text stringlengths 16 3.88k | source stringlengths 60 201 |
|---|---|
.t. p ′ A = c ′
p ≥ 0
4 Weak Duality
Theorem:
If x is primal feasible and p is dual feasible then p ′ b ≤ c ′ x
Proof
p ′ b = p ′ Ax ≤ c ′ x
2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Corollary:
If x is primal feasible, p is dual feasible, and p ′ b = c ′ x, then x is optimal in... | https://ocw.mit.edu/courses/6-251j-introduction-to-mathematical-programming-fall-2009/496d9a385fd1d7e1aa82837d91adb23e_MIT6_251JF09_lec08.pdf |
between primal and dual
Finite opt. Unbounded
Infeasible
Finite opt.
Unbounded
Infeasible
*
*
*
*
7 Economic Interpretation
•
x optimal nondegenerate solution: B−1b > 0
•
Suppose b changes to b + d for some small d
•
How is the optimal cost affected?
•
For small d feasibilty unaffected
•
•
Optima... | https://ocw.mit.edu/courses/6-251j-introduction-to-mathematical-programming-fall-2009/496d9a385fd1d7e1aa82837d91adb23e_MIT6_251JF09_lec08.pdf |
for all i, j, then c ′ x = p ′ b,
• ⇒ x and p are optimal.
4
8.3 Example
min 13x1 + 10x2 + 6x3
s.t.
5x1 +
3x1 +
,
x1
x2 + 3x3 = 8
x2
= 3
x3 ≥ 0
x2
,
Is x ∗ = (1, 0, 1) ′ optimal?
Objective=19
max 8p1 + 3p2
s.t. 5p1 + 3p2 ≤ 13
p1 + p2 ≤ 10
≤ 6
3p1
Slide 15
Slide 16
5... | https://ocw.mit.edu/courses/6-251j-introduction-to-mathematical-programming-fall-2009/496d9a385fd1d7e1aa82837d91adb23e_MIT6_251JF09_lec08.pdf |
MIT OpenCourseWare
http://ocw.mit.edu
3.23 Electrical, Optical, and Magnetic Properties of Materials
Fall 2007
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
3.23 Fall 2007 – Lecture 9
BAND STRUCTURE
3.23 Electronic, Optical and Magnetic Properties of Materia... | https://ocw.mit.edu/courses/3-23-electrical-optical-and-magnetic-properties-of-materials-fall-2007/49728ee6fbac8503c94b5a9aab74242c_lec9.pdf |
2
C
⎞
⎞
⎟
⎟
⎟
⎛
⎟
⎜
⎟
⎜
⎟
⎜
⎟ ⎜
⎟ C
⎜
⎟
⎜
⎜
C
C
⎟ ⎝
⎝
⎟
⎟
⎟
⎟
⎠
−
q G
2
⎞
⎟
C
⎟
−
q G
⎟C
q
⎟
⎟
⎟
⎟
⎠
⎠
q G+
2
+
q G
⎛
⎜
⎜
= E ⎜
⎜
⎜
⎜⎜
⎝
⎝
C
C
−
q G
C
−
q G
2
⎞
⎟
⎟
⎟
⎟
q G ⎟
+
⎟⎟
⎠
⎠
2G
q
C
C
C
+q
3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)
4
... | https://ocw.mit.edu/courses/3-23-electrical-optical-and-magnetic-properties-of-materials-fall-2007/49728ee6fbac8503c94b5a9aab74242c_lec9.pdf |
⎟
⎟
⎠
3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)
Band Edge
3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)
7
Ψnk (r) is not a momentum eigenstate
3.23 Electronic, Optical and Magnetic Properties of Materials -... | https://ocw.mit.edu/courses/3-23-electrical-optical-and-magnetic-properties-of-materials-fall-2007/49728ee6fbac8503c94b5a9aab74242c_lec9.pdf |
://www.phys.ufl.edu/fermisurface/
http://www phys ufl edu/fermisurface/
3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)
10
(cid:10) | https://ocw.mit.edu/courses/3-23-electrical-optical-and-magnetic-properties-of-materials-fall-2007/49728ee6fbac8503c94b5a9aab74242c_lec9.pdf |
BUILDIT Cast Corn Sheller
BUILD-IT
This project is a low-cost device for removing corn kernels from the cob. It is cast in aluminum using a
casting pattern made on the 3-D printer. This project is inspired by a plastic corn sheller from Malawi
and a cast aluminum sheller from Ghana. In order to make it you will need... | https://ocw.mit.edu/courses/ec-720j-d-lab-ii-design-spring-2010/4974d72f6e55f3b812da88af46058e3a_MITEC_720JS10_bldit_cncst.pdf |
tutorial instructs you in making a basic sheller you
may also add ridges or other features to the outside surface of the sheller.
The model should be completed before class so that it can be printed during
class. You will need to sand the surface of the part to make it smooth so that
the sand won’t stick to it whil... | https://ocw.mit.edu/courses/ec-720j-d-lab-ii-design-spring-2010/4974d72f6e55f3b812da88af46058e3a_MITEC_720JS10_bldit_cncst.pdf |
5.0 > Solidworks 2007
Start a new document by clicking on the new document button or File >
New Document. In the menu click on New Part – a 3D representation of
a single design component. Run through the Solidworks Tutorial lessons
1 and 2 to practice making simple objects and assemblies.
Screenshots of SolidWorks... | https://ocw.mit.edu/courses/ec-720j-d-lab-ii-design-spring-2010/4974d72f6e55f3b812da88af46058e3a_MITEC_720JS10_bldit_cncst.pdf |
lines parallel slanting. Smart Dimension the inside edge to be 5/8” (0.63”)
from the origin.
6
66
6
Rotate the fin
- Click Revolved Boss/Base and choose the angled line nearest to the
origin as the center of rotation.
- Choose Two Direction, and set the rotation to 45 degrees for each
Add multiple fins
- Insert ... | https://ocw.mit.edu/courses/ec-720j-d-lab-ii-design-spring-2010/4974d72f6e55f3b812da88af46058e3a_MITEC_720JS10_bldit_cncst.pdf |
Concurrent Plan Recognition &
Execution for Human-Robot Teams
Cognitive Robotics 2016 Lecture
Steven J. Levine
Wednesday, March 16666666th, 2016
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Intent recognition & adaptation are siblings
• Intent recognition & robot adaptation are b... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
et al. 2000
SAM
Pecora 2012
Tsamardinos, Muscettola, Morris 1998
Teller, Walter, et al. 2010
Morris 1998
HOTRiDE
Ayan et al. 2007
Finzi, Ingrand, and Muscettola 2004
Effinger et. al 2009
Hofmann et. al. 2005
IPEM
Ambros-Ingerson and Steel 1998
Smith, Shah, da Vitoria Lobo 2004
Vidal 1999
Tedrake, Manchester, Tobenkin... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
Robot adaptation
making
• Assume rational, cooperative agents
• Prune any (irrational) decisions resulting in plan failure:
• Unmet action preconditions: (cid:15482) Causal link reasoning
• Missed deadlines:
(cid:15482) Temporal conflicts
• Unanticipated failures:
(cid:15482) Online execution monitoring
Concurrent Plan ... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
…so can’t pour juice later…
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide 16
…so robot should get coffee now.
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide 17
• Intent Recognition: recognizing human’s choices
consistent with at least on... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
-Robot Teams | Steven J. Levine
Slide
19
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide
20
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide 21
Causal links justify action preconditions
Producer
Consumer
• Insufficient for contingent, temp... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
= 1}
[0, ∞]
p : {ac = c3}
[0, ∞]
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide
28
Causal link extraction in a nutshell*
• For each precondition of each consumer event:
• Find all producers provably before or during consumer
• Add propositional & temporal constraints for each pr... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
ausal link extraction in a nutshell*
• For each precondition of each consumer event:
• Find all producers provably before or during consumer
• Add propositional & temporal constraints for each producer
• Find all potential threats probably before or during causal link
p : {ac = c1}
p : {ac = c2 ∧ y = 1}
Concurrent Plan... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
all producers provably before or during consumer
• Add propositional & temporal constraints for each producer
• Find all potential threats probably before or during causal link
• Resolve via additional propositional & temporal constraints
p : {ac = c2 ∧ y = 1}
(cid:2)
[0, ∞]
b =
1
2
if threat comes before
if threat com... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
(cid:4)
φC
φC
[(cid:4), ∞] : φC from ec to eti
φC
[(cid:4), ∞] : φC from epi to eti
φC
[(cid:4), ∞] :{b ec,p,epi
[(cid:4), ∞] :{b ec,p,epi
,eti = 1} ∧ φC from eti to epi
,eti = 2} ∧ φC from ec to eti
⇓
Producers precede consumers
Temporal conflicts (Conrad 2009)
Threat resolutions
Threat resolutions
Threat resolutions
T... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)
(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)
(cid:14)(cid:15)(cid:16)(cid:3)(cid:5)(cid:17)(cid:8)(cid:2)(cid:3)(cid:3)
(cid:14)(cid:15)(cid:16)(cid:3)(cid:5)(cid:17)(cid:8)(cid:2)(cid:3)(cid:3)
(cid:18)(cid... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
48
Experimental results
)
s
(
e
m
T
i
103
102
101
100
10−1
10−2
10−3
100
100
10−1
10−2
)
s
(
e
m
T
i
10−3
100
Offline Compilation Time
101
102
Worst Online Commit Latency
103
• Randomly-generated TPNU’s with
randomly-generated causal link
structure (probably harder)
• Compilation time roughly
104
proportional to candid... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
Teams | Steven J. Levine
Slide 54
Labeled all-pairs shortest path (APSP)
(cid:6)
[6, 11]
[2, 11]
if x = 1
if x = 2
• Causal link extraction: provides ordering
• In this case, producer guaranteed to precede consumer
• Labeled causal link extracted
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
• Generalization of Floyd Warshall algorithm that uses LVS
operations instead of standard + and <
• See (Conrad 2010) for details
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide 58
Optimization: Causal link dominance
Concurrent Plan Recognition & Execution for Human-Robot Teams |... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
sumes iff contains all
e2
e2
e1
assignments in
e1
•
ex., subsumes xR1 = j
}
{xR1 = juice
{
uice, xA3 = bagel}
• Intuitively, all subplans represented by also
e2
represented by (subset)
e1
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide
67
Labeled causal links
Concurrent Plan Rec... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
4)
φC
φC ← {aec,p = epi } ∧ φepi
(cid:5)
(cid:5)
if epi ≺ eti
φC
AddConstraint
and eti ≺ ec
(cid:2)
¬φC
and eti (cid:9) ec
φC
Add [(cid:4), ∞] : φC from ec to eti
(cid:5)
(cid:5)
and eti ≺ ec
(cid:5)
(cid:5)
φC
φC
Add [(cid:4), ∞] : φC from epi to eti
else if epi ≺ eti
(cid:5)
(cid:5)
else if epi (cid:9) eti
φC
else if... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
:6)(cid:7)(cid:8)(cid:10)(cid:15)
(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:10)(cid:16)
(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:10)(cid:17)
(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:10)(cid:9)
(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:10)(cid:13)
(cid:2)(cid:3)(cid:4)(c... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
Human-Robot Teams | Steven J. Levine
Slide
74
Encoding in an ATMS
(cid:6)
z = 1⇒ (ac = 1 ∨ (ac = 2 ∧ y = 1))
¬(ac = 1 ∧ x = 2 ∧ z = 1)
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide 75
A basic threat
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levi... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
Chapter 4 and 5 Wear Mechanisms
1
Delamination Wear Mechanisms
•
Four mechanisms of delamination wear
1. Plastic deformation of the surface
2. Crack nucleation at the sub-surface due to
plastic deformation
3. Crack propagation from these nucleated cracks
due to plastic deformation
4. Creation of loose wear s... | https://ocw.mit.edu/courses/2-800-tribology-fall-2004/49841547dcddc87b82263b982a60486e_ch5_wear_mech.pdf |
+
∂ ( σ xz ) r = 0
∂z
∂(σ zz ) r = 0
∂z
f 3 = c 1
f 2 = c 2
(σ ) = f ( z )
r
xx
r
(σ yy ) = νf ( z )
(σ ) = 0
r
(σ ) = 0
r
xz
zz
10
Plastic Deformation of a Semi-Infinite
Elastoplastic Solid
Residual Stress Calculation -- Equilibrium Equations
(σzz )' r
( ) = −
ε
zz r
(
γxz r
) = −
1− 2ν
2(1 −ν)G
(σxz )'
G... | https://ocw.mit.edu/courses/2-800-tribology-fall-2004/49841547dcddc87b82263b982a60486e_ch5_wear_mech.pdf |
formed sphere
of the Imaginary
sphere
15
Criteria for Crack Nucleation
Energy Criterion and Strength Criterion
Energy criterion
e
,
n
i
a
r
t
S
Strength criterion
d*
Particle size, d
Figure 4.37
16
Rigid Cylinder under a General State of Stress
σr r
θ
φ
x
z
τmax
Figure 4.38
17
Crack Nucleation... | https://ocw.mit.edu/courses/2-800-tribology-fall-2004/49841547dcddc87b82263b982a60486e_ch5_wear_mech.pdf |
24
Crack Propagation
•
However, crack propagation in sliding wear
is due to a combined loading of
compression and shear on the crack -
compressive stress on the crack and shear
deformation at the crack tip.
25
Crack Propagation
•
•
The rate of crack propagation under sliding
wear conditions is very slow,... | https://ocw.mit.edu/courses/2-800-tribology-fall-2004/49841547dcddc87b82263b982a60486e_ch5_wear_mech.pdf |
crack extension per cycle versus the
logarithm of the change in the stress intensity factor
10-2
10-4
)
e
l
c
y
c
/
m
m
(
N
d
/
a
d
Kc
Final failure
C
da/dN = C(
∆K)m
m
B
1
1
10-6
Threshold
∆K0
A
Figure 4.47
log ∆K
35
Void formation around inclusions and crack
propagation from these voids near the... | https://ocw.mit.edu/courses/2-800-tribology-fall-2004/49841547dcddc87b82263b982a60486e_ch5_wear_mech.pdf |
Fast Fourier Transform:
Theory and Algorithms
Lecture 8
Vladimir Stojanović
6.973 Communication System Design – Spring 2006
Massachusetts Institute of Technology
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts I... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
Suppose all Il sets have same number
of elements N1 so, N=N1*N2, r=N2
Each inner-most sum takes N1
2 multiplications
The outer sum will need N2 multiplications per output point
N2*N for the whole sum (for all output points)
Hence, total number of multiplications
6.973 Communication System Design
4
Cite as: Vla... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
no arithmetic operations)
6.973 Communication System Design
6
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
FFTs with twiddle factors
Reintroduced b... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
2-D view of Cooley-Tukey mapping
N=15 (N1=3, N2=5)
x12
x13
x14
x9
x10
x11
x12
x9
x6
x3
x4
x5
x0
x1
x2
DFT-5
DFT-5
DFT-5
x6
x7
x8
x3
x4
x5
x0
x1
x2
x0
x1...............
x13
x14
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x4
x9... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
– DIT)
“Butterfly”
(sum or difference followed or
preceeded by a twiddle factor multiply)
Xm and XN/2+m outputs of N/2 2-pt DFTs on outputs of
2, N/2-pt DFTs weighted with twiddle factors
6.973 Communication System Design
11
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, S... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
) radix-2 implementation
If reverse the role of N1 and N2, get DIF
N1=N/2, N2=2
X2k1
=
N / 2-1
n1=0
W
n1k1
N / 2(xn1
+xN / 2+n1
),
X2k1+1
=
N / 2-1
n1=0
W
n1k1
N / 2 Wn1(xn1
N
-xN / 2+n1
).
X0
X1
X2
X3
X4
X5
X6
X7
DFT
N = 2
DFT
N = 2
DFT
N = 2
DFT
N = 2
w1
8
w2
8
w3
8
DFT
N = 4
{ }x2k
DFT
N = 4
{ }x2k+1
X0
X2
X4
X6... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
X3
X7
X0
X1
X2
X3
X4
X5
X6
X7
DFT
N = 2
DFT
N = 2
DFT
N = 2
DFT
N = 2
w1
8
w2
8
w3
8
DFT
N = 4
{ }x2k
DFT
N = 4
{ }x2k+1
X0
X2
X4
X6
X1
X3
X5
X7
Division
into even and
odd numbered
sequences
DFT of
N / 2
Multiplication
by twiddle
factors
DFT of
2
DFT of
2
Multiplication
by twiddle
factors
DFT of
N / 2
Figure by MIT Op... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
Radix-4
N=4n, N1=4, N2=N/4
4 DFTs of length N/4
3N/4 twiddle multiplies
N/4 DFTs of length 4
Cost of length-4 DFT
No multiplication
Only 16 real additions
DFT
2
DFT
4
x0
x8
x15
x0
x4
x8
x12
x15
DFT
8
DFT
8... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
x8
x12
x15
x0
x4
x8
x12
DFT
8
DFT
8
DFT
4
DFT
4
DFT
4
DFT
4
X0
X12
X1
X13
X2
X14
X3
X15
DFT
8
DFT
4
DFT
4
X0
X14
X1
X15
X0
X14
X1
X13
X3
X15
R2
R4
S-R
Figure by MIT OpenCourseWare.
6.973 Communication System Design
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
17
M... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
n1
),
+xN / 2+n1
X4k1+1
=
N / 4-1
n1=0
n1k1W
N / 4Wn1
N
X[(xn1
-xN / 2+n1
)
+j(xn1+N / 4-xn1+3N / 4)],
Even samples X2k in DIF should
be computed separately from
other samples
With same algorithm (recursively) as
the original sequence
No general rule for odd samples
Radix-4 is more efficient than radix-2 ... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
FFTs without twiddle factors
Divide and conquer requirements
N-long DFT computed from DFTs with lengths that are
factors of N (allows the inner sum to be a DFT)
Provided that subsets Il guarantee perio... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
1 and N2 are coprime
All congruences modulo N1 obtained
For a given congruence modulo N2 and vice versa
Figure by MIT OpenCourseW. are.
6.973 Communication System Design
21
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
Impact on DFT
Formulating the true multi-dimensional transform
k
N N
2
1
= N t k + N t k
2 2 ... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
CourseWare.
True bidimensional transform!
(no extra twiddle factors)
6.973 Communication System Design
23
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
x9
x12
input additions
input additions
N = 3
N = 5
X5
X11
X2
X8
X14
X4
X9
point wise
multiplication
output additions output additions
N = 5
N = 3
Figure by MIT OpenCourseWare.
B1xB2’ only involves additions
D – diagonal (so point multiply)
Winograd transform has many more additions than
twiddle FFTs
6.973 Co... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49a17bd0078f7723100ac1395a476595_lecture_8.pdf |
Fast Fourier Transform:
Practical aspects and Basic Architectures
Lecture 9
Vladimir Stojanović
6.973 Communication System Design – Spring 2006
Massachusetts Institute of Technology
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
27652
61444
30
60
120
240
504
1008
2520
384
888
2076
4812
384
888
2076
5016
13388
14540
29548
34668
84076
99628
16
32
64
128
256
512
1024
2048
16
32
64
128
256
512
1024
2048
Real multiplies
Real adds
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
Figure by MIT OpenCo... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
ovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
6.973 Communication System Design
5
In-place computation
(cid:137) Most algorithms allow in-place computation
(cid:132) Cooley-Tuke... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
ed on [DD Month YYYY].
6.973 Communication System Design
7
Quantization noise
(cid:137) Roundoff noise generated by finite precision of operations inside FFT (adds,
multiplies)
(cid:137) CTFFT (lengths 2n)
(cid:132) Four error sources per butterfly (variance 2-2B/12)
(cid:132) Total variance per butterfly 2-2B/3
(cid... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
6.973 Communication System Design
8
Particular cases
(cid:137) DFT algorithms for real data sequence xk
(cid:132) Xk has Hermitian symmetry (XN-k=Xk
*)
(cid:132) X0 is real, and when N even, XN/2 real as well
(cid:132) N input values map to
(cid:132) 2 real and N/2-1 complex conjugate values when N even
(cid:132) 1 r... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
6.973 Communication System Design
10
Related transforms
(cid:137) Mostly focused on efficient matrix-vector product
involving Fourier matrix
(cid:137) No assumption made on the input/output vector
(c... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
6.973 Communication System Design
13
Relationship with FFT
(cid:137) DHT, DCT, DST and related transforms can all ... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
2n
+2 additions
3.2n-1 odd DFT 2n-1 + 1 complex DFT 2n-1x2n-1
+ n.2n additions
1 real symmetric DFT 2n + 1 real antisymmetric DFT 2n
+ (6n+10), 4n-1 additions
1 real symmetric DFT 2n-1 + 1 inverse real DFT
+ 3(2n-3-1)+1 multiplications + (3n-4).2n-3+1 additions
(cid:137) All transforms use split-radix algorithms Figure... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
and tailoring to cache
size (aspect ratio)
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
6.973 Communication System Design
16
Digital Signal Processors
... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
ptotic lower bound for AT2
(cid:132) Achieved by several micro-architectures
(cid:132) Shuffle-exchange networks
(cid:132) Square grids
(cid:132) Outperform the more traditional micro-architectures only for very large N
(cid:132) Cascade connection with variable delay
(cid:137) Dedicated chips often based on traditiona... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
21
1 multiply-add cell
(cid:137) Performance O(N2logN)
COEF
ROM
DATA IN
INPUT
BUFFER
BUTTERFLY
DATA OUT
FFT
RAM
Figure by MIT OpenCourseWare.
N
CONTROL
(cid:137) For large FFTs storage of intermediate results is a problem
(cid:132) N-long FFT requires
(cid:132) N/r*logrN, radix-r butterfly operations
(cid:132) 2N*logr... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
2
Figure by MIT OpenCourseWare.
(cid:132) Produces the output values in bit-reversed order
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
6.973 Communicati... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
:137) General scheme for interconnections
(cid:132) Number the cells naturally
(cid:132) 0 to N/2-1, from left to right
(cid:132) Cell i in the first row is connected to two cells in
the second row
(cid:132) Cell i and (i+N/4) mod N/2
X0X2
X1X3
X6X4
X7X5
X0X1
X3X2 X4X5
X7X6
(cid:132) Cell i in the second row is connec... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
are shuffled among cells
(cid:137) At the end of logN steps, final data is in cell registers in bit-
reversed order
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
N
N log N
log N
N log2 N
N log N
N log N
N2
log N
N2 / log2 N
log2 N
N2 / log2 N log2 N
N log2 N
N
N5log3N
N3log3N
N2log3N
N3log5N
N3log3N
N2log2N
N2log2N
N2log2N
N2log2N
N2log N
N2log N
N2log N
N log2N
N log2N
log2N
log2N
log2N
N
(cid:137) Cascade FFT has the best trade-off
(cid:132) Less complicated wiring and Nlog... | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
6.973 Communication System Design
30 | https://ocw.mit.edu/courses/6-973-communication-system-design-spring-2006/49aa5e11da2190ceb1dcadbf5abf7393_lecture_9.pdf |
Lecture 4
van Emde Boas
6.046J
Spring 2015
Lecture 4: Divide and Conquer:
van Emde Boas Trees
• Series of Improved Data Structures
• Insert, Successor
• Delete
• Space
This lecture is based on personal communication with Michael Bender, 2001.
Goal
We want to maintain n elements in the range {0, 1, 2, . .... | https://ocw.mit.edu/courses/6-046j-design-and-analysis-of-algorithms-spring-2015/49c8fa24dffce58052c90d46ac800387_MIT6_046JS15_lec04.pdf |
0
12
0
13
0
14
0
15
1
Figure 1: Bit vector for u = 16. THe current set is {1, 9, 10, 15}.
Split Universe into Clusters
√
We can improve performance by splitting up the range {0, 1, 2, . . . , u − 1} into u
clusters of size u. If x = i u + j, then V[x] = V.Cluster[i][j].
√
√
√
low(x) = x mod u = j
x
high(x)... | https://ocw.mit.edu/courses/6-046j-design-and-analysis-of-algorithms-spring-2015/49c8fa24dffce58052c90d46ac800387_MIT6_046JS15_lec04.pdf |
- u van Emde Boas structure (∀ 0 ≤ i < u)
√
√
√
• V.summary is a size- u van Emde Boas structure
√
• V.summary[i] indicates whether V.cluster[i] is nonempty
INSERT(V, x)
1
2
Insert(V.cluster[high(x)], low[x])
Insert(V.summary, high[x])
So, we get the recurrence:
√
T(u) = 2T( u) + O(1)
'(log u) = 2T
T
=... | https://ocw.mit.edu/courses/6-046j-design-and-analysis-of-algorithms-spring-2015/49c8fa24dffce58052c90d46ac800387_MIT6_046JS15_lec04.pdf |
)
j = V.cluster[i].min
√
T(u) = T( u) + O(1)
=⇒ T(u) = O(log log u)
Don’t store Min recursively
The Successor call now needs to check for the min separately.
if x < V.min : return V.min
(1)
4
Lecture 4
van Emde Boas
6.046J
Spring 2015
I O(1) time
if V.min == None
V.min = V.max = x
return
if x... | https://ocw.mit.edu/courses/6-046j-design-and-analysis-of-algorithms-spring-2015/49c8fa24dffce58052c90d46ac800387_MIT6_046JS15_lec04.pdf |
) + O(1)
=⇒ T(u) = O(log log u)
5
Lecture 4
van Emde Boas
6.046J
Spring 2015
Lower Bound [Patrascu & Thorup 2007]
Even for static queries (no Insert/Delete)
• Ω(log log u) time per query for u = n
(log n)O(1)
• O(n · poly(log n)) space
Space Improvements
We can improve from Θ(u) to O(n log log u).
• Onl... | https://ocw.mit.edu/courses/6-046j-design-and-analysis-of-algorithms-spring-2015/49c8fa24dffce58052c90d46ac800387_MIT6_046JS15_lec04.pdf |
6.897: Selected Topics in Cryptography
Lectures 7 and 8
Lecturer: Ran Canetti
Highlights of past lectures
• Presented a basic framework for analyzing the
security of protocols for multi-party function
evaluation.
• Presented the notion of modular composition.
• Stated and proved the non-concurrent.
composition theo... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/4a4bd69a1e3c2fe6208174e2d38a9146_lecture7_8.pdf |
Only non-concurrent composition.
Wish-list for a more general framework
• Deal with more “real-life” settings such as:
– Asynchronous communication
– Unreliable and unauthenticated communication
– Variable (even unbounded) number of participants
– Variable identities
• Deal with reactive tasks (e.g., encryption, ... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/4a4bd69a1e3c2fe6208174e2d38a9146_lecture7_8.pdf |
target ITM and tape, code for the target ITM.
– Contents
If the control function C allows the tuple (source id, target id, code,
tape) then the instruction is carried out. If no ITM with target id
exists then a copy is invoked, with said code, identity, and sec.
param.
• The machine written to is the next to be ac... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/4a4bd69a1e3c2fe6208174e2d38a9146_lecture7_8.pdf |
comm. Tape of ITM M. Then:
• M writes “Corrupted” on subr. output tape of Z
• From now on, in each activation M sends its entire state to A
• A assumes all write privileges of M.
• Notes:
– Z interacts with A freely throughout the computation.
– All communication between parties is done “via A”.
– Asynchronous c... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/4a4bd69a1e3c2fe6208174e2d38a9146_lecture7_8.pdf |
versary), and multiple
copies of ITMs running P, and write to their input tapes.
However, here A is “ideally replaced” with an ITM S, and the parties
running P are “ideally replaced” by dummy parties for F.
– F can write to the comm. tape of S and to the subroutine output tapes of
all dummy parties.
– S can write... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/4a4bd69a1e3c2fe6208174e2d38a9146_lecture7_8.pdf |
F knows who is corrupted then
the security properties of the protocol under corruptions can be explicitly
expreseed in the code of F.)
Variants
• Passive (semi-honest) adversaries: The corrupted parties
continue running the original protocol.
• Unconditional security: Allow Z, A to be computationally
unbounded. ... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/4a4bd69a1e3c2fe6208174e2d38a9146_lecture7_8.pdf |
:
– All inputs from Z are forwarded to A, and all outputs from A go to Z.
– When A sends message m to party id, S gives input “send m to id” to Sd.
– When Sd outputs “got m from id”, write “m from id” to comm. tape of A.
– All messages from F are forwarded to Sd, and all messages from Sd to F
are forwarded.
S,Z ~... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/4a4bd69a1e3c2fe6208174e2d38a9146_lecture7_8.pdf |
•
the following system of interacting ITMs:
Initial ITM:
– Environment Z (the initial ITM, with fixed ID)
• Permission list:
– Z can activate a (single copy of) an ITM A (adversary), and multiple
ITMs running P, all having the same SID, and write to their input tapes.
– A can write to the incoming comm. tapes of... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/4a4bd69a1e3c2fe6208174e2d38a9146_lecture7_8.pdf |
,pid).
• Each output of the ITM (sid,pid) is treated as usual (I.e., as an output
coming from a dummy party for F with ID=(sid,pid).
Note:
•
•
In QP there may be multiple copies of P running concurrently.
If P is a protocol in the real-life model then so is QP. If P is a protocol in the
F’-hybrid model for some fun... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/4a4bd69a1e3c2fe6208174e2d38a9146_lecture7_8.pdf |
(Will use the alternative formulation of the definition: security w.r.t. the
dummy adversary).
From the fact that P realizes F, we know that there exists an ideal
process adversary S such that IDEALF
Consider the protocol QP in the real-life model.
We will construct an adversary H that interacts with protocol Q in ... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/4a4bd69a1e3c2fe6208174e2d38a9146_lecture7_8.pdf |
P).
We use a hybrid argument:
–
Consider m “hybrid systems”: in the i-th system, the first i instances
of F are replaced by copies of P. (Here m is a bound on the number
of instances of P with this Z.) Then:
•
•
Î There exists an i such that Z distinguishes with proability e/m between
an interaction with the I... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/4a4bd69a1e3c2fe6208174e2d38a9146_lecture7_8.pdf |
,m) to S
3. Halt.
Example:
The secure message transmission functionality,
F
smt
1. Receive input (sid,pids,pidr,m) from party
(sid,pids). Then:
1. Output (sid,pids,pidr,m) to party (sid,pidr)
2. Send (sid,pids,pidr,|m|) to S
3. Halt.
Example:
The key-exchange functionality FKE (I)
Wait to receive:
(sid,pida... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/4a4bd69a1e3c2fe6208174e2d38a9146_lecture7_8.pdf |
1. Upon receiving (sid,pidp,pidv ,“commit”,x) from
(sid,pidp), do:
1. Record x
2. Output (sid,pidp,pidv, “receipt”) to (sid,pidv)
3. Send (sid,pidp,pidv, “receipt”) to S
2. Upon receiving (sid,“open”) from (sid,pidp), do:
1. Output (sid,x) to (sid,pidv)
2. Send (sid,x) to S
3. Halt.
Example:
The Synchronous Co... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/4a4bd69a1e3c2fe6208174e2d38a9146_lecture7_8.pdf |
t
cos
θ
i
L10-3
SOLVE TE BOUNDARY EQUATIONS
We found:
1+ Γ = T
and
Solving yields:
1− Γ = T
ηi cos θt
ηt cos θi
) =
Γ θ(
i
t
η cos θ − η cos θ
t =
η cos θ + η cos θ
t
i
t
i
i
i
η −' 1
n
'
η + 1
n
where η ' (cid:22)
n
t
η cos θ
i
η cos θ
t
i
Normal incidence: θ = 0, cosθ = 1, and ηn’ = ηt/ηi... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-spring-2009/4a6f6970935940d8e2b391f9dbadf598_MIT6_013S09_lec10.pdf |
−μ
H
∂
t
∂
E
∂
t
∂
E 0
H
∇ × = ε
∇ ε =
i
H
E
∂
→ ∇ × = ε
t
∂
H
∂
→ − ∇ × = μ
t
∂
E
→ ∇ μ =
H 0
i
∇ μ =
H 0
i
→
∇ ε =
E 0
i
Are they valid?
Under what circumstances does the solution to the resulting
set of equations satisfy Maxwell’s Equations?
They ARE Maxwell’s Equations, just reord... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-spring-2009/4a6f6970935940d8e2b391f9dbadf598_MIT6_013S09_lec10.pdf |
2
1
TE
Critical
angle
θ
90o
0
TM
90o
θ
0
TM
θ
90o
Brewster’s angle θB
Brewster’s angle θB
High power
laser beam
Brewster’s angle
laser window
Horizontally
polarized glasses
cut glare
Ocean wave
No reflection
at θB
L10-8
MIT OpenCourseWare
http://ocw.mit.edu
6.013 Electromagnetics and Applicatio... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-spring-2009/4a6f6970935940d8e2b391f9dbadf598_MIT6_013S09_lec10.pdf |
Massachusetts Institute of Technology
6.270 Autonomous LEGO Robot Competition
IAP 2005: Attack of the Drones
Workshop 1 — Basic LEGO Structure and Bracing
Monday, January 3, and Tuesday, January 4, 2005
1
Items to Bring
• All of your LEGOs
2 Reading
• Section 6.3 of course notes
3 LEGO Measurements
• A Funda... | https://ocw.mit.edu/courses/6-270-autonomous-robot-design-competition-january-iap-2005/4aa718211a3d9142118d5dd0f138e54b_1_basiclego.pdf |
conform to
Pythagoras’ theorem. Using Pythagoras’ theorem not only leads to stronger bracing, but also saves beams. For
the purposes of LEGO, this means that the only useful combinations are 3-4-5, 5-12-13, and 6-8-10 (Figure 4).
• Other Bracing. Try experimenting with unconventional bracing. Many successful robots ... | https://ocw.mit.edu/courses/6-270-autonomous-robot-design-competition-january-iap-2005/4aa718211a3d9142118d5dd0f138e54b_1_basiclego.pdf |
4.4. You will also see some creative uses of
bracing when you complete Assignment 1.
6 A few things for the future
• Drop Test Blues Doing the drop test can really scary when it is nearing the deadline and you have become
one with your robot. to reduce this stress, we recommend that you incrementally test your robo... | https://ocw.mit.edu/courses/6-270-autonomous-robot-design-competition-january-iap-2005/4aa718211a3d9142118d5dd0f138e54b_1_basiclego.pdf |
Effective Innovation
Don Clausing
ESD 33, MIT
July 2004
Three types of innovations
• Launch
• Growth
• Library
July 2004
MIT
2
Enterprise Processes
INTEGRATION & DIRECTION
July 2004
MIT
3
Product acquisition process
GLOBAL ECONOMY
I
S
E
G
O
L
O
N
H
C
E
T
E
L
B
A
L
I
A
V
A
L
L
A
PRODUCT
PORTFOLIO
ARCHITECTURE
BUSIN... | https://ocw.mit.edu/courses/esd-33-systems-engineering-summer-2004/4ab81884f461adfcb659b04d7e62349e_s8_efctv_invtn.pdf |
”
Decline
Saturation
Present system
Next-generation system
Leapfrog
α
Infancy
Rapid growth
Maturity
Typical steps of evolution of technological systems can be illustrated by an S-shaped curve that reflects changes of the system's benefit-to cost ratio with time since the inception
of the system. In the infancy phase t... | https://ocw.mit.edu/courses/esd-33-systems-engineering-summer-2004/4ab81884f461adfcb659b04d7e62349e_s8_efctv_invtn.pdf |
OF INVENTIONS
PROFITABILITY
OF INVENTIONS
July 2004
MIT
9
TIME
Levels of invention
• 1. A component intended for the task is used
• 2. Existing system is slightly modified
• 3. At least one system component is radically
changed or eliminated; within one discipline
• 4. A new system is developed; interdisciplinary
• 5... | https://ocw.mit.edu/courses/esd-33-systems-engineering-summer-2004/4ab81884f461adfcb659b04d7e62349e_s8_efctv_invtn.pdf |
system performing certain functions becomes less complicated/costly, or it becomes capable of performing its functions better or performs more functions. A combination of
these evolutionary processes also often occurs.
July 2004
MIT
13
Bicycle
• 1813
• 1840
• 1845
• 1860s
• 1870s
• 1884
• 1890
• 1897
Feet pushed on ... | https://ocw.mit.edu/courses/esd-33-systems-engineering-summer-2004/4ab81884f461adfcb659b04d7e62349e_s8_efctv_invtn.pdf |
Invention came from separating the two
requirements; one to front, second to back
July 2004
MIT
18
Role of science
• TRIZ laws suggest new “rooms” in which we
might find a new invention
• Then use scientific data base to combine scientific
effects with suggested pattern of invention
• Thousands of scientific effect... | https://ocw.mit.edu/courses/esd-33-systems-engineering-summer-2004/4ab81884f461adfcb659b04d7e62349e_s8_efctv_invtn.pdf |
dipole
Sheet charge
Traveling
July 2004
MIT
28
Changes to substances
• Phase changes
• Changes in electromagnetic properties
• Composite materials
• Introduction of voids
• Introduction of additives
• Replacement of solid with particles
• Combinations of two substances
• Form substance from the environment
• Separate ... | https://ocw.mit.edu/courses/esd-33-systems-engineering-summer-2004/4ab81884f461adfcb659b04d7e62349e_s8_efctv_invtn.pdf |
• Assure robustness is achieved in production
• Provides:
– Early specification maturity
– Early technology readiness
– Early identification of special manufacturing
requirements
• Critical parameter drawing is key
July 2004
MIT
35
Technology transfer
Effective technology innovation can only succeed
if it is accompa... | https://ocw.mit.edu/courses/esd-33-systems-engineering-summer-2004/4ab81884f461adfcb659b04d7e62349e_s8_efctv_invtn.pdf |
Development.pdf
Womak_Lean Thinking Introduction.pdf
Stanke_Murman_Lifecycle Value in Aerospace.pdf
Ward_The Second Toyota Paradox.pdf
Suh_Axiomatic Design Theory for Systems.pdf
Frey_Cognition and Complexity.pdf
Hazelrigg_Axiomatic Engineering Design.pdf
Gigerenzer_Bounding Rationality to the World.pdf
Brooks_... | https://ocw.mit.edu/courses/esd-33-systems-engineering-summer-2004/4ab81884f461adfcb659b04d7e62349e_s8_efctv_invtn.pdf |
3 AUG
s
e
i
d
u
t
R 5 AUG
S
e
s
a
C
July 2004
T 10 AUG
R 12 AUG
Examination #2
Aircraft Engines (GE)
Automobiles
Work on Aircraft Engines Assignment
Project Oxygen
NORAD Command and Control (Mitre)
Tactical Tomahawk
Course Summary / Feedback
Steele_TBD.pdf
Folk_TBD.pdf
Cummings_TBD.pdf
MIT
#1
#2
#3
#4... | https://ocw.mit.edu/courses/esd-33-systems-engineering-summer-2004/4ab81884f461adfcb659b04d7e62349e_s8_efctv_invtn.pdf |
18.417 Introduction to Computational Molecular Biology
Lecture 5: September 23, 2004
Lecturer: Ross Lippert
Scribe: Tony Scelfo
Editor: Athicha Muthitacharoen
Local/Multi Alignments
Introduction
Last Time
• Global Alignment
This Time
• Local Alignment Method of aligning two sequences that share a highly commo... | https://ocw.mit.edu/courses/18-417-introduction-to-computational-molecular-biology-fall-2004/4acde14888af72996f60ab92a9a430bf_lecture_05.pdf |
Homeobox Genes are good to study when looking at local alignments. The reason
for this is that the region that codes for the Homeobox Gene has been identified in
many species and biologists can look for the Homeobox Gene in new species or test
the performance of local alignment algorithms.
• Why are two sets of gene... | https://ocw.mit.edu/courses/18-417-introduction-to-computational-molecular-biology-fall-2004/4acde14888af72996f60ab92a9a430bf_lecture_05.pdf |
� �i,j��j GlobalScore(S1[i� · · · i], S2[j� · · · j])
Time: O(n4 · n2) = O(n6)
cell(i,j) = GlobalAlignmentScore(S1 [1 · · · i], S2[1 · · · j])
• reduces local alignment to O(n4).
By using the same grid but different recurrence, can reduce local alignment to O(n2)
(Smith-Waterman).
scorei,j = max
scorei−1,j−1 + �(S... | https://ocw.mit.edu/courses/18-417-introduction-to-computational-molecular-biology-fall-2004/4acde14888af72996f60ab92a9a430bf_lecture_05.pdf |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.