application, presentation, session, transport, network, datalink, physical

Application:to allow access to network resource, FTP, http
Presentation: to translate, encrypt, & compress data
Session: to establish, manage, and terminate sessions
Transport: reliable process-to-process msg delivery, tcp, udp
network: packet transport and internetworking
data link: bits -> frames, hop-to-hop delivery
physical: transmit bits over a medium

Each layer communicate logically with intermediate node.

RTT: Round Trip Time
WAN is much greater than that of LAN.
TCP flow control -> Three way handshake,

CPS Concepts

Physical World
– sensing, actuation
Communication Network
Cyber System

IoT, Clud, M2M, WSN, Big Data

Interoperability attributes composability, scalability, heterogeneity
Predictability attributes accuracy, compositonality

Security objective: Availability
Network topology: static
Patching: infrequent updates

Random Testing (Fuzzing)

-Feed random inputs to a program
-Observe whether it behaves “correctly”
execution satisfies given specification
or just does not crash
-Special case of mutation analysis

“The infinite monkey theorem”

Thread 1:

...
p = null;

Thread 2:

...
if(p != null){
 ...
 p.close();
}

black-box and white box

black-box testing
-can work with code that cannot be modified
-does not need to analyze or study code
-code can be in any format(managed, binary, obfuscated)

White-box testing
-efficient test suite
-potentially better coverage

HttpPost localHttpPost = new HttpPost(...);
(new DefaultHttpClient()).execute(localHttpPost;

Automated testing is hard to do
probably impossible for entire system

A pre-condition is a predicate
A post-condition is a predicate

class Stack{
	T[] array;
	int size;

	Pre: s.size() > 0
	T pop() { return array[--size]; }
	Post: s'.size() == s.size() -1

	int size() { return size; }
}

int foo(int[] A, int[] B){
	int r = 0;
	for (int i = 0; i < A.length; i++){
		r += A[i] * B[i];
	}
	return r;
}

Software Testing

Learn methods to improve software quality
-reliability, security, performance
-Become a better software developer

Security Vulnerabilities
-Exploits of errors in programs

Dynamic, static, hyprid

An invariant at the end of the program

int p(int x){ return x * x; }
void main(){
	int z;
	if(getc() == 'a')
		z = p(6) + 6;
	else
		z = p(-7) -7;

	if (z != 42)
		disaster();
}
void main(){
	z = 3;
	while (true){
 	 if(x == 1)
 	 	y = 7;
 	 else
 	 	y = z + 4;
 	 assert (y == 7);
	}
}

Functions for Lines

from decimal import Decimal, getcontext

from vector import vector
getcontext().prec = 30


class Line(object):
	NO_NONZERO_ELTS_FOUND_MSG = 'No nonzero element found'

	def __init__(self, normal_vector=None, constant_term=None):
		self.dimension = 2

		if not normal_vector:
			all_zeros = ['0']*self.dimension
			normal_vector = Vector(all_zeros)
		self.normal_vector = normal_vector

Ax + By + Cz = k1
Dx + Ey + Fz = k2
[A B C], [D E F] not parallel
dx = vector from x0 to x
Since x0, x in plane 1, dx is orth to n1

-One equation in two variables defines a line
-One equation in three variables define a plane

Caution: Count variables with coefficient 0
x + y = 2 defines a line in 2D
x + y = 2 defines a plane in 3D

systematically manipulate the system to make it easier to find the solution
– Manipulations should preserve the solution
– Manipulations should be reversible