text stringlengths 16 3.88k | source stringlengths 60 201 |
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-Attribute Tradespace
Exploration with Concurrent Design as a Value-Centric Framework for Space System
Architecture and Design,” Master of Science Thesis in Aeronautics and Astronautics,
Massachusetts Institute of Technology, June 2003, and Diller, N. P., “Utilizing Multiple
Attribute Tradespace Exploration with Concur... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5c7b371feea1c1563d917c1858f58ec7_03010lec3framev5.pdf |
offs. 2nd ed. Cambridge: Cambridge University Press, 1993. Chapters 1 and 4.
© 2003 Massachusetts Institute of Technology
11/6/03
52
ALPHA DRAFT- For Review Only
41 Miller, G. A. (1956). "The Magical Number Seven, Plus or Minus Two: Some Limits on Our
Capacity for Processing Information." The Psychological Review 63... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5c7b371feea1c1563d917c1858f58ec7_03010lec3framev5.pdf |
8.701
0. Introduction
0.3 Teaching Staff
Introduction to Nuclear
and Particle Physics
Markus Klute - MIT
1
Short Bio - Instructor: Markus Klute
Markus Klute joined the MIT Physics Department in
April 2009. He received his Diploma and Ph.D from
Rheinische Friedrich-Wilhems University, Bonn,
Germany in 2004 with re... | https://ocw.mit.edu/courses/8-701-introduction-to-nuclear-and-particle-physics-fall-2020/5c9317e4704966ef8d82f0d4a1a3dc6d_MIT8_701f20_lec0.3.pdf |
about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms. | https://ocw.mit.edu/courses/8-701-introduction-to-nuclear-and-particle-physics-fall-2020/5c9317e4704966ef8d82f0d4a1a3dc6d_MIT8_701f20_lec0.3.pdf |
Representing Complexity
MIT Student
Lecture 6 Discussion
�
Dynamic Models of Segregation
Examine how individual incentives/actions aggregate
•
to cause segregation
Develop set of rules governing individual preference/ tolerance and
•
movement
Many simplifying assumptions
•
• Representing the complexity of so... | https://ocw.mit.edu/courses/ids-900-doctoral-seminar-in-engineering-systems-fall-2011/5cb05eb8bb0eaaa7e2df65c5e776db99_MITESD_83F11_lec06_discuss.pdf |
•
worthwhile to get some idea of the kind of picture or pattern that emerges from a
random distribution” (156)
Van Ham, van Wijk: ““Providing both detailed information as well as a global
•
context in one image is one of the fundamental problems in Information
Visualization” (5)
Vi li i
” (5)
sua zat on
Quest... | https://ocw.mit.edu/courses/ids-900-doctoral-seminar-in-engineering-systems-fall-2011/5cb05eb8bb0eaaa7e2df65c5e776db99_MITESD_83F11_lec06_discuss.pdf |
?
By focusing on individual incentives, Schelling divorced a socioeconomic
•
phenomena from most of its social and economic context. Given his lengthy set of
assumptions, do we trust his model?
Schelling’s simplified model is able to explain behavior that has been observed
•
(for example, tipping). Are we more... | https://ocw.mit.edu/courses/ids-900-doctoral-seminar-in-engineering-systems-fall-2011/5cb05eb8bb0eaaa7e2df65c5e776db99_MITESD_83F11_lec06_discuss.pdf |
Coordinates and
Transformations
MIT ECCS 6.837
Wojciech Matusik
many slides follow Steven Gortler’s book
1
Hierarchical modeling
• Many coordinate systems:
• Camera
• Static scene
• car
• driver
• arm
• hand
• ...
Image courtesy of Gunnar A. Sjögren on Wikimedia Commons. License: CC-BY-SA. This conten... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/5cbb1bf32a92fad91e8ad6c37a473240_MIT6_837F12_Lec03.pdf |
system of the
car, express it in the coordinate
system of the world
7
Goals for today
• Make it very explicit what coordinate system is
used
• Understand how to change coordinate systems
• Understand how to transform objects
• Understand difference between points, vectors,
normals and their coordinates
8
... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/5cbb1bf32a92fad91e8ad6c37a473240_MIT6_837F12_Lec03.pdf |
matrix notation
• Given the coordinates c in basis
the transformed vector has coordinates Mc in
22
Why do we care
• We like linear algebra
• It’s always good to get back to an abstraction
that we know and for which smarter people have
developed a lot of tools
• But we also need to keep track of what
basis/... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/5cbb1bf32a92fad91e8ad6c37a473240_MIT6_837F12_Lec03.pdf |
5km North-East
• Adding points is not meaningful
• Boston location + New York location = ?
• Multiplying a point by a scalar?
• The zero vector is meaningful (no movement)
• Zero point ?
32
Affine space
• Points are elements of an affine space
• We denote them with a tilde
• Affine spaces are an extension of... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/5cbb1bf32a92fad91e8ad6c37a473240_MIT6_837F12_Lec03.pdf |
More notation properties
• Adding a point
to a vector
• Gives us
a point (4th coordinate=1)
46
More notation properties
• vectors are not affected by the translation part
• because their 4th coordinate is 0
• If I rotate my moving car in the world, I want its
motion to rotate
• If I translate i... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/5cbb1bf32a92fad91e8ad6c37a473240_MIT6_837F12_Lec03.pdf |
3
1
1
2
0
0
0
2
0
0
0
1
=
2
0
0
0
2
0
3
1
1
Caution: matrix multiplication is NOT commutative!
53
53
Non-commutative Composition
Scale then Translate: p' = T ( S p ) = TS p
(1,1)
(0,0)
Scale(2,2)
(2,2)
Translate(3,1)
(5,3)
(3,1)
(0,0)
Translate the... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/5cbb1bf32a92fad91e8ad6c37a473240_MIT6_837F12_Lec03.pdf |
-vectors and 3 x 3 matrices
• In 3D, we use 4-vectors and 4 x 4 matrices
•The extra coordinate is now an arbitrary value, w
• You can think of it as “scale,” or “weight”
• For all transformations
except perspective, you can
just set w=1 and not worry
about it
=
x'
y‘
1
a b
d e
0 0
c
f
1
x
y
1
59
... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/5cbb1bf32a92fad91e8ad6c37a473240_MIT6_837F12_Lec03.pdf |
0, 0, 1) = (0, 0, 2) = …
w = 1
(7, 1, 1) = (14, 2, 2) = …
(4, 5, 1) = (8, 10, 2) = …
w = 2
66
Homogeneous Visualization
• Divide by w to normalize (project)
Points at infinity (directions)
• w = 0?
(0,0,0)
(0, 0, 1) = (0, 0, 2) = …
w = 1
(7, 1, 1) = (14, 2, 2) = …
(4, 5, 1) = (8, 10, 2) = …
w = 2
67
... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/5cbb1bf32a92fad91e8ad6c37a473240_MIT6_837F12_Lec03.pdf |
camera poses
• For each point in each image, write perspective
equations
Minimize f(R,T,P)
p1
Camera 1 R1,t1
Camera 3
R3,t3
Camera 2 R2,t2
72
Eye candy: photo tourism
73
QuickTime™ and aMPEG-4 Video decompressorare needed to see this picture. And that’s it for today
• The rest on Thursday
74
Normal
• ... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/5cbb1bf32a92fad91e8ad6c37a473240_MIT6_837F12_Lec03.pdf |
Mˉ¹) vWS = 0
vWS is perpendicular to normal nWS:
nOS
vOS
nWS
nWSᵀ = nOSᵀ (Mˉ¹)
nWS = (Mˉ¹)ᵀ nOS
vWS
nWSᵀ vWS = 0
84
Digression
nWS = (Mˉ¹)ᵀ nOS
• The previous proof is not quite rigorous; first
you’d need to prove that tangents indeed
transform with M.
• Turns out they do, but we’ll take it on faith... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/5cbb1bf32a92fad91e8ad6c37a473240_MIT6_837F12_Lec03.pdf |
MIT OpenCourseWare
http://ocw.mit.edu
6.854J / 18.415J Advanced Algorithms
Fall 2008
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
�
�
18.415/6.854 Advanced Algorithms
October 1, 2008
Lecturer: Michel X. Goemans
Lecture 8
Previously, we introduced the dynamic... | https://ocw.mit.edu/courses/6-854j-advanced-algorithms-fall-2008/5cccdb7dca0aa81810781ba75d0a1d46_lec8.pdf |
trees. In a virtual tree,
each solid path is represented by a splay tree such that the following conditions hold:
•
A successor node in a splay tree is an ancestor in the rooted tree.
•
For each splay tree, its largest node is linked to the parent of the root in the rooted tree.
•
In the virtual tree, each node ... | https://ocw.mit.edu/courses/6-854j-advanced-algorithms-fall-2008/5cccdb7dca0aa81810781ba75d0a1d46_lec8.pdf |
we
run Expose on node 15.
2.1 Step 1
Step 1 consists of walking from v to the root of the virtual tree. Whenever the walk enters a splay
tree (solid edges) at some node w, a Splay(w) operation is performed, bringing w to the root of
that tree. Middle children are not affected in this step. For instance, we splay no... | https://ocw.mit.edu/courses/6-854j-advanced-algorithms-fall-2008/5cccdb7dca0aa81810781ba75d0a1d46_lec8.pdf |
solid subpath with the solid path
corresponding to the splay tree rooted at v still leaves the rooted tree decomposed into a node-disjoint
union of paths.
Note that after performing this operation on every edge to the root of the virtual tree, there will
be a solid path from the root of the rooted tree to the node ... | https://ocw.mit.edu/courses/6-854j-advanced-algorithms-fall-2008/5cccdb7dca0aa81810781ba75d0a1d46_lec8.pdf |
tree. If such
a path is the prefix of a path corresponding to a splay tree, it seems that, knowing the minimum
cost in any subtree of any our splay trees might be helpful. So, in addition to cost(x), we would like
to keep track of the value mincost(x), given by
mincost(x) = min{cost(y) | y in the subtree rooted at x... | https://ocw.mit.edu/courses/6-854j-advanced-algorithms-fall-2008/5cccdb7dca0aa81810781ba75d0a1d46_lec8.pdf |
min(x) and
Δ min�(x). Observe that during a rotation, only the nodes b, w and v have their Δ cost(x) change.
One can check that the updates are as follows:
Δ cost�(v) = Δ cost(w) + (cost(v) − cost(w))
= Δ cost(w) + Δ cost(v),
Δ cost�(w) = −Δ cost(v),
Δ cost�(b) = Δ cost(b) + (cost(v) − cost(w)) = Δ cost(b) + Δ co... | https://ocw.mit.edu/courses/6-854j-advanced-algorithms-fall-2008/5cccdb7dca0aa81810781ba75d0a1d46_lec8.pdf |
when we perform the splicing step given in Figure 3, Δ cost only change for v and u and
only Δ min(w) changes. The updates are:
Δ cost�(v) = Δ(cost(v)) − Δ(cost(w)),
Δ cost�(u) = Δ cost(u) + Δ cost(w),
Δ min�(w) = max(0, Δ min(v) − Δ cost�(v), Δ min(z) − Δ cost(z)).
3.2
Implementation of Operations
We now descri... | https://ocw.mit.edu/courses/6-854j-advanced-algorithms-fall-2008/5cccdb7dca0aa81810781ba75d0a1d46_lec8.pdf |
Once we have found the minimum,
we splay it.
8-6
• add-cost(v, x)
First, run Expose(v). Add x to Δ cost(v) and subtract x from Δ cost(left(v)). Also update
Δ min(v) (using (1)). (The Δ min value of other nodes is unchanged.)
• cut(v)
First, run Expose(v). Add Δ cost(v) to Δ cost(right(v)). Remove the edge (v, r... | https://ocw.mit.edu/courses/6-854j-advanced-algorithms-fall-2008/5cccdb7dca0aa81810781ba75d0a1d46_lec8.pdf |
4.2 Runtime of the Expose Operation
We first analyze the runtime of Expose(v), since it is used in all other operations. We look at each
step of Expose(v) separately. Let k be the number of middle edges separating v from the root of
the entire virtual tree. Equivalently, k is the number of splay operations performed ... | https://ocw.mit.edu/courses/6-854j-advanced-algorithms-fall-2008/5cccdb7dca0aa81810781ba75d0a1d46_lec8.pdf |
) + k (since r(root) − r(v) ≤ log n).
• Step 2: Splicing does not change the value of φ(T ), so the amortized cost for this step is the
same as its actual cost of k.
• Step 3: We are using the splay operation once on node v at distance k from the root, so this
has an actual cost of k. Using the fact that our potent... | https://ocw.mit.edu/courses/6-854j-advanced-algorithms-fall-2008/5cccdb7dca0aa81810781ba75d0a1d46_lec8.pdf |
tial function. Removing the edge (v, right(v)) decreases s(v) by s(right(v)) and leaves s(x)
unchanged for all other x, so it decreases φ(T ), which we can safely ignore. This gives an
amortized runtime of O(log n).
•
link
We use Expose twice. Now, when we link w to v, we see that r(v) increases by O(log n), and
... | https://ocw.mit.edu/courses/6-854j-advanced-algorithms-fall-2008/5cccdb7dca0aa81810781ba75d0a1d46_lec8.pdf |
Lab 1 - Revisited
• Display signals on scope
• Measure the time, frequency, voltage
visually and with the scope
• Voltage measurement*
• Build simple circuits on a protoboard.*
• Oscilloscope demo
6.091 IAP Lecture 2
1
RMS Voltage
• 0-5v square wave (50%) duty cycle has a
rms value of 5 / = 3.54v
2
• 5v peak-peak sq... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/5cf021d5f88ec7ce343a8f31bff527f4_lec2.pdf |
7
Bipolar Junction Transistors
collector
ic = β ib
+
Vce
-
β ~50-300
emitter
ie = β ib +ib
NPN
base
ib
PNP
• BJT can operate in a linear
mode (amplifier) or can
operate as a digital switch.
• Current controlled device
• Two families: npn and pnp.
• BJT’s are current controlled
devices
• NPN – 2N2222
• PNP – 2N2907... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/5cf021d5f88ec7ce343a8f31bff527f4_lec2.pdf |
• Isolation up to 4000
Vrms
6.091 IAP Lecture 2
12
Figure by MIT OpenCourseWare.
Proto-Board
• +5v, +15v, -15v
available
• Pins within row or
column connected
• Use bypass
capacitors liberally
6.091 IAP Lecture 2
13
Op-Amps
• Active device: V0 = A(V+-V-);
note that it is the difference
of the input voltage!
V+
... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/5cf021d5f88ec7ce343a8f31bff527f4_lec2.pdf |
.0001uA
Input resistance
0.3 MΩ
106 MΩ
Slew rate*
0.5 v/us
7.5 v/us
Gain Bandwidth product
1 Mhz
5 Mhz
Output short circuit duration
Continuous continuous
Identical pin out
* comparators have >50 v/us slew rate
6.091 IAP Lecture 2
21
Comparator Operation
• Supply voltage = +15v, -15V
• V- = +5 V
Vin
• For Vin = +4, Vo... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/5cf021d5f88ec7ce343a8f31bff527f4_lec2.pdf |
the output on an oscilloscope. How
is the output related to the input?
• What is the peak output voltage?
• What is the minimum output voltage?
• What at frequency does the gain start to
drop below ten?
6.091 IAP Lecture 2
25
Negative Feedback
1k
Vin
10k
V-
V+
Vo
• Take product with
100,000 gain and
reduce it to 10... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/5cf021d5f88ec7ce343a8f31bff527f4_lec2.pdf |
n
e
r
r
u
C
n
a
r
D
i
-
O
I
5
4
3
2
1
0
0
2N5459
iD
29
Common Drain-Source
TYP V GS(OFF) = -1.8V
TA = 25o C
VGS = 0V
VGS = -0.25V
VGS = -0.5V
VGS = -0.75V
VGS = -1V
VGS = -1.25V
5
2
1
VDS - Drain-Source Voltage
3
4
Figure by MIT OpenCourseWare.
Voltage Control Current Source*
+15
RE=100
+15
R3
V-
V+
+15
Vo
-15... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/5cf021d5f88ec7ce343a8f31bff527f4_lec2.pdf |
3.15
Transistors
C.A. Ross, Department of Materials Science and Engineering
Reference: Pierret, chapter 10, 15.1-2, 16.1-2 and 17.1.
Transistors are three-terminal devices that use a small voltage (or current)
applied to one contact to modulate (i.e. control) a large voltage (or current)
between the other two contacts.... | https://ocw.mit.edu/courses/3-15-electrical-optical-magnetic-materials-and-devices-fall-2006/5d3ca8e27b90844252ee7d300b5c9c89_lecture7.pdf |
ND,B is determined by doping.
‘Common base’ circuit: by setting VEB and IE we control VCB and IC
‘Common emitter’ circuit: by setting VEB and IB we control VEC and IC
Digital logic: make the transistor act like a switch by running between
saturation and cutoff.
Junction Field Effect Transistor
Apply a reverse volta... | https://ocw.mit.edu/courses/3-15-electrical-optical-magnetic-materials-and-devices-fall-2006/5d3ca8e27b90844252ee7d300b5c9c89_lecture7.pdf |
.
If VD = 0, channel has uniform width.
If VD > 0, channel is thinner towards the D and may pinch-off; also the
depletion width is larger.
At pinch-off, the current ISD cannot increase any more.
Example application: a DRAM (dynamic random access memory) stores one
bit in a cell consisting of a MOSFET plus a MOS-capacit... | https://ocw.mit.edu/courses/3-15-electrical-optical-magnetic-materials-and-devices-fall-2006/5d3ca8e27b90844252ee7d300b5c9c89_lecture7.pdf |
Lecture 4
Acoustics of Speech and Hearing
Lecture 4:The Interaction of Sound and Objects: Scattering and Diffraction
6.551J/HST714J
P(r, θ)
A. Definitions:
1. Scattering
Scattering refers to the alteration in
sound path produced by the interaction of a
sound ‘ray’ and an object. Scattering implies
that the inc... | https://ocw.mit.edu/courses/6-551j-acoustics-of-speech-and-hearing-fall-2004/5d477f7380c5b24a6c6f5e739036f9a2_lec_4_2004.pdf |
raction?
Image removed due to copyright considerations.
Source: Olsen, H. F. Music Physics and Engineering. Dover Press, 1967 .
Figure 4.3 (a) Scattering from an object positioned at an angle relative to the direction of
propagation of the incident wave. The angle of reflection is equal to the angle of incidence. (b... | https://ocw.mit.edu/courses/6-551j-acoustics-of-speech-and-hearing-fall-2004/5d477f7380c5b24a6c6f5e739036f9a2_lec_4_2004.pdf |
a
point located on the surface of a spherical
artificial head where the angle between the
source and the midline of the sphere
perpendicular to the measurement point is
controlled.
21-Sept-2004
page 3
Lecture 4
Acoustics of Speech and Hearing
6.551J/HST714J
Figure 4.5B
An alternative geom... | https://ocw.mit.edu/courses/6-551j-acoustics-of-speech-and-hearing-fall-2004/5d477f7380c5b24a6c6f5e739036f9a2_lec_4_2004.pdf |
at the
measurements point on the sphere’s surface,
θ=90° and the sound pressure is a maximum.
When the source is directed at a point directly
on the opposite side of the sphere, θ=-90° and
the sound pressure is either equal to or a little
larger than the pressure of the plane-wave
stimulus. When the source is on... | https://ocw.mit.edu/courses/6-551j-acoustics-of-speech-and-hearing-fall-2004/5d477f7380c5b24a6c6f5e739036f9a2_lec_4_2004.pdf |
J/HST714J
1. Contribution of the external-ear components to the sensitivity of the ear
The effect of different external-ear structures on the gain between the sound pressure at the eardrum
and the free-field sound pressure for a sound source positioned on the horizontal plane at 45°
relative to the midline (the azi... | https://ocw.mit.edu/courses/6-551j-acoustics-of-speech-and-hearing-fall-2004/5d477f7380c5b24a6c6f5e739036f9a2_lec_4_2004.pdf |
490.
Measurements and theoretical values for azimuthal dependence (HRTF normalized by HRTF(0)left )
and interaural intensity differences (right) of the magnitude of sound pressure at the ear drum
normalized by the stimulus pressure in the plane wave. (SHAW 1974).
21-Sept-2004
page 10
Lecture 4
Acous... | https://ocw.mit.edu/courses/6-551j-acoustics-of-speech-and-hearing-fall-2004/5d477f7380c5b24a6c6f5e739036f9a2_lec_4_2004.pdf |
1974)
21-Sept-2004
page 12
Lecture 4
Acoustics of Speech and Hearing
G. Interaural time and phase differences
6.551J/HST714J
A simple model of the interaural time differences is presented below:
Incident plane waves
q
A'
Left
A
q
q
a
Right
aq
a sinq
4.13 The Geometric model of Interaural
Time Difference... | https://ocw.mit.edu/courses/6-551j-acoustics-of-speech-and-hearing-fall-2004/5d477f7380c5b24a6c6f5e739036f9a2_lec_4_2004.pdf |
in
the azimuthal plane. J.
Acoust. Soc. Am. 62: 157-
167).
21-Sept-2004
page 13
Lecture 4
6.551J/HST714J
Acoustics of Speech and Hearing
The root of the simple model’s underestimation of interaural time is that, ITD varies with frequency,
being longer at low frequencies than at higher. This ... | https://ocw.mit.edu/courses/6-551j-acoustics-of-speech-and-hearing-fall-2004/5d477f7380c5b24a6c6f5e739036f9a2_lec_4_2004.pdf |
used in its quantification are long duration tone
bursts, and you can consider the system in the
sinusoidal steady state. Localization
performance is best (MAA is smallest) for
sources on the midline.
(From Mills AW (1958). On the minimum
audible angle. J. Acoust. Soc. Am. 30: 237-
246.)
Courtesy of Acoustical S... | https://ocw.mit.edu/courses/6-551j-acoustics-of-speech-and-hearing-fall-2004/5d477f7380c5b24a6c6f5e739036f9a2_lec_4_2004.pdf |
. Used with permission.
While the difference between elevation and
azimuth is irrelevant when discussing the
symmetric sphere, asymmetries in the
placement of the external ear and in the
structures of the external ear, generate
differences in the frequency dependence of
the ear with sounds of varied elevation. T... | https://ocw.mit.edu/courses/6-551j-acoustics-of-speech-and-hearing-fall-2004/5d477f7380c5b24a6c6f5e739036f9a2_lec_4_2004.pdf |
BETA DRAFT- For Review Only
Space Systems, Policy, and Architecture Research Consortium
(SSPARC)
“Beta plus” Revised Draft 5/26/04
“SSPARC BOOK” MATERIAL
for Lecture 4
Prepared by:
Hugh McManus
Metis Design
Adam Ross
MIT
----
Draft for evaluation only. Do not distribute.
© 2004 Massachusetts Institute of Tech... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
-book on the MATE-CON method. It is
provided for class use as a draft. Suggestions for improvement are welcome, as are warnings of
errors or omissions. The notes below apply to the entire work in progress; the work or excepts of
it should not be reproduced in any form without these notes.
This document is dedicated... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
has been supported by an active group of industry practitioners, through
both an Industrial Advisory Board (IAB) and on-site implementation activities.
The text of this manual is built on SSPARC research and member documents. Much of its
contents are excerpts, modifications, or paraphrases of published or unpublishe... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
The purpose of using utility theory in MATE-CON is to make better decisions. Both the theory
and its typical application have weaknesses that we will not understate. However, utility theory
provides a better way at getting at user preferences and needs than most other techniques, and
can be quantitatively coupled to... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
ETA DRAFT- For Review Only
4.1.Single Attribute Utilities
Single attribute utilities map single attributes onto user needs. Here, we will explore typical
forms of single attributes utilities and provide some practical examples. Note for the purpose of
this discussion we are assuming that the attributes and their ac... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
requirements
often require tedious negotiations if requirements are not met, even if the harm to the user is
small, and do not reward “extra” performance at all, even if the benefit to the user is potentially
great.
n
o
i
t
c
a
f
s
i
t
a
s
r
e
s
U
Extra Value
OK
Negotiable
Not OK
Attribute value
a) Soft target... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
better” case from Figure 4-2)
this limit may need to be chosen arbitrarily. Values greater than one (“bonus points”) create
mathematical difficulties and should not be used.
€
We will concern ourselves with the range of values of attributes that produce utilities between
zero and one (the gray box in Figure 4-3). I... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
Excluded Attribute Values
y
t
i
l
i
t
U
1
0
Excess Attribute Values
(typically assigned Utility = 1)
Attribute value
Figure 4-3 Utility as function of a single attribute
Figure 4-4 shows several possible forms of a utility function. The simplest is a linear relation
between the attributes and utilities. This fo... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
the user must always prefer a greater value over a lesser.
These criteria simply imply that the function Ui exist for all xi of interest, and be monotonic.
The utility function is (and must be) an “ordered metric scale,” which has the following
properties:
• Utilities have meaning only compared to other utilities; they... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
as was done in
the Spacetug example) is appropriate.
If the stakeholder needs are known or can be determined in detail, the Lottery Equivalent
Probability (LEP) method for accurately extracting utility functions from participating
© 2004 Massachusetts Institute of Technology
2/4/04
9
BETA DRAFT- For Review Only
stakeh... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
with probability
• Avoiding questions involving very small or very large probabilities (including certainties)
which will often invoke either mis-estimations or innate biases in the users.
The LEP method is correctly viewed not as an absolutely accurate method for extracting user
utilities, but rather the best availabl... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
2, show similar but not
identical results from identical interviews. The hand-drawn results show similar noise, and are
also consistently somewhat different from the LEP results. The difference between the LEP
interview utilities and the hand-drawn ones is typical. In this case, both show diminishing
returns, but the h... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
then a diminishing returns curve (which favors, under this assumption, the more-certain
attainment of a lower performance level) could be described as expressing risk-adverse behavior.
Likewise, a preference for high performance (with the implication of high risk) could be
described as risk seeking.
© 2004 Massachusett... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
The challenge in
constructing these scenarios is keeping the user focused on the model, instead of a satellite
solution they may have in mind. Use of this method requires a sophisticated and patient user,
willing to suspend disbelief and go with the somewhat confusing process of the interviews. As
the questions are exp... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
chance that the boat will never leave
port due an ongoing seamen’s strike. If you elect to use traditional methods there
is a 50% chance that you will get XX degrees of diversity in latitude of your data,
or a 50% chance that you will get 0 degrees diversity of latitude in your data. The
boat-based sensor offers a ## c... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
easy – a 45% chance of excellent performance vs. a 50% chance of only 30 deg. of diversity.
The second was less so, pairing a 10% chance of excellence vs. a 50% chance of 30 deg.; the
user chose the latter. The fourth question, with 20% chance of excellence, has also decided in
favor of the satellite; all the others we... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
very typical case. The utility shows a diminishing return on the diversity of latitude in the data
set, with good utility being achieved with modest (60 deg.) diversity.
© 2004 Massachusetts Institute of Technology
2/4/04
16
BETA DRAFT- For Review Only
Time Spent in Equatorial Region
The question was:
New instru... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
any misalignment will cause the sensor to extract data at 1000
km. You must decide between using this sensor, or traditional methods. The
traditional methods will give you a 50% chance of getting data at XX km, or a
50% chance of getting data at 1000 km. The new sensor has a ## chance of
extracting data at 150 km or a ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
has discrete values, assumed to correspond to increasing utility as shown in Figure 4-13. The
response time of a real system would be a complex function of many factors; at the level of the
current analysis it is reduced to a binary attribute, valued at one for high impulse systems, and
zero for low impulse ones.
)
s
s... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
4000
6000
8000
10000
12000
0
5000
10000
15000
20000
25000
30000
35000
40000
Delta-V (m/sec)
Delta-V (m/sec)
Figure 4-12 Alternate delta-V utilities for GEO-centric user and delta-V hungry user
Figure 4-13 Single attribute utility for grappling and observation equipment capability
© 2004 Massachusetts Institute of Techn... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
is a reasonable choice if there is reason to
believe that the single attribute utilities are independent and simplicity and ease of understanding
and manipulation are important.
€
Simple Multiplicative Utility Function
Another simple function is
U =
n
∏
i=1
Ui
(4-7)
This function implies a high degree of interaction b... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
restriction of Eq. 4-6, and K is the largest
non-zero solution to
€
K + 1 =
n
∏
i=1
)
(
Kki + 1
(4-11)
This function allows a single interaction between the utilities, expressed by the value of K. This
interaction can be understood, intuitively if not strictly rigorously, as spanning the continuum of
simple interactio... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
Utility Function
Formally, for the Keeney-Raiffa MAU function to be valid, the single attribute utility functions
are under two additional constraints:
•
If a user chooses a pair of attributes, consisting of attribute x with value x1 and attribute y
with value y1, over a second pair x2 and y2, that choice will not be ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
as the constituents all improve. The full range of Keeney-Raiffa Functions are shown,
with k1 and k2 values (assumed equal for this example) ranging from almost one to almost zero.
The top line shows the inverse multiplicative function. Total utility rises quickly, reaching 0.75
when the two component utilities have re... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
of 0.07; examination of Figure 4-14 and Figure 4-15 shows this is
indistinguishable from a weighted sum. This implies that the X-TOS attributes were fully
independent, and can be traded simply by treating the ki as weights. Interestingly, when the ki’s
were changed quite drastically late in the study, K changed to 0.28... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
0.6
0.8
1
Single Attribute Utility U1
Figure 4-15 Family of MAU functions for two attributes moving in opposite directions (U2=1-U1)
© 2004 Massachusetts Institute of Technology
2/4/04
25
BETA DRAFT- For Review Only
In contrast to these examples, the B-TOS study7 used a Keeney-Raiffa function which had a K of
–0.9... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
ascending measure of value, one could simply
invert CPF and measure Function Per Cost.
A single, quantifiable metric such as CPF makes comparisons between a broad range of different
systems easy. This approach is limited, however, to situations where the function desired can be
expressed simply and quantitatively as a ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
many possibilities without requiring the user to rank preferences exhaustively across thousands
of choices. A very interesting approach is presented by Belegundu et al.15 A “design by
shopping” paradigm is proposed, where the user is presented with many possible designs,
represented as a multi-dimensional data set, pro... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
OS Multi-attribute Utilities
The X-TOS study used a Keeney-Raiffa MUA function. The coefficients ki were determined
using the relation in Eq. 4-5. They were collected by the MIST software at the same time as the
single attribute utilities. They are shown in the figure below.
ORIGINAL Weight Factors of each Attribute (k... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
0.4
0.3
0.2
0.1
0
Figure 4-17: New weights and Lifespan utility function
© 2004 Massachusetts Institute of Technology
2/4/04
28
BETA DRAFT- For Review Only
4.6. Spacetug Multi-Attribute Utilities
The space tug study used weights determined for a number of hypothetical users. These are
summarized in Table 2.
Tabl... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
iteratively determine this by choosing which trade-off
strategy appears most appropriate, and to allow the designer to modify any and all
of these initial choices. ... Design problems are commonly solved in an iterative
manner, not usually with a single formalization and subsequent optimization. In
an iterative design ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
C:
Attribute A Utility
50
100
150
200
250
300
0.0
0.2
0.4
0.6
0.8
1.0
Attribute B
1
2
3
5
7
10
Utility
0.0
0.3
0.6
0.8
0.9
1.0
Attribute C Utility
5
7
8
9
12
15
1.0
0.9
0.7
0.3
0.1
0.0
The user states a design with attributes (300,1,15) would have multiattribute utility 0.9, a
design with attributes (50,10,15) would ha... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
onautics, Massachusetts Institute of Technology, June 2003.
3 Most of the time, the utility of the key stakeholders, or decision makers, is what we desire.
See Chapter 3, section 4.3, for further discussion of this issue.
4 de Neufville, Richard, Applied Systems Analysis: Engineering Planning and Technology
Management,... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
per
Billable Minute Metric for Comparing Satellite Systems, Journal of Spacecraft and Rockets,
Vol. 34, No. 6, 1997, pp. 837-846.
13 Shaw, G. M., Miller, D. W., and Hastings, D. E., “Development of the Quantitative
Generalized Information Network Analysis (GINA) Methodology for Satellite Systems,”
Journal of Spacecraft... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5d55ba3f4c86851ee274c8914b58d6c4_04010lec4frame13.pdf |
OpenCourseWare
2.5 Pitch Accents with more than one tone: Bi-tonal accents L+H* and L*+H
9 August 2006
All pitch accents described so far have been produced with a single tonal element, either a High
(H*) or a Low (L*) aligned with the accented syllable. There are other choices open to speakers
however, to convey ... | https://ocw.mit.edu/courses/6-911-transcribing-prosodic-structure-of-spoken-utterances-with-tobi-january-iap-2006/5d68a5b367b536661becde2f4202e4dd_chap2_5.pdf |
tone sequence (L-H%), the
same break labels, and the same words (Amelia knew him), but in one case the prominence is
associated with the H* and in the other case with the L*.
1
Figure 2.5.1 L+H*
<amelia1>
Figure 2.5.2 L*+H
<amelia2>
In both files, there is a stretch of low f0 followed by a rise to ... | https://ocw.mit.edu/courses/6-911-transcribing-prosodic-structure-of-spoken-utterances-with-tobi-january-iap-2006/5d68a5b367b536661becde2f4202e4dd_chap2_5.pdf |
’ll see
later that f0 peaks and valleys do not invariably occur on the accented syllable; here we simply
illustrate that the L*+H / L+H* contrast is generally reflected in peak alignment differences.
2.5.2 Bitonal vs single-tone pitch accents
The bitonal pitch accents L+H* and L*+H differ from the single-tone H* an... | https://ocw.mit.edu/courses/6-911-transcribing-prosodic-structure-of-spoken-utterances-with-tobi-january-iap-2006/5d68a5b367b536661becde2f4202e4dd_chap2_5.pdf |
High
boundary tone, L-H%). The example with the single-tone L*, <amelia3>, also shows a low f0 on
the pitch-accented syllable (again, the -mel- of Amelia). However, the f0 stays low and flat
following the prominent syllable all the way through the end of the word Amelia, and then
through the word knew, until the ri... | https://ocw.mit.edu/courses/6-911-transcribing-prosodic-structure-of-spoken-utterances-with-tobi-january-iap-2006/5d68a5b367b536661becde2f4202e4dd_chap2_5.pdf |
A- and the following /m/ to a fairly low level. This
Low tone is the L of the bitonal pitch accent L+H* in this example. The first intonational phrase
in the same file <Amelia> gives a contrasting example of the single-tone H* pitch accent on the
same word. Compared to the L+H* version, the rise into the peak of the... | https://ocw.mit.edu/courses/6-911-transcribing-prosodic-structure-of-spoken-utterances-with-tobi-january-iap-2006/5d68a5b367b536661becde2f4202e4dd_chap2_5.pdf |
in interpreting the tones of the intonational contour. Since the labeller can
generally hear the intended contour “through” these segmental effects, this is an example of how
listening trumps looking in labelling. )
5
Figure 2.5.5 L+H* L-L%
<marmalade5>
Figure 2.5.6 H* L-L%
<marmalade2>
6
Pitch Ac... | https://ocw.mit.edu/courses/6-911-transcribing-prosodic-structure-of-spoken-utterances-with-tobi-january-iap-2006/5d68a5b367b536661becde2f4202e4dd_chap2_5.pdf |
+H* are clearest when there is at least one non-pitch-
accented syllable preceding the prominent syllable, so that the L tone of the pitch accent can be
realized on preceding syllable(s). Such is the case in the examples discussed above. However,
when the pitch accented syllable is the first syllable of an Intonation... | https://ocw.mit.edu/courses/6-911-transcribing-prosodic-structure-of-spoken-utterances-with-tobi-january-iap-2006/5d68a5b367b536661becde2f4202e4dd_chap2_5.pdf |
2.5.7 H* vs. L+H*
<anna2>
Summary of ToBI labels introduced so far:
Tones:
H*: high pitch accent
L*: low pitch accent
L+H*: bitonal low tone with high tone on accented syllable
L*+H: bitonal high tone with low tone on accented syllable
L-L%: low phrase accent, low boundary tone
H-H%: high phrase accent, high bo... | https://ocw.mit.edu/courses/6-911-transcribing-prosodic-structure-of-spoken-utterances-with-tobi-january-iap-2006/5d68a5b367b536661becde2f4202e4dd_chap2_5.pdf |
OUTLIERS: Feb. 4, 2005, R. Dudley, 18.465 notes
A rough definition of an outlier is that it’s an observation far away from the bulk of
the data. There may be multiple outliers in a given data set, especially if it’s large. For
example, Bill Gates’s wealth would be an outlier among those of all individuals.
One of th... | https://ocw.mit.edu/courses/18-465-topics-in-statistics-nonparametrics-and-robustness-spring-2005/5d70b3b85c48f657003af200517c2930_outliers.pdf |
−∞, when it keeps the same rank 1.
But, what is an outlier? It turns out to be even harder to give a precise definition
than for a sample quantile. Some books give examples of outliers and a few try to give
specific rules for identifying them.
An example, given in a book by D. Freedman, Pisani, and R. Purves, is that... | https://ocw.mit.edu/courses/18-465-topics-in-statistics-nonparametrics-and-robustness-spring-2005/5d70b3b85c48f657003af200517c2930_outliers.pdf |
wrong normality assumption.
√
There’s a problem though with defining outliers in terms of standard deviations if the
standard deviation is estimated from the sample, because the sample standard deviation is
itself so much influenced by the outlier. Specifically, just looking at the formula for sample
variance, to hav... | https://ocw.mit.edu/courses/18-465-topics-in-statistics-nonparametrics-and-robustness-spring-2005/5d70b3b85c48f657003af200517c2930_outliers.pdf |
to
if we move data in the lower quarter or upper quarter of the order statistics
outliers:
outward, it won’t change the IQR. An attempted definition of outlier is an observation
that’s distant by at least 3IQR from the interval [q1, q3].
1
But here’s an example where that definition doesn’t work well. Let Xj be ob... | https://ocw.mit.edu/courses/18-465-topics-in-statistics-nonparametrics-and-robustness-spring-2005/5d70b3b85c48f657003af200517c2930_outliers.pdf |
about rainfall.
It seems that we might only want to call a daily amount of rain or snow an outlier if
we compared it to for example the 10 or 20 days with most rain in a typical year. So the
choice of what to call an outlier may depend on what kind of data we’re looking at, not
on any universal numerical rule.
2 | https://ocw.mit.edu/courses/18-465-topics-in-statistics-nonparametrics-and-robustness-spring-2005/5d70b3b85c48f657003af200517c2930_outliers.pdf |
18.417 Introduction to Computational Molecular Biology
Lecture 6: September 28, 2004
Lecturer: Ross Lippert
Scribe: Lele Yu
Editor: Sam Kaufman
Dynamic Programming: Gene Discovery
Introduction
This lecture discusses some techniques for gene discovery using dynamic programming
algorithms. We begin with some nece... | https://ocw.mit.edu/courses/18-417-introduction-to-computational-molecular-biology-fall-2004/5d9b3d4a5a1557de90cbcc60b2c718f5_lecture_06.pdf |
to randomly get a region of 40aa than 300aa.
6.3
Intron/exon structure
In eukaryotes, splicing (the presence of introns, i.e. noncoding regions interspersed in
exons) can foul this up. Exons are 2% of the gene. Exons average length is 130 bp �
43 aa.
The basic intron exon/structure is as in the diagram:
Exon1 GT... | https://ocw.mit.edu/courses/18-417-introduction-to-computational-molecular-biology-fall-2004/5d9b3d4a5a1557de90cbcc60b2c718f5_lecture_06.pdf |
2004
6-3
6.5.1 Matching known (spliced) mRNA
Suppose we have known (spliced) mRNA, corresponding (roughly) to the transcribed
exons. There are two schools of thought on how to align such an mRNA to the full
DNA sequence containing both introns and exons. One is to do a gapped alignment,
with a strong mismatch pen... | https://ocw.mit.edu/courses/18-417-introduction-to-computational-molecular-biology-fall-2004/5d9b3d4a5a1557de90cbcc60b2c718f5_lecture_06.pdf |
relative to iDNA.
6.6 Spliced alignment problem
The spliced alignment problem shows up in a setting where regions of spliced cDNA
have been aligned to a target genome in pieces, producing a series of high scoring local
alignments. The input is a set of boxes with scores, represent as 5-tuples (li, ri, ti, bi, si)
... | https://ocw.mit.edu/courses/18-417-introduction-to-computational-molecular-biology-fall-2004/5d9b3d4a5a1557de90cbcc60b2c718f5_lecture_06.pdf |
CMOS Technology and Logic Gates
Only 15,432,758 more
mosfets to do...
meta
l
pdiff
ndiff
poly
6.884 – Spring 2005
2/07/2005
L03 – CMOS Technology 1
Quality of Design
Quality of a hardware design primarily judged by:
– Price
– Performance
– Power and/or Energy
Other important metrics can include:
– Operatin... | https://ocw.mit.edu/courses/6-884-complex-digital-systems-spring-2005/5db68ba6abd100ecc232604ccfeb9f46_l03_cmos_gates.pdf |
10 trillion transistors/system?)
– Carbon Nanotubes?
– Molecular Electronics?
CMOS VLSI is the digital implementation technology of choice for
the foreseeable future (next 10-20 years)
– Excellent energy versus delay characteristics
– High density of wires and transistors
– Monolithic manufacturing of devices and... | https://ocw.mit.edu/courses/6-884-complex-digital-systems-spring-2005/5db68ba6abd100ecc232604ccfeb9f46_l03_cmos_gates.pdf |
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