text stringlengths 30 4k | source stringlengths 60 201 |
|---|---|
use a set of derivation rules for this
2/24/2016
Cognitive Robotics
110
Temporal Relaxed Planning Graph
.
lb
up
Action1
Action2
Action3
Fact1
Fact2
Fact3
…
Fact4
Fact1
Fact2
Fact3
…
2/24/2016
Cognitive Robotics
111
•
Temporal Landmarks for Flashlight Match Cellar
•
The goal must hold from some time point g until the... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/478e717152ec908cd81662e07167d745_MIT16_412JS16_L7.pdf |
holds(light)
START
(fix-fuse)
END
(fix-fuse)
holds(fuse-fixed)
E
2/24/2016
Cognitive Robotics
113
Temporal Landmarks for Flashlight Match Cellar
•
The only possible achiever of have-flashlight is END(find-flashlight), so
– occursshf(END(find-flashlight)
The find-flashlight action must start
– occurssf(START(find-flash... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/478e717152ec908cd81662e07167d745_MIT16_412JS16_L7.pdf |
Temporal Landmarks Derivation Rules
• If fact F must hold for a duration of d, then:
– F must be achieved. Furthermore, this must be by an action which does
not delete F at the end, if its duration is shorter than d.
– F must be achieved for the first time
• Every action must have a start and an end. Its
invariant co... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/478e717152ec908cd81662e07167d745_MIT16_412JS16_L7.pdf |
0
20
4
0
9
0
53
20
20
4
0
8
0
52
matchcellar (2011)
matchcellar (2014)
tms (2011)
tms (2014)
turnandopen (2011)
turnandopen (2014)
TOTAL
20
20
0
0
19
7
66
20
20
2
0
19
1
62
18
20
0
0
0
0
38
0
0
0
0
0
0
0
Number of solved problems
2/24/2016
Cognitive Robotics
119
(Interesting) Results on Non-Temporally Expressive Do... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/478e717152ec908cd81662e07167d745_MIT16_412JS16_L7.pdf |
19
5
5
17 17
6
5
0
0
openstacks (2011)
20 20 20
parcprinter (2011)
10
0
0
parking (2011)
parking (2014)
pegsol (2011)
satellite (2014)
sokoban (2011)
20 10 10
20 20 19
19 19
17
5
8
1
0
1
0
6
6
0
0
0
0
0
0
0
0
0
TOTAL
173 139 61
12
orig e1 e4 e
∞
driverlog (2014)
elevators (2011)
floortile (2011)
floortile (2014)... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/478e717152ec908cd81662e07167d745_MIT16_412JS16_L7.pdf |
14)
– Oversubscription Planning (Mirkis & Domshlak, 2014)
– Temporal planning
• At least, when the problems are temporally expressive
2/24/2016
Cognitive Robotics
121
…
2/24/2016
Cognitive Robotics
122
MIT OpenCourseWare
https://ocw.mit.edu
16.412J / 6.834J Cognitive Robotics
Spring 2016
For information about citing ... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/478e717152ec908cd81662e07167d745_MIT16_412JS16_L7.pdf |
Lecture 3
8.321 Quantum Theory I, Fall 2017
11
Lecture 3 (Sep. 13, 2017)
3.1 Even More Math
3.1.1 More on Matrix Representations
Last time, we described that in a given basis, there is an exact correspondence between n×n matrices
and operators, where n is the dimension of the Hilbert space. Let {|a(cid:105)} form an or... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/47a22b9e37fbdba8448bb927004fed18_MIT8_321F17_lec3.pdf |
, then Aii = ai, so the trace becomes
Tr A =
(cid:88)
ai .
i
(3.4)
(3.5)
This is a statement of the familiar fact that the trace of an operator is the sum of its eigenvalues.
3.1.2 Unitary Transformations
Suppose we are given two orthonormal bases {|ai(cid:105)} and {|bi(cid:105)}. How are these bases related? We
can d... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/47a22b9e37fbdba8448bb927004fed18_MIT8_321F17_lec3.pdf |
(cid:105)} and {|bi(cid:105)}. We can express |α(cid:105) in two
ways as
|α(cid:105) =
(cid:88)
i
ci
|ai(cid:105) =
(cid:88)
i
di
|bi(cid:105) .
(3.11)
How are these two sets of coefficients {ci} and {di} related? Using the definition of U , we can write
|α(cid:105) =
=
=
(cid:88)
j
(cid:88)
j
(cid:88)
i,j
dj
|bj(cid:105)... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/47a22b9e37fbdba8448bb927004fed18_MIT8_321F17_lec3.pdf |
3.14)
(3.15)
Theorem 2. A Hermitian matrix Hij = (cid:104)φi|H|φj(cid:105) can always be diagonalized by a unitary trans-
formation.
Lecture 3
8.321 Quantum Theory I, Fall 2017
13
Proof. Consider a general orthonormal basis {|φi(cid:105)}, and let {|hi(cid:105)} be the orthonormal basis of
eigenstates of the operator ... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/47a22b9e37fbdba8448bb927004fed18_MIT8_321F17_lec3.pdf |
5) ,
(3.17)
(3.18)
and so AB = BA. This proves the forward direction.
Now consider two diagonalizable operators A, B that commute, AB = BA, and let {|ai(cid:105)} be a
basis of eigenvectors of A,
Then we have
A|ai(cid:105) = ai|ai(cid:105) .
A(B|ai(cid:105)) = AB|ai(cid:105)
= BA|ai(cid:105)
= Bai|ai(cid:105)
= ai(B|ai... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/47a22b9e37fbdba8448bb927004fed18_MIT8_321F17_lec3.pdf |
on the
diagonal of A. Diagonalizing the block Bi only mixes eigenkets of A with the same eigenvalue, so
we can diagonalize B while leaving A diagonal. This proves the backward direction.
Lecture 3
8.321 Quantum Theory I, Fall 2017
14
3.2 Measurement
Consider a quantum mechanical system. We know that the state of such ... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/47a22b9e37fbdba8448bb927004fed18_MIT8_321F17_lec3.pdf |
22)
(3.23)
(3.24)
Historically, there has been a lot of worry about the collapse of the wavefunction. In the modern
language, there is a way to understand this collapse in a very palatable way, which we may discuss
later in the course.
The concept of measurement is worth pondering. Consider making a measurement on a st... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/47a22b9e37fbdba8448bb927004fed18_MIT8_321F17_lec3.pdf |
ψ(cid:105), the expectation value of A is
(cid:88)
(cid:104)A(cid:105) :=
ai Prob(A = ai)
ai
(cid:88)
ai
=
(cid:88)
ai
j:a
j =a
i
= (cid:104)ψ|A|ψ(cid:105) ,
| (cid:105)
ψ aj aj ψ
(cid:105)(cid:104)
(cid:104) |
(3.27)
where in the final line we have used
A =
(cid:88)
a
i
ai
|ai(cid:105)(cid:104)ai| .
(3.28)
3.3 Spin- 1
... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/47a22b9e37fbdba8448bb927004fed18_MIT8_321F17_lec3.pdf |
efficients in the form
−
R
c+ = cos
θ
2
,
c− = eiφ sin
θ
2
,
(3.30)
with 0 ≤ θ < π and 0 ≤ φ < 2π. Specifying these two angles specifies the state exactly, and we note
that specifying these angles is equivalent to specifying a point on the surface of the unit sphere S2.
This parametrization of the Hilbert space is known a... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/47a22b9e37fbdba8448bb927004fed18_MIT8_321F17_lec3.pdf |
0
0 −1
,
(3.33)
Sx
=
Sy =
(cid:126)
2
−i(cid:126)
2
(|+(cid:105)(cid:104)−| + |−(cid:105)(cid:104)+|) =
(cid:126)σx
2
=
(cid:126)
2
(cid:19)
(cid:18)0 1
1 0
(cid:18) −i
(cid:126)
0
0
i
2
(cid:19)
(|+(cid:105)(cid:104)−| − |−(cid:105)(cid:104)+|) =
(cid:126)σy
2
=
We can check explicitly (left as an exercise) that these... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/47a22b9e37fbdba8448bb927004fed18_MIT8_321F17_lec3.pdf |
MIT OpenCourseWare
http://ocw.mit.edu
6.006 Introduction to Algorithms
Fall 2011
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. | https://ocw.mit.edu/courses/6-006-introduction-to-algorithms-fall-2011/47a412008dc74679e9072891be09f351_MIT6_006F11_lec07_orig.pdf |
MIT OpenCourseWare
http://ocw.mit.edu
6.641 Electromagnetic Fields, Forces, and Motion, Spring 2005
Please use the following citation format:
Markus Zahn, 6.641 Electromagnetic Fields, Forces, and Motion, Spring
2005. (Massachusetts Institute of Technology: MIT OpenCourseWare).
http://ocw.mit.edu (accessed MM DD, ... | https://ocw.mit.edu/courses/6-641-electromagnetic-fields-forces-and-motion-spring-2005/47fbb5ff17cb74a5d6a5b9c1eeda9c23_lecture3.pdf |
41, Electromagnetic Fields, Forces, and Motion
Prof. Markus Zahn
Lecture 3
Page 1 of 12
B. Estimate of Error introduced by EQS approximation
Courtesy of Hermann A. Haus and James R. Melcher. Used with permission.
E =
_
_
i z = E0 i z
V
d
⎪⎧−εE0
σ = ⎨
su
⎪+εE0
⎩
z = d
z = 0
K 2 b π + π b2 dσsu = 0 ⇒ K =... | https://ocw.mit.edu/courses/6-641-electromagnetic-fields-forces-and-motion-spring-2005/47fbb5ff17cb74a5d6a5b9c1eeda9c23_lecture3.pdf |
εµ d E0 (r2 − b2 )
4 dt2
If 0 ( ) = A cos
E t
ωt
Eerror
=
E0
2
εµ d E
2
4E
0 dt
0 (b2 − r2 ) =
1
ω2εµ(b2 − r2 )
4
Eerror (cid:19) 1 ⇒
E0
2ε 2
ω µb
4
(cid:19) 1
fλ = c =
1
εµ
ω
2π
λ = c ⇒ ω =
2ε 2
2 c ω µ b
4
π
λ
⇒
=
2
π
λ2
2
b (cid:19) 1 ⇒ b (cid:19)
λ
π
f=1 MHz in free space ⇒ λ =
×
3 10 8
6 ... | https://ocw.mit.edu/courses/6-641-electromagnetic-fields-forces-and-motion-spring-2005/47fbb5ff17cb74a5d6a5b9c1eeda9c23_lecture3.pdf |
2JL
=
εµL2
τ2
=
L2
)2
cτ
(
(cid:19) 1 ⇒ L (cid:19) cτ
Courtesy of Hermann A. Haus and James R. Melcher. Used with permission.
τem =
L
c
= L εµ
6.641, Electromagnetic Fields, Forces, and Motion
Prof. Markus Zahn
Lecture 3
Page 4 of 12
III. Boundary Conditions
1. Gauss’ Continuity Condition ... | https://ocw.mit.edu/courses/6-641-electromagnetic-fields-forces-and-motion-spring-2005/47fbb5ff17cb74a5d6a5b9c1eeda9c23_lecture3.pdf |
= 0
Han = H
bn
n i ⎡
⎣
H a - H b
= 0
⎤
⎦
i da
∫ ε0E
S
H ds - H at ds = Kds
bt
H - H = K
at
bt
n × ⎡
⎣
H a - H b
= K
⎤
⎦
5. Conservation of Charge Boundary Condition
d
(cid:118)∫ J da +
dt ∫ ρdV = 0
i
V
S
n i ⎡ J a - Jb
⎣
⎤ +
⎦
∂
∂t
σ s = 0
6.641, Electromagnetic Fields, Forces, and Motion
Prof. ... | https://ocw.mit.edu/courses/6-641-electromagnetic-fields-forces-and-motion-spring-2005/47fbb5ff17cb74a5d6a5b9c1eeda9c23_lecture3.pdf |
rL =
S
λ0 L
λ0
E =
r 2πε0r
6.641, Electromagnetic Fields, Forces, and Motion
Prof. Markus Zahn
Lecture 3
Page 8 of 12
b. Electric Field from a Sheet Charge
dE =
y
dλ
2πε0 (x2 + y2 )1
2
cos θ =
σ0ydx
2πε0 (x2 + y2 )
E =
y
+∞
∫
x = −∞
dE
y
=
=
+∞
σ0y
2πε0 ∫ x2 + y2
dx
x = −∞
σ0y 1
2πε0 y
tan−... | https://ocw.mit.edu/courses/6-641-electromagnetic-fields-forces-and-motion-spring-2005/47fbb5ff17cb74a5d6a5b9c1eeda9c23_lecture3.pdf |
⎪ 2ε0
_
⎪ σ0
i y
⎪
⎩2ε0
y > a
y < a
=
E E + E
1
2
=
_
i y
σ0
ε0
0
y < a
y > a
6.641, Electromagnetic Fields, Forces, and Motion
Prof. Markus Zahn
Lecture 3
Page 10 of 12
7. Magnetic Field from a Sheet of Surface Current
From a line current I
Hφ =
I
π2 r
_
i = − sin
φ
_
φ i + cos
x
_
φ i
y
Thus... | https://ocw.mit.edu/courses/6-641-electromagnetic-fields-forces-and-motion-spring-2005/47fbb5ff17cb74a5d6a5b9c1eeda9c23_lecture3.pdf |
. Markus Zahn
Lecture 3
Page 12 of 12 | https://ocw.mit.edu/courses/6-641-electromagnetic-fields-forces-and-motion-spring-2005/47fbb5ff17cb74a5d6a5b9c1eeda9c23_lecture3.pdf |
(13.1)
(13.2)
(13.3)
(13.4)
(13.5)
(13.6)
(13.7)
tS
δ 0eij
0
0
ij d V
(13.8)
(13.9)
MIT 2.094
13. Total Lagrangian formulation, cont’d
tK
0 L =
tK =
0 N L
tF =
0
�
0V
�
0V
�
0V
tBT
0
0 L 0C 0 Ld V
tB
T
tB
0 N L 0
tBN Ld V
0
0
tS
����
matrix
tB tSˆ d V
T
0
0 L 0
����
vector
The iterat... | https://ocw.mit.edu/courses/2-094-finite-element-analysis-of-solids-and-fluids-ii-spring-2011/484bed6dca1e54c56a6b993cdf635560_MIT2_094S11_lec13.pdf |
+
tP
0L
⎢
⎢
⎣
�
0 −1
1
0
1
0
1
0
−1
0
0 −1
��
tK0 N L
0
−1
0
1
⎤
⎥
⎥
⎦
�
When θ = 0, 0
tKL doesn’t give stiffness corresponding to u2
2, but 0
tKN L does.
56
MIT OpenCourseWare
http://ocw.mit.edu
2.094 Finite Element Analysis of Solids and Fluids II
Spring 2011
For information about citing these mat... | https://ocw.mit.edu/courses/2-094-finite-element-analysis-of-solids-and-fluids-ii-spring-2011/484bed6dca1e54c56a6b993cdf635560_MIT2_094S11_lec13.pdf |
15.082J, 6.855J, and ESD.78J
Sept 16, 2010
Lecture 3. Graph Search
Breadth First Search
Depth First Search
Intro to program verification
Topological Sort
Overview
Today: Different ways of searching a graph
a generic approach
breadth first search
depth first search
program verification
data structures to supp... | https://ocw.mit.edu/courses/15-082j-network-optimization-fall-2010/487a2b4c96b8a42c4c3e6372b71b7be6_MIT15_082JF10_lec03.pdf |
is fully scanned
5
Algorithm Search
Initialize as follows:
unmark all nodes in N;
mark node s;
pred(s) = 0; {that is, it has no predecessor}
LIST = {s}
while LIST ≠ ø do
select a node i in LIST;
if node i is incident to an admissible arc (i,j) then
mark node j;
pred(j) := i;
add node j to the end of LIST;
else delet... | https://ocw.mit.edu/courses/15-082j-network-optimization-fall-2010/487a2b4c96b8a42c4c3e6372b71b7be6_MIT15_082JF10_lec03.pdf |
properties that are true throughout the
running of the algorithm
Things that change: functions that increase
monotonically every time the algorithm reenters
the same loop.
12
Algorithm Search
Initialize
loop
while LIST ≠ ø do
select a node i in LIST;
if node i is incident to an admissible arc (i,j) then
mark node... | https://ocw.mit.edu/courses/15-082j-network-optimization-fall-2010/487a2b4c96b8a42c4c3e6372b71b7be6_MIT15_082JF10_lec03.pdf |
terminates when LIST = ∅.
Let S = marked
nodes.
Let T = unmarked
nodes.
S
5
5
s
s
6
6
2
2
4
4
1
3
t
T
By invariant 1, all nodes in S are reachable from s.
By invariant 3, all arcs out of S have been scanned.
Then no arc (i,j) is directed from S to T. Otherwise, by Invariant 2,
j would have been marked when (i, j) wa... | https://ocw.mit.edu/courses/15-082j-network-optimization-fall-2010/487a2b4c96b8a42c4c3e6372b71b7be6_MIT15_082JF10_lec03.pdf |
. Presidents have worn glasses
True
No President (before Obama) has been an only child
True
No President was a bachelor
False. James Buchanan was a bachelor.
George Washington grew marijuana on his Plantation.
True
Mental Break
George Washington’s false teeth were made of wood.
False. They were made of whale bone.
Th... | https://ocw.mit.edu/courses/15-082j-network-optimization-fall-2010/487a2b4c96b8a42c4c3e6372b71b7be6_MIT15_082JF10_lec03.pdf |
) < d(j), then i is marked before j. (Note that
no unmarked node has a distance that is less than
d(4).)
26
Preliminary to Topological Sorting
LEMMA. If each node has at
least one arc going out, then
the first inadmissible arc of
a depth first search
determines a directed cycle.
6
6
2
2
4
5
5
7
7
1
1
8
If G has ... | https://ocw.mit.edu/courses/15-082j-network-optimization-fall-2010/487a2b4c96b8a42c4c3e6372b71b7be6_MIT15_082JF10_lec03.pdf |
If the algorithm ends before labeling all nodes, then
there is a directed cycle in the unmarked nodes.
Every unmarked node has at least one incoming arc, and
so there is a directed cycle.
29
More on Topological Sorting
Runs in O(n+m) time.
Useful starting point for many algorithms that
involve acyclic graphs.
30
... | https://ocw.mit.edu/courses/15-082j-network-optimization-fall-2010/487a2b4c96b8a42c4c3e6372b71b7be6_MIT15_082JF10_lec03.pdf |
Course 18.327 and 1.130
Wavelets and Filter Banks
Modulation and Polyphase
Representations:
Noble Identities;
Block Toeplitz Matrices
and Block z-transforms;
Polyphase Examples
Modulation Matrix
Matrix form of PR conditions:
[F0 (z) F1 (z)] H0(z) H0(-z)
H1(z) H1(-z)
&'(&'(&'(&'(
Modulation matrix, H m(z)
= [ 2z œ... | https://ocw.mit.edu/courses/18-327-wavelets-filter-banks-and-applications-spring-2003/48b610fc0f1cc941fb7d1677d48b7a1f_Handout5.pdf |
H p(z) =
h0[0] h0[1]
h1[0] h1[1]
+ z -1 h0[2] h0[3]
h1[2] h1[3]
=
h0[0] + z -1 h0[2] h0[1] + z -1 h0[3]
h1[0] + z -1 h1[2] h1[1] + z -1 h1[3]
= H0,even (z)
H1,even (z)
H0,odd (z)
H1,odd (z)
This is the polyphase matrix for a 2-channel filter bank.
11
12
6
Similarly, for the synthesis filter bank:
Fb ... | https://ocw.mit.edu/courses/18-327-wavelets-filter-banks-and-applications-spring-2003/48b610fc0f1cc941fb7d1677d48b7a1f_Handout5.pdf |
transpose
convention for
synthesis
polyphase matrix
• Perfect reconstruction condition in polyphase domain:
F p(z) H p(z) = I (centered form)
This means that H p(z) must be invertible for all z on the
unit circle, i.e.
det H p(eiwwww) òòòò 0 for all frequencies wwww.
14
7
• Given that the analysis filters ar... | https://ocw.mit.edu/courses/18-327-wavelets-filter-banks-and-applications-spring-2003/48b610fc0f1cc941fb7d1677d48b7a1f_Handout5.pdf |
0(w + p)|^2 = 2
w + pw + pw + p
www
25
Magnitude Response of Daubechies 4-tap filter.
Ma g nitud e re s po ns e o f Da u be c h ie s 4 -ta p filte r.
2. 5
2
1. 5
1
0. 5
e
s
a
h
p
e
s
n
o
p
s
e
r
y
c
n
e
u
q
e
r
F
0
-1
-0. 8
-0. 6
-0.2
-0.4
0
Ang ula r fre que nc y (no rm a liz e d b y p)
0.2
0.4
0... | https://ocw.mit.edu/courses/18-327-wavelets-filter-banks-and-applications-spring-2003/48b610fc0f1cc941fb7d1677d48b7a1f_Handout5.pdf |
Key Concepts for this section
1: Lorentz force law, Field, Maxwell’s equation
2: Ion Transport, Nernst-Planck equation
3: (Quasi)electrostatics, potential function,
4: Laplace’s equation, Uniqueness
5: Debye layer, electroneutrality
Goals of Part II:
(1) Understand when and why electromagnetic (E and B)
interaction ... | https://ocw.mit.edu/courses/20-330j-fields-forces-and-flows-in-biological-systems-spring-2007/48b63e1bf2248a838f837d85cb37a515_fields_lec5.pdf |
(cid:71)
B
mag
=
(
μ
r
≥
1)
+
(cid:71)
E
∂
t
∂
(cid:71)
Bμ
r
ext
(cid:71)
E
∂
t
∂
(cid:71)
B
∇ × =
(cid:71)
J
μμ μμεε
+
r
0
0
0
r
r
(cid:71)
J
=
μ με
+
μr : relative magnetic permeability of the medium
μο : free space permeability (4π×10-7 H/m)
μ of various media
μr for water : very close to 1
μr (Ni)~600, μr (Fe)~500... | https://ocw.mit.edu/courses/20-330j-fields-forces-and-flows-in-biological-systems-spring-2007/48b63e1bf2248a838f837d85cb37a515_fields_lec5.pdf |
Comparative Number densities and Conductivities
Material
DI water
0.1M NaCl
Copper
Si (intrinsic)
Si (doped)
Nd=1016
Quartz
ni (#/cm3)
~1017
6×1019
~1022
n=p~1010
ne=1016
Np=104
σ (m-1Ω-1)
4 ×10-6
1.07
5.8 ×107
3.36 ×10-4
2.4
10-18
In silicon (semiconductor), n×p~1020 (constant)
In aqueous solutions, [H+][OH-] = 10-14 ... | https://ocw.mit.edu/courses/20-330j-fields-forces-and-flows-in-biological-systems-spring-2007/48b63e1bf2248a838f837d85cb37a515_fields_lec5.pdf |
and mass spec; radioisotope)
Data acquisition
Capillary inlet
Capillary outlet
10 - 200 mm
Detector
+
Reservoir
Electrolyte buffer
Electrolyte buffer
Reservoir
105 V/m
HV
+
Generic diagram of a capillary electrophoresis system.
Figure by MIT OCW.
Micro Total Analysis System (microTAS): Parallelism
• 96~356 samples an... | https://ocw.mit.edu/courses/20-330j-fields-forces-and-flows-in-biological-systems-spring-2007/48b63e1bf2248a838f837d85cb37a515_fields_lec5.pdf |
6.02 Fall 2012
Lecture #16
• DTFT vs DTFS
• Modulation/Demodulation
• Frequency Division Multiplexing
(FDM)
6.02 Fall 2012
Lecture 16 Slide #1
Fast Fourier Transform (FFT) to compute
samples of the DTFT
signals of finite dura
for
tion
For an x[n] that is zero outside of the interval [0,L-1], choose
P ≥ ... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/48f208ee650147f6c3d6f7bcc602cc66_MIT6_02F12_lec16.pdf |
1)1)(cid:5)
6.02 Fall 2012
Lecture 16 Slide #3
Fast Fourier Transform (FFT) to compute
samples of the DTFT
signals of finite dura
for
tion
For an x[n] that is zero outside of the interval [0,L-1], choose
P ≥ L (with P preferably a power of 2; we’ll assume that it’s at
least a multiple of 2, i.e., even):
X(Ω... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/48f208ee650147f6c3d6f7bcc602cc66_MIT6_02F12_lec16.pdf |
k=−P/2
k )e jΩ
kn
• Evaluating this eqn. for n in [0,P-1] recovers the original x[n] in this
interval
• Evaluating it for n outside this interval results in periodic
replication of the values in [0,P-1], producing a periodic signal x[n]
• So this eqn. is also called a DT Fourier Series (DTFS) for the
periodic... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/48f208ee650147f6c3d6f7bcc602cc66_MIT6_02F12_lec16.pdf |
Re(Xk)
(cid:1)Ω
m
+Ω
m
Im(Xk)
Re(Tk)
modulation
(cid:1)Ω
c
+Ω
c
Im(Tk)
demodulation
Signal centered at 0
6.02 Fall 2012
Signal centered at Ω
c
Lecture 16 Slide #7
Modulation by Heterodyning or
Amplitude Modulation (AM)
x[n]
×
t[n]
Re(X )
k
(cid:1)Ω
m
+Ω
m
Im(Xk)
A
B
cos(Ω
cn)
To get this nice ... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/48f208ee650147f6c3d6f7bcc602cc66_MIT6_02F12_lec16.pdf |
the noise-free case y[.] is related to x[.] by
an approximately LTI relationship!)
cn)
cn)
cn)}
• What does the spectrum of d[n], i.e., D(Ω), look like?
• What constraint on the bandwidth of x[n] is needed for perfect
recovery of x[n]?
6.02 Fall 2012
Lecture 16 Slide #10
Demodulation Frequency Diagra m... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/48f208ee650147f6c3d6f7bcc602cc66_MIT6_02F12_lec16.pdf |
3)/2, we are demodulating
by a sine rather than a cosine, and we get y[n]=0 .
6.02 Fall 2012
Lecture 16 Slide #13
Demodulation with sin(Ω
Ωc n)
Re(Tk)
R(Ω)
(cid:1)Ω
c
+Ω
c
Im(Tk)
A/2
B/2
–2Ω
c
D(Ω)
+
+2Ω
c
6.02 Fall 2012
Lecture 16 Slide #14
… produces
Note combining of signals around 0
resul... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/48f208ee650147f6c3d6f7bcc602cc66_MIT6_02F12_lec16.pdf |
channel
LPF
I[n] = x[n-D]·cos(θ)
θ = φ - Ω
cD
LPF
Q[n] = x[n-D]·sin(θ)
×
cos(Ωcn)
×
sin(Ωcn)
6.02 Fall 2012
Lecture 16 Slide #17
Quadrature Demodulation
If we let
w[n] = I[n]+ jQ[n]
then
w[n]
= I[n]2 + Q[n]2
=| x[n − D] | cos2 θ+ sin2 θ
=| x[n − D] |
OK for recovering x[n] if it
never goes negative, ... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/48f208ee650147f6c3d6f7bcc602cc66_MIT6_02F12_lec16.pdf |
+
t[n]
Q
(-1,1)
(1,1)
I
(-1,-1)
(1,-1)
Samples from second bit stream
×
Q[n]
6.02 Fall 2012
Lecture 16 Slide #20
Phase Shift Keying underlies many
familiar modulation schemes
The wireless LAN standard, IEEE 802.11b-1999, uses a variety of different PSKs depending on the data-
rate required. At the basic-ra... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/48f208ee650147f6c3d6f7bcc602cc66_MIT6_02F12_lec16.pdf |
2 will yield a higher
data-rate. A similar technology, IEEE 802.15.4 (the wireless standard used by ZigBee) also relies on PSK.
IEEE 802.15.4 allows the use of two frequency bands: 868–915 MHz using BPSK and at 2.4 GHz using
OQPSK.
http://en.wikipedia.org/wiki/Phase-shift_keying
6.02 Fall 2012
Lecture 16 Slide #2... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/48f208ee650147f6c3d6f7bcc602cc66_MIT6_02F12_lec16.pdf |
CS II: Digital Communication Systems
Fall 2012
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/48f208ee650147f6c3d6f7bcc602cc66_MIT6_02F12_lec16.pdf |
Mechanisms of
Diffusion in
Materials
3.205 L4 11/7/06
1
A final point on interdiffusion…
The composition profiles resulting from inter-
diffusion are generally constrained by phase
equilibria. Consider the an Ir–Re diffusion couple
annealed at 2400°C:
Equilibrium diagram
Diffusion couple
3.205 L4 11/7/06
2... | https://ocw.mit.edu/courses/3-205-thermodynamics-and-kinetics-of-materials-fall-2006/48fa40fa1298230d445991e2325d132d_lecture04_slides.pdf |
Atomistic mechanisms, cont’d
Additional mechanisms include the interstitialcy
mechanism in crystals containing significant
numbers of self-interstitials (e.g., produced by
irradiation); and the reptation mechanism in
molten (hence non-crystalline) polymers.
Interstialcy
Reptation
3.205 L4 11/7/06
6
Atomistic... | https://ocw.mit.edu/courses/3-205-thermodynamics-and-kinetics-of-materials-fall-2006/48fa40fa1298230d445991e2325d132d_lecture04_slides.pdf |
! R2=nr2! D="r26 Diffusion & random walks, cont’d
Diffusion in alloys: intrinsic diffusivity and
interdiffusivity
These can involve correlated jumps and the
resulting value of the mean square displacement
can be either greater than, or less than, that for
self-diffusion. The correlation factor, f, accounts
for ... | https://ocw.mit.edu/courses/3-205-thermodynamics-and-kinetics-of-materials-fall-2006/48fa40fa1298230d445991e2325d132d_lecture04_slides.pdf |
fkT()[]=expSVfk[]exp"HVfkT()[] Self-diffusion of solute atoms
via vacancy mechanism, cont’d
Using equations for D and
The correlation factor, f, for vacancy diffusion in
metals is about 0.7 and can be calculated more
precisely for various specific cases.
3.205 L4 11/7/06
14
! DA=Xvz"vr26f=zr2#6exp$GVf+GVm()kT()... | https://ocw.mit.edu/courses/3-205-thermodynamics-and-kinetics-of-materials-fall-2006/48fa40fa1298230d445991e2325d132d_lecture04_slides.pdf |
6.02 Fall 2012
Lecture #10
• Linear time-invariant (LTI) models
• Convolution
6.02 Fall 2012
Lecture 10, Slide #1
Modeling Channel Behavior
codeword
bits in
1001110101
x[n]
generate
digitized
symbols
modulate
DAC
NOISY & DISTORTING ANALOG CHANNEL
ADC
demodulate
& filter
sample &
threshold
y[n]
1... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/49242956b17f47b9c85bd6784aa5d6b8_MIT6_02F12_lec10.pdf |
]
6.02 Fall 2012
Lecture 10, Slide #4
Linear Systems
Let y1[n] be the response of S to an arbitrary input x1[n]
and y2[n] be the response to an arbitrary x2[n].
If, for arbitrary scalar coefficients a and b, we have:
ax1[n]+ bx2[n]
S
ay1[n]+ by2[n]
then system S is said to be linear. If the input... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/49242956b17f47b9c85bd6784aa5d6b8_MIT6_02F12_lec10.pdf |
Fall 2012
h[n] s[n]
6.02 Fall 2012
Lecture 10, Slide #8
h[n] s[n]
6.02 Fall 2012
Lecture 10, Slide #9
h[n] s[n]
6.02 Fall 2012
Lecture 10, Slide #10
Unit Step Decomposition
“
“Rectangular-wave” digital
signaling waveforms, of the sort
s
we have been considering, are
w
easily decomposed into time-
... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/49242956b17f47b9c85bd6784aa5d6b8_MIT6_02F12_lec10.pdf |
5V
6.02 Fall 2012
Lecture 10, Slide #15
Faster Tr
ansmission
Fall 2012
6.02 Fall 2012
Noise m
Noise margin? 0.5 (cid:1) y[28]
Lecture 10, Slid
Lecture 10, Slide #16
Unit Sample
Decomposition
A discrete-time signal can be decomposed
into a sum of time-shifted, scaled unit
samples.
Example: in the figur... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/49242956b17f47b9c85bd6784aa5d6b8_MIT6_02F12_lec10.pdf |
the output signal y in terms of the input x and
unit-sample response h. Some constraints are needed to ensure
this infinite sum is well behaved, i.e., doesn’t “blow up” --- we’ll
discuss this later.
∗
We use to denote convolution, and write y=x h. We can then
write the value of y at time n, which is given by the a... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/49242956b17f47b9c85bd6784aa5d6b8_MIT6_02F12_lec10.pdf |
= h ∗ x
Convolution is associative:
x ∗ (h1
(
∗ h2 ) = x ∗ h1
)
∗ h2
Convolution is distributive:
(
x ∗ h1
+ h2
)
= (x ∗
h1) + (x ∗ h2 )
6.02 Fall 2012
Lecture 10, Slide #21
Series Interconnection of LT
I Systems
x[n]
h2[.]
y[n]
y = h2
∗ w = h2
∗ x
(
) = h2
∗ h1
) ∗ x
w[n]
h1[.]
(
∗ h1
x[n]
x[n] ... | https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/49242956b17f47b9c85bd6784aa5d6b8_MIT6_02F12_lec10.pdf |
Suspensions and suspension
mechanics
1
Suspensions may be distinguished by
the shape and size of the discrete phase
Debye Length
in 1mM NaCl
Visible Light
micro-CT
resolution
(Optical limit)
gap in PP rheometer
10-10
10-9
10-8
10-7
10-6
10-5
gap in CP rheometer
10-3
10-4
10-2
[m]
Au nanoparticle
Colloidal
silica
... | https://ocw.mit.edu/courses/2-341j-macromolecular-hydrodynamics-spring-2016/4940640c8f594be8046e044b571e02c6_MIT2_341JS16_Lec23-slides.pdf |
�0.313dD0.138dD The Farris effect
Contours: volume fraction
5:1 ratio in particle size
What are the paths
PS and PQ?
© source unknown. All rights reserved. This content is excluded from our Creative
Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use/.
<0.75
6
Particle shape is also i... | https://ocw.mit.edu/courses/2-341j-macromolecular-hydrodynamics-spring-2016/4940640c8f594be8046e044b571e02c6_MIT2_341JS16_Lec23-slides.pdf |
9
Despite this scaling, we still see a
shear rate dependence at large Pe#
Remarks:
1. This is a non-colloidal
suspension of spheres
2. Brownian diffusion is weak.
3.
4. How did we construct the
Shear thinning is observed (?)
earlier viscosity curves with
no rate dependence?
5. Glass particles in a
Newtonian matrix
© ... | https://ocw.mit.edu/courses/2-341j-macromolecular-hydrodynamics-spring-2016/4940640c8f594be8046e044b571e02c6_MIT2_341JS16_Lec23-slides.pdf |
capture problem,
dependence on Pe
Morris, J. F. “A review of microstructure in concentrated suspensions and its implications
for rheology and bulk flow” (2009) 48:909-923
14
© Springer. All rights reserved. This content is excludedfrom our Creative Commons
license. For more information, see https://ocw.mit.edu/help/fa... | https://ocw.mit.edu/courses/2-341j-macromolecular-hydrodynamics-spring-2016/4940640c8f594be8046e044b571e02c6_MIT2_341JS16_Lec23-slides.pdf |
0, φ = .45
Pe = 25, φ = .3
Color indicates density of particle centers
• At low Pe, randomized
• At higher Pe, induced structure from flow
Increased particle density
along shoulders of particles,
attempting to align in rows
Morris, J. F. “A review of microstructure in concentrated suspensions and its implications
fo... | https://ocw.mit.edu/courses/2-341j-macromolecular-hydrodynamics-spring-2016/4940640c8f594be8046e044b571e02c6_MIT2_341JS16_Lec23-slides.pdf |
All rights reserved. This content is excluded from our Creative
Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use/.
23
Laun, H. M. Angew. Makro. Chem. 1984, 124:335-359
Mechanisms for non-Newtonian
suspension behavior
y
t
i
s
o
c
s
i
V
Shear rate or stress
Newtonian plateau
Structure no... | https://ocw.mit.edu/courses/2-341j-macromolecular-hydrodynamics-spring-2016/4940640c8f594be8046e044b571e02c6_MIT2_341JS16_Lec23-slides.pdf |
” JoR (2006) 50:293-311
Experiments,
Brownian
26
Experimental agreement?
Experiments, non-Brownian
© AIP Publishing LLC. All rights reserved. This content is excludedfrom our Creative
Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use/.
Gamonpilas, C., Morris, J. F., Denn, M. M. “Shear a... | https://ocw.mit.edu/courses/2-341j-macromolecular-hydrodynamics-spring-2016/4940640c8f594be8046e044b571e02c6_MIT2_341JS16_Lec23-slides.pdf |
8.871 Lecture 2
M. Padi
October 20, 2004
1
Electrically and Magnetically Charged Branes
We would like to build a general understanding of branes, the gauge fields to which they are coupled, and
the gauge fields living on their world volume. First, we review electromagnetism in four dimensions. Define
F (2) = dA(1) ... | https://ocw.mit.edu/courses/8-871-selected-topics-in-theoretical-particle-physics-branes-and-gauge-theory-dynamics-fall-2004/4944d4a313d2399badde634815961996_lec2.pdf |
an arbitrary 1-form, H (3) is invariant. An F1-string, which propagates in 9+1 dimensions, is electrically
charged under B(2), with a charge Q. We therefore write a source equation d � H (3)
. The string is
localized in 8 of the 9 space coordinates and hence we have a delta function in 8 directions. On the other
ha... | https://ocw.mit.edu/courses/8-871-selected-topics-in-theoretical-particle-physics-branes-and-gauge-theory-dynamics-fall-2004/4944d4a313d2399badde634815961996_lec2.pdf |
11d SUGRA is the low energy effective theory of M-theory. Applying the ideas outlined above we find
that in M-theory, we should have an M2-brane which is electrically charged under C (3) and an M5-brane
which is magnetically charged under C (3). Similarly, we can find the branes which are charged under massless
gauge fi... | https://ocw.mit.edu/courses/8-871-selected-topics-in-theoretical-particle-physics-branes-and-gauge-theory-dynamics-fall-2004/4944d4a313d2399badde634815961996_lec2.pdf |
µ and � can be
anything except 10. That leaves us with a 2-form in 9+1 dimensions which we call B (2). We can also have
�, µ, � ⊗= 10 (but constrained to be antisymmetric). Then we end up with a 3-form in 9+1 dimensions. The
3-form has 8 = 56 components and the 2-form has 2 = 28 components. We can check this decompo... | https://ocw.mit.edu/courses/8-871-selected-topics-in-theoretical-particle-physics-branes-and-gauge-theory-dynamics-fall-2004/4944d4a313d2399badde634815961996_lec2.pdf |
) there is a triality that acts on the 8 dimensional
and the 56 dimensional representations and we therefore have three different representations of the same
dimension which we distinguish by these subscripts.
We now look at the bosonic massless fields to determine the kinds of branes that can exist in Type
IIA theor... | https://ocw.mit.edu/courses/8-871-selected-topics-in-theoretical-particle-physics-branes-and-gauge-theory-dynamics-fall-2004/4944d4a313d2399badde634815961996_lec2.pdf |
M10 × S1 is S-dual to Type IIA theory on M10, where Mj is an arbitrary j-dimensional manifold. When
the M2-brane wraps one of its own dimensions on the S 1, it is dual to an F1 string in Type IIA. If instead we
use dimensional reduction on M-theory, the M2-brane will reduce to a D2-brane. Similarly, if the M5-brane
... | https://ocw.mit.edu/courses/8-871-selected-topics-in-theoretical-particle-physics-branes-and-gauge-theory-dynamics-fall-2004/4944d4a313d2399badde634815961996_lec2.pdf |
coupled to B(2)). Similarly, in heterotic theories, we have an F1-string and NS5-brane. In
addition to these objects we also have small instantons which are branes that are present in any theory that
has non-abelian massless gauge fields. An instanton is an object which is localized in 4 space coordinates
and therefo... | https://ocw.mit.edu/courses/8-871-selected-topics-in-theoretical-particle-physics-branes-and-gauge-theory-dynamics-fall-2004/4944d4a313d2399badde634815961996_lec2.pdf |
8
+
�
�
2
Note that 528 = 32·33 , because the LHS of (8) is a symmetric 32 × 32 matrix. The 5-form on the RHS
corresponds to the charge of the M5-brane. The 2-form corresponds to the M2-brane. To get this result,
we could also decompose (32 � 32)sym, the symmetrized tensor product of spinor representations of SO(11... | https://ocw.mit.edu/courses/8-871-selected-topics-in-theoretical-particle-physics-branes-and-gauge-theory-dynamics-fall-2004/4944d4a313d2399badde634815961996_lec2.pdf |
of the charge on the brane.
3 | https://ocw.mit.edu/courses/8-871-selected-topics-in-theoretical-particle-physics-branes-and-gauge-theory-dynamics-fall-2004/4944d4a313d2399badde634815961996_lec2.pdf |
15.081J/6.251J Introduction to Mathematical
Programming
Lecture 8: Duality Theory I
Slide 1
Slide 2
1 Outline
• Motivation of duality
• General form of the dual
• Weak and strong duality
• Relations between primal and dual
• Economic Interpretation
• Complementary Slackness
2 Motivation
2.1 An idea from L... | https://ocw.mit.edu/courses/6-251j-introduction-to-mathematical-programming-fall-2009/496d9a385fd1d7e1aa82837d91adb23e_MIT6_251JF09_lec08.pdf |
Ax ≥ b
max p ′ b
s.t. p ′ A ≤ c ′
′ b
max p
s.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 ... | https://ocw.mit.edu/courses/6-251j-introduction-to-mathematical-programming-fall-2009/496d9a385fd1d7e1aa82837d91adb23e_MIT6_251JF09_lec08.pdf |
p2a2
p1a1
a2
.
x *
3
Slide 11
Slide 12
Slide 13
Slide 14
6 Relations 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... | https://ocw.mit.edu/courses/6-251j-introduction-to-mathematical-programming-fall-2009/496d9a385fd1d7e1aa82837d91adb23e_MIT6_251JF09_lec08.pdf |
strong duality theorem, if x and p are optimal, then c x = p ′ b ⇒
ui = vj = 0 for all i, j.
′
• Conversely, if ui = vj = 0 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
,
... | 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 |
⎜
= 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
Free electron dispersions, 1-d
3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)... | https://ocw.mit.edu/courses/3-23-electrical-optical-and-magnetic-properties-of-materials-fall-2007/49728ee6fbac8503c94b5a9aab74242c_lec9.pdf |
⎟ C
C
⎛
⎛
⎟
⎟
⎜
⎟ C
⎜
−
q G
⎟
⎜
C
⎟
⎜
⎟ C
⎜
⎟
⎜
C
⎟⎝
⎟
⎟
⎟
⎠
q G+
q
+
2
q G
⎞
⎞
⎟
⎟
⎟ = E
⎟
⎟
⎟
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C
⎛
⎛
−
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G
2
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C
⎜
−
q G
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+
2
q G
+
q G
q
⎞
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)
Band Edge
3.23 Electronic, Optical... | https://ocw.mit.edu/courses/3-23-electrical-optical-and-magnetic-properties-of-materials-fall-2007/49728ee6fbac8503c94b5a9aab74242c_lec9.pdf |
1
3
2'
5
2
3
1
A
1
2'
3
A
3
Q+
Q_
Q+
Q_
3
A
3
Q+
1
A
1
S
3
S
S
1
S
4 S
2 K2
K4
K3
K1
K1
1
X
W
L
G K
Figure by MIT OpenCourseWare.
9
The Fermi surface
3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)
Images from the Fermi Surface Database. Used with permission.
Please se... | 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 |
the SolidWorks model of the sheller can be found at the
end of this handout. The 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 ... | https://ocw.mit.edu/courses/ec-720j-d-lab-ii-design-spring-2010/4974d72f6e55f3b812da88af46058e3a_MITEC_720JS10_bldit_cncst.pdf |
,
Mechatronics Lab, AMP Lab.
MIT computer cluster.
Starting Solidworks
Open Solidworks 2007 SP5.0 by going to:
Start > All Documents > Solidworks 2007 SP5.0 > 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... | https://ocw.mit.edu/courses/ec-720j-d-lab-ii-design-spring-2010/4974d72f6e55f3b812da88af46058e3a_MITEC_720JS10_bldit_cncst.pdf |
.
- Choose the axis you just drew to be the center of rotation and rotate 360
degrees
Draw the cross section of the fin
In a new Sketch on the Front Plane, make the cross section of the fin.
Trace the profile of the sheller body with lines. Add a Relation to make the
lines parallel slanting. Smart Dimension the in... | https://ocw.mit.edu/courses/ec-720j-d-lab-ii-design-spring-2010/4974d72f6e55f3b812da88af46058e3a_MITEC_720JS10_bldit_cncst.pdf |
Please use the following citation format:
D-Lab Cast Corn Sheller Build-It Copyright © Massachusetts Institute
of Technology (Accessed on [insert date]).
8
88
8
MIT OpenCourseWare
http://ocw.mit.edu
EC.720J / 2.722J D-Lab II: Design
Spring 2010
For information about citing these materials or our Terms of Use, visit... | 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 |
odic et al. 2009
Dechter, Meiri, Pearl 1991
Chaski
(Shah, Conrad, Williams 2009)
Drake
(Conrad, Shah, and Williams 2009)
Chien 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
Hof... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
human-robot teams
• Given a plan with choice (contingent, temporally flexible):
• Make decisions online (consistent with human’s intent)
• Dispatch activities at proper times
• Monitor execution for problems
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide 6
How to recognize intent... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
ent, temporally-flexible plans
Temporal Planning Network with Uncertainty (TPNU)
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide
12
First part: making a drink
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide
13
Extracting labeled causal lin... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
)(cid:8)(cid:9)
(cid:10)(cid:11)(cid:6)(cid:12)(cid:13)(cid:7)(cid:6)(cid:14)(cid:15)
(cid:16)(cid:17)(cid:6)(cid:12)(cid:18)(cid:12)(cid:6)(cid:19)
(cid:20)(cid:12)(cid:11)(cid:21)(cid:7)(cid:6)(cid:17)(cid:22)(cid:8)(cid:15)
(cid:27)(cid:31)(cid:7)(cid:25)(cid:6)
(cid:3)
(cid:4)
(cid:2)
• Activity Recognizer: observe... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
Execution for Human-Robot Teams | Steven J. Levine
Slide
25
Causal link extraction in a nutshell*
• For each precondition of each consumer event:
• Find all producers provably before or during consumer
[0, ∞]
[0, ∞]
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide
26
Causal lin... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
1)
∨
(ac = c2 ∧ y = 1)
∨
(ac = c3)
(cid:5)
p : {ac = c1}
p : {ac = c2 ∧ y = 1}
p : {ac = c3}
[0, ∞] : {ac = c3}
[0, ∞]
[0, ∞]
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide
30
Causal link extraction in a nutshell*
• For each precondition of each consumer event:
• Find all produc... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
1)
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide 34
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 producer
• Find all potential th... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
: {ac = c2 ∧ y = 1}
[0, ∞] :{b = 1 ∧ z = 1 ∧ ac = c2 ∧ y = 1 ∧ x = 2}
[0, ∞]
[0, ∞]
Concurrent Plan Recognition & Execution for Human-Robot Teams | Steven J. Levine
Slide
38
Causal link extraction in a nutshell*
• For each precondition of each consumer event:
• Find all producers provably before or during consumer
•... | https://ocw.mit.edu/courses/16-412j-cognitive-robotics-spring-2016/497c66f8f0334208d69fc5a29ff2a956_MIT16_412JS16_L13.pdf |
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