II. Information Systems
The term information system suggests the use of
computer technology in an organization
Information
System
Information for
Decision Making
Hardware
Data
Software
A.
Electronic Data Processing (EDP) or Data Processing (DP)
B. Managem
12.010 Computational Methods of
Scientific Programming
Matlab Lecture 4
Lecturers
Thomas A Herring
Chris Hill
Review of Last Lecture
Analysis of the some of the functions needed for the
GUI development in Matlab
Look at functions which would be appropri
12.010 Computational Methods of
Scientific Programming
Matlab Lecture 3
Lecturers
Thomas A Herring
Chris Hill
Summary of last class
Continued examining Matlab operations
path and addpath commands
Variables and constants
IO using fopen, scanf etc.
For
12.010 Computational Methods of
Scientific Programming
Matlab Lecture 1
Lecturers
Thomas A Herring
Chris Hill
Summary of Todays class
We will look at Matlab:
History
Getting help
Variable definitions and usage
Math operators
Control statements: Synt
Decoding
Filtering and smoothing produce distributions of states at each time
step.
Maximum likelihood estimation chooses the state with the highest
probability at the best estimate at each time step.
However, these are pointwise best estimate: the sequen
Searching over policies
Value iteration converges exponentially fast, but still asymptotically.
Recall how the best policy is recovered from the current estimate of
the value function:
i (s) = arg max E R(s, a, s 0 ) + Vi (s 0 ) ,
8s 2 S.
a
In order to gu
12.010 Computational Methods of
Scientific Programming
Lecturers
Thomas A Herring
Chris Hill
Overview
Part 1: Python Language Basics getting started.
Part 2: Python Advanced Usage the utility of Python
11/15/2011
12.010 Lec P2
2
Refresh
Previous class:
18.415/6.854 Advanced Algorithms
Problem Set Solution 5
Lecturer: Michel X. Goemans
1. Consider the linear programming relaxation of the vertex cover problem seen in
class.
Min
C wixi
subject to:
(a) Argue that any basic feasible solution x of the above l
12.010 Computational Methods of
Scientific Programming
Lecturers
Thomas A Herring
Chris Hill
Subroutines (declaration)
name[v1_Type, ] := Module[cfw_local variables, body]
Type is optional for the arguments (passed by value)
Invoked with
name[same list o
12.010 omputational ethods of
cientific rogramming
Lecturers
homas
erring
hris ill
Overview Today
olution of ordinary differential equations with
athematica and atlab.
Examine formulations
athematica 2-nd order (and higher order) DE
can be directly solv
From deterministic to stochastic planning problems
A basic planning model for deterministic systems (e.g., graph/tree search
algorithms, etc.) is :
Planning Model
(Transition system + goal)
A (discrete, deterministic) feasible planning model is dened by
A
12.010 Computational Methods of
Scientific Programming
Lecturers
Thomas A Herring
Chris Hill
Simple 3-D graphics
Simple line and scatter plots use plot3 which takes 3
vectors as arguments and plots them much like 2-D
plot.
t = linspace(0,10*pi);
figure(1
Q1. In some elds, especially those related to the Federal government, a distinction is made between
INFoRNAPRMlsEcuRIT
(which focuses on protection of information assetsyrrd information assurance (which focuses on
the correctness of information).
Q2. One
Game Theory
Games
Multiple players independently choose actions, based on the available information,
to pursue individual goals.
Created by John Von Neumann in the late 1920s.
Applications
Economics
Political Science/Diplomacy/Military Strategy
Biology
Co
Markov Chains
Denition (Markov Chain)
A Markov chain is a sequence of random variables X1 , X2 , X3 , . . . , Xt ,
. . . , such that the probability distribution of Xt+1 depends only on t and
xt (Markov property), in other words:
Pr [Xt+1 = x|Xt = xt , Xt
Game theory (Recap)
Zero-sum Games
Gains/losses of each player is balanced by the gains/losses of the all the other players.
Cooperative vs. non-cooperative.
Cooperative if groups of players may enforce binding agreements.
Nash equilibrium
No player can g
12.010 Computational Methods of
Scientific Programming
Lecturers
Thomas A Herring
Chris Hill
Overview
Part 1: Python Language Basics getting started.
Part 2: Python Advanced Usage the utility of Python
11/10/2011
12.010 Lec P1
2
Part1: Summary of Python
12.010 Computational Methods of
Scientific Programming
Matlab Lecture 2
Lecturers
Thomas A Herring
Chris Hill
Summary of Introduction to Matlab
Looked at the basic features of Matlab:
Getting help
Variable definitions and usage
Math operators
Control
18.415/6.854 Advanced Algorithms
Problem Set Solution 2
1. The Min s-t-Cut problem is the following:
G i v e n a n undirected graph G = (V, E), a weight function w : E + R+ ,
and t w o vertices s, t E V, find
Min s - t
- Cut(G) = mincfw_w(S(S)
: S c V, s
18.415/6.854 Advanced Algorithms
Problem Set Solution 1
1. Consider P = cfw_x : Ax 5 b, x 2 0), where A is m x n. Show that if
x is a vertex of P then we can find sets I and J with the following
properties.
c
c
(a) I cfw_I,. . . , m , J cfw_ I 7 . . , n
18.415/6.854 Advanced Algorithms
Problem Set Solution 6
Lecturer: Michel X. Goemans
1. The betweenness problem is defined as follows: We are given n and a set T of m
triples of the elements of (1,. . , n). We say that an ordering 7r of (1, . . ,n) satisfi