U.C. Berkeley CS270: Algorithms
Professor Vazirani and Professor Rao
Lectures 13, 14
Scribe: Anupam
Last revised
Lectures 13, 14
1
Streaming Algorithms
The streaming model is one way to model the prob
CS 170
Fall 2014
Algorithms
David Wagner
HW 1
Due Sept. 5, 6:00pm
Instructions. This homework is due Friday, September 5, at 6:00pm electronically. It must be submitted
electronically via Pandagrader
Problem Set : Solutions
. We view the random variables T1 and T2 as interarrival times in two independent Poisson processes both with rate S as the interarrival time in a third Poisson process (indepe
Introduction and historical overview
1
A time of crisis
$79 billion
Annual indirect cost of mental illness to US economy (Office of the Surgeon
General, 1999)
24.4%
Americans who had a DSM-IV disord
Anokhi Kastia
25017423
GSI: Alice Hua
Friday 2-3 PM
Girl Interrupted (1999)
History: The primary character in the movie that we are analyzing is Susanna Kaysen played by
Winona Ryder. She is an eighte
Multiplicative Weight Update Algorithm
or Learning with Experts
Notes adapted from cs270 lecture notes Rao & Vazirani, scribed by Anupam Prakash.
1
The multiplicative weights update (MWU) method
The m
U.C. Berkeley CS270: Algorithms
Professor Vazirani and Professor Rao
Lecture 15
Scribe: Anupam
Last revised
Lecture 15
1
Streaming Algorithms: Frequent Items
Recall the streaming setting where we have
CS 170
Spring 2017
1.
Efficient Algorithms and Intractable Problems
Prasad Raghavendra and Sanjam Garg
Final
Review II-3
Cryptography
Let G = (V, E) be a graph that is three-colorable and let c1 , c2
CS 170
Spring 2017
Efficient Algorithms and Intractable Problems
Prasad Raghavendra and Sanjam Garg
Final Review
NP-Completeness
1. 4D Matching
Recall the 3-D IMENSIONAL M ATCHING problem, asking you
EECS 16A
Fall 2016
Designing Information Devices and Systems I
Babak Ayazifar, Vladimir Stojanovic
Discussion 7B
1. Derive Series and Parallel Caps!
Derive Ce f f for the following diagrams.
C1
C1
C1
EECS 16A
Fall 2016
Designing Information Devices and Systems I
Babak Ayazifar, Vladimir Stojanovic
Discussion 6B
1. Equivalence Find the Thvenin and Norton equivalents across terminals a and b for the
EECS 16A
Fall 2016
Designing Information Devices and Systems I
Babak Ayazifar, Vladimir Stojanovic
Discussion 12A
1. Ohms Law with noise
Sometimes we are quite fortunate to get nice numbers. Often tim
CS 170
Spring 2016
1
Efficient Algorithms and Intractable Problems
Alessandro Chiesa and Umesh Vazirani
Final Review
Approximation Algorithms
Suppose we have an approximation algorithm A that takes in
EECS 16A
Fall 2016
Designing Information Devices and Systems I
Babak Ayazifar, Vladimir Stojanovic
Discussion 9A
1. Modular Circuits
In this problem we will explore the design of circuits that perform
EECS 16A
Fall 2016
Designing Information Devices and Systems I
Babak Ayazifar, Vladimir Stojanovic
Discussion 9B
1. Noise Cancelling Headphones Part 1
Almost everyone has tried "noise cancelling" head
EECS 16A
Fall 2016
Designing Information Devices and Systems I
Babak Ayazifar, Vladimir Stojanovic
Discussion 7A
1. Equivalence Find the Norton equivalent of the following circuit across the terminals
Current paradigms in
psychopathology
Scientific Paradigms
Conceptual framework that guides science
and scientists
Ontology: What is real?
Epistemology: How do we know things?
Methodology: How do w
Diagnosis and assessment
The what and the why of it
What?
The classification of disorders based on
symptoms (subjective) and signs (objective).
Why?
Facilitates communication among professionals
Problem Set 3 Solutions
1. The hats of n persons are thrown into a box. The persons then pick up their hats at random (i.e.,
so that every assignment of the hats to the persons is equally likely). Wha
Problem Set 1: Solutions
1. (a) A B C
(b) (A B c C c ) (Ac B C c ) (Ac B c C) (Ac B c C c )
(c) (A B C)c = Ac B c C c
(d) A B C
(e) (A B c C c ) (Ac B C c ) (Ac B c C)
(f) A B C c
(g) A (Ac B c )
A
A
Problem Set 10 Solutions
1.
or just use the formula for computing the random incidence pdf for a given
! !
interarrival pdf: ! ! = !
2.
3.
a) Using Markovs Inequality:
! !
for all a>
Problem Set 2: Solutions
1. (a) The tree representation during the winter can be drawn as the following:
0.8
Rain
0.2
No Rain
The forecast is
"Rain"
p
1-p
0.1
Rain
0.9
No Rain
The forecast is
"No Rain
Problem Set 5: Solutions
1. (a) Because of the required normalization property of any joint PDF,
$
$
!
" 2 !" 2
" 2
23 13
2
2
2
1=
ax dy dx =
ax(2 x) dx = a 2 1
+
= a
3
3
3
x=1
y=x
x=1
so a = 3/2.
(b
Problem Set 6: Solutions
1. Let us draw the region where fX,Y (x, y) is nonzero:
y
2
1
y-x=z
0
1
2
x
! x=2 ! y=x
The joint PDF has to integrate to 1. From x=1 y=0 ax dy dx = 73 a = 1, we get a = 37 .
Problem Set 4: Solutions
1. (a) From the joint PMF, there are six (x, y) coordinate pairs with nonzero probabilities of
occurring. These pairs are (1, 1), (1, 3), (2, 1), (2, 3), (4, 1), and (4, 3). T
CS 170
Fall 2017
Efficient Algorithms and Intractable Problems
Prasad Raghavendra and Sanjam Garg
Homework 2
Instructions: You are welcome to form small groups (up to 4 people total) to work through t
Types of Computers
Workstation
Supercomputer
PalmtopComputer
LaptopComputer
PersonalDataAssistant
New Learning Technologies
Internet
Multimedia
Virtualreality
Distancelearning
Datawarehousing
The Info
EECS 16A
Fall 2016
Designing Information Devices and Systems I
Babak Ayazifar, Vladimir Stojanovic
Discussion 7A
1. Equivalence Find the Norton equivalent of the following circuit across the terminals