Split (1)

train · 100k rows

text stringlengths 30 4k	source stringlengths 60 201
specifications and utility functions and try to map from classes of environments to structures of programs. To try to say that "if you need an agent to try to solve this class of problem in that kind of environment, then here is a good way to structure the computation." 27 Thinking • Is all this off-line work AI?...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
at all or if you live for very long, the table is way too big. Way, way too big. There are too many ways the world could be, there are too many sequences of percepts that you could have of the world. There is no way that you could, off-line, anticipate them. 30 Thinking • Is all this off-line work AI? Aren’t t...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
that would do the job of being the table. But there are other domains in which you quite clearly can't do that and those are the domains that we are going to focus on. 31 Thinking • Is all this off-line work AI? Aren’t the agents supposed to think? • Why is it ever useful to think? If you can be endowed with a...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
in and you'd start figuring out what to do about it. So, you could respond very flexibly to a very broad range of stimuli but there's no way that you could have stored your responses to them. 32 Learning • What if you don’t know much about the environment when you start or if the environment changes? • Learn!...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
coefficient of friction of the dust on the Martian surface. • I know a lot about the world dynamics but I have to leave a free parameter representing this coefficient of friction. • Part of the agent’s job is to use sequences of percepts to estimate the missing details in the world dynamics. Lecture 1 • 34 Inste...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
we tend to call perception, things like noticing where I am with respect to a wall; things that are on a shorter time scale; things that don't seem so built-in. But there is no hard and fast distinction between learning and perceiving. 35 Classes of Environments Lecture 1 • 36 Let's think about environments and ...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
world and the action that an agent takes, into another state of the world. In some domains that's usefully thought of as being deterministic. The only domains that are really deterministic are artificial ones, like games. Even clicking on a link and going to a Web page, you know that doesn't always work. Most thing...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
continuous (like reals)? Lecture 1 • 40 And then there's "discrete" versus "continuous". This is not really an intrinsic property of the environment, but more a property of how we choose to model the environment. So, you can think of your perceptions of the world or your actions as being discrete or continuous. 4...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
– – Motor voltages of the robot arm moving the stones? Change the (x,y) location of stones? Change which point a stone is on? [“Logical” actions] Lecture 1 • 42 For an agent playing backgammon, what's the action space? The action space is the set of backgammon moves, such as putting a piece on point number 7. I...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
that backgammon books take. Which is, the moves are putting the stones on points, and the percepts are where (again at a logical level) the stones are. 43 Backgammon Environment • Accessible? • Yes! Backgammon is one of those few domains that is accessible; you can see everything there is to know about the sta...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
! • Deterministic? • No! Two sources of non-determinism: the dice and the opponent • Static? • Yes! (unless you have a time limit) • Discrete? • Yes! (if using logical actions and percepts) • No! (e.g. if using (x,y) positions for actions and percepts) • Images are discrete but so big and finely sampled tha...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
a single percept to an action and so it has no memory. So, reactive agents have no memory. Remember that we've said that, in general, an agent maps strings of percepts into actions, allowing it to integrate information over time. 49 Structures of Agents • Reflex (“reactive”) agent • No memory p a • What can...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
finite state machine and decompose it like this. 51 Structures of Agents • Agent with memory p State Estim ator Mental state a Policy • State estimator/Memory • What we’ve chosen to remember from the history of percepts • Maps what you knew before, what you just perceived and what you just did, into ...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
an accurate gas gauge, does this problem require memory? No. Your choice of actions depend not just on what's going on right now but what's going to happen in the future. Whether you stop now or not depends on what future events (like running out of gas, or running out of money) might be caused by your choice of ac...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
way to organize a computation for choosing an action to take next. It’s particularly appropriate when there are a lot of different possible states you could find yourself in, too many to plan for in advance, and when you are not under so much time pressure that you must have an immediate reaction. 55 Planning Age...	https://ocw.mit.edu/courses/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/37cc451f7925405c3cf9274863d488ba_Lecture1Final.pdf
Type Inference and the Hindley-Milner Type System Armando Solar-Lezama Computer Science and Artificial Intelligence Laboratory M.I.T. With slides from Arvind. Used with permission. September 29, 2011 September 29, 2011 L07-1 Type Inference • Consider the following expression – (𝜆f:int int. f 5) (𝜆x:int. ...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
0 -> t0) -> t0 -> t0 September 8, 2011 L06-5 The language of Equality Constraints • Consider the following Language of Constraints • Constraints in this language have a lot of good properties – Nice and compositional – Linear time solution algorithm L06-6 Building Constraints from Typing Rules...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
06-9 Simple Type Substitutions needed to define type unification Types  ::=  \| t \|  ->  base types (Int, Bool ..) type variables Function types A substitution is a map S : Type Variables  Types S = [1 / t1,..., n / tn] ’ is a Substitution Instance of  ’ = S  Example: S =...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
fail (11->12, 21 ->22) = let S1=Unify(11, 21) S2=Unify(S1(12), S1(22)) in S2 S1 otherwise = fail Does the order matter? No September 27, 2011 L06-11 Type inference strategy 2 • Like strategy 1, but we solve the constraints as we see them – Build the substitution map incrementally...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
let (S1, 1) = W(TE, e1); (S2, 2) = W(S1(TE), e2); S3 = Unify(S2(1), 2 -> u); in (S3 S2 S1, S3(u)) September 27, 2011 L06-14 Simple Inference Algorithm (cont-1) Def W(TE, e) = Case e of c x = = x.e = (e1 e2) = ({}, Typeof(c)) if (x  Dom(TE)) then Fail else let  = TE(x);...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
(TE, e) = Case e of … x.e = let (S1, 1) = W(TE + { x : u }, e) in (S1, S1(u) -> 1) (e1 e2) = let (S1, 1) = W(TE, e1); (S2, 2) = W(S1(TE), e2); S3 = Unify(S2(1), 2 -> u); in (S3 S2 S1, S3(u)) 𝑊 𝑓: 𝑢0 , 𝑓 = (∅, 𝑢0) 𝑊 𝑓: 𝑢0 , 5 = (∅, 𝐼𝑛𝑡) 𝑈𝑛𝑖𝑓𝑦 𝑢0, 𝐼𝑛𝑡 → 𝑢1 = 𝑊 𝑓: 𝑢0 , 𝑓 ...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
1, 21) S2=Unify(S1(12), S1(22)) in S2 S1 𝑊 𝑓: 𝑢0 , 𝑓 = (∅, 𝑢0) 𝑊 𝑓: 𝑢0 , 5 = (∅, 𝐼𝑛𝑡) 𝑈𝑛𝑖𝑓𝑦 𝑢0, 𝐼𝑛𝑡 → 𝑢1 = [(𝐼𝑛𝑡 → 𝑢1) 𝑢0 ] 𝑊 𝑓: 𝑢0 , 𝑓 5 = 𝑊 ∅, 𝜆𝑓. 𝑓 5 = 𝑊(∅, 𝜆𝑓. 𝑓 5 𝜆𝑥. 𝑥 ) Example Def W(TE, e) = Case e of … x.e = let (S1, 1) = W(TE + { x : u }, ...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
], 𝑢1) 𝑊 ∅, 𝜆𝑓. 𝑓 5 = ( (𝐼𝑛𝑡 → 𝑢1) 𝑢0 , 𝐼𝑛𝑡 → 𝑢1 → 𝑢1) 𝑊(∅, 𝜆𝑓. 𝑓 5 𝜆𝑥. 𝑥 ) Example Def W(TE, e) = Case e of … x.e = let (S1, 1) = W(TE + { x : u }, e) in (S1, S1(u) -> 1) (e1 e2) = let (S1, 1) = W(TE, e1); (S2, 2) = W(S1(TE), e2); S3 = Unify(S2(1), 2 -> u); in (S3 S...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
2) = [2 / t1] provided t1  FV(2) (1, 2) = if (eq? 1 2) then [ ] else fail (11->12, 21 ->22) = let S1=Unify(11, 21) S2=Unify(S1(12), S1(22)) in S2 S1 𝑈𝑛𝑖𝑓𝑦 𝐼𝑛𝑡 → 𝑢1 , 𝑢3 → 𝑢3 = 𝐼𝑛𝑡 𝑢3 ; 𝐼𝑛𝑡 𝑢1 𝑈𝑛𝑖𝑓𝑦 𝐼𝑛𝑡, 𝑢4 = [𝐼𝑛𝑡 𝑢4 ] 𝑈𝑛𝑖𝑓𝑦 𝐼𝑛𝑡 → 𝑢1 → 𝑢1, 𝑢3 → 𝑢3...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
3 S2 S1, S3(u)) 𝑊 ∅, 𝜆𝑓. 𝑓 5 = ( (𝐼𝑛𝑡 → 𝑢1) 𝑢0 , 𝐼𝑛𝑡 → 𝑢1 → 𝑢1) 𝑊 ∅, 𝜆𝑥. 𝑥 = (∅, 𝑢3 → 𝑢3) 𝑈𝑛𝑖𝑓𝑦 𝐼𝑛𝑡 → 𝑢1 → 𝑢1, 𝑢3 → 𝑢3 → 𝑢4 = 𝐼𝑛𝑡 𝑢3 ; 𝐼𝑛𝑡 𝑢1 ; 𝐼𝑛𝑡/𝑢4 𝑊 ∅, 𝜆𝑓. 𝑓 5 𝜆𝑥. 𝑥 = ( (𝐼𝑛𝑡 → 𝑢1) 𝑢0 ; 𝐼𝑛𝑡 𝑢3 ; 𝐼𝑛𝑡 𝑢1 ; 𝐼𝑛𝑡/𝑢4 , 𝐼𝑛𝑡) What about...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
Unify(S1(u), 1); (S3, 2) = W(S2 S1(TE) + {x : }, e2); in (S3 S2 S1, 2) September 29, 2011 L06-22 Polymorphism September 27, 2011 L06-23 Some observations • A type system restricts the class of programs that are considered “legal” • It is possible a term in the untyped – calculus may be redu...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
::= 𝑏 𝜏1 → 𝜏2 𝑇 \| ∀𝑇. 𝜏 e ::= 𝑥 𝜆𝑥: 𝜏. 𝑒 𝑒1𝑒2 ΛT. e e[𝜏] • Very powerful – Although you still can’t express recursion • Type inference is undecidable ! L06-26 Different Styles of Polymorphism • Predicative Polymorphism 𝜏 ::= 𝑏 𝜏1 → 𝜏2 𝑇 𝜎 ∷= 𝜏 ∀𝑇. 𝜎 𝜎1 → 𝜎2 e ::= 𝑥 𝜆𝑥: �...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
2 𝑒1 – Except x can be polymorphic • Good engineering compromise – Enhance expressiveness – Preserve decidability • This is the Hindley Milner type system September 29, 2011 L06-29 Type inference with polymorphism September 27, 2011 L06-30 Polymorphic Types let id = x. x in Constraints: ...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
 cannot contain a type scheme  September 29, 2011 L06-33 Instantiations  = t1...tn.  • Type scheme  can be instantiated into a type ’ by substituting types for the bound variables of , i.e., ’ = S  for some S s.t. Dom(S)  BV() - ’ is said to be an instance of  ( > ’) - ’ is s...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
� ∈Γ 𝜎≥𝜏 Γ⊢𝑥:𝜏 𝑡𝑦𝑝𝑒𝑜𝑓(𝑐)≥𝜏 Γ⊢𝑐:𝜏 𝑥 can be considered of type 𝜏 as long as its type as specified in the environment can be specialized to 𝜏 (i.e. 𝜏 is an instance of 𝜎) Note: x has a different type in 𝑒1 than in 𝑒2. In 𝑒1, x is not a polymorphic type, but in 𝑒2 it gets generalized into one....	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
let (S1, 1) = W(TE + {x : u}, e1); S2 = Unify(S1(u), 1);  = Gen(S2 S1(TE), S2(1) ); (S3, 2) = W(S2 S1(TE) + {x : }, e2); in (S3 S2 S1, 2) September 29, 2011 L06-37 Hindley-Milner: Example x. let f = y.x B in (f 1, f True) A W(, A) = ( [ ] , u1 -> (u1,u1) ) W({x : u1}, B) ...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
-38 Important Observations • Do not generalize over type variables used elsewhere • Let is the only way of defining polymorphic constructs • Generalize the types of let-bound identifiers only after processing their definitions September 29, 2011 L06-39 Properties of HM Type Inference • It is sound wit...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
��)  TE TE ├ x :  TE+{x:} ├ e1:  TE+{x:} ├ e2:’ TE ├ (let x = e1 in e2) : ’ (App) and (Abs) rules remain unchanged. Sound but no inference algorithm ! September 29, 2011 L06-43 MIT OpenCourseWare http://ocw.mit.edu 6.820 Fundamentals of Program Analysis Fall 2015 For ...	https://ocw.mit.edu/courses/6-820-fundamentals-of-program-analysis-fall-2015/3805b29885701911f983fc8299f9d9ac_MIT6_820F15_L07.pdf
Vectors Our very ﬁrst topic is unusual in that we will start with a brief written presentation. More typically we will begin each topic with a videotaped lecture by Professor Auroux and follow that with a brief written presentation. As we pointed out in the introduction, vectors will be used throughout the course....	https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/38223d6ec70b12de9d01446438100b9d_MIT18_02SC_notes_0.pdf
by placing them head to tail. As the ﬁgure shows, this can be done in 11� either order B / / / / / A/ / / / / / / A + B / / / / / / / A / / / / / B It is often useful to think of vectors as displacements. In this way, A + B can be thought of as the displacement A followed by the displ...	https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/38223d6ec70b12de9d01446438100b9d_MIT18_02SC_notes_0.pdf
j i Notation and terminology 1. (a1, a2) indicates a point in the plane. 2. (a1, a2) = a1i + a2j. This is equal to the vector drawn from the origin to the point (a1, a2). 3. For A = a1i + a2j, a1 and a2 are called the i and j components of A. (Note that they are scalars.) −→ −−→ 5. P = OP is the vector from the ...	https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/38223d6ec70b12de9d01446438100b9d_MIT18_02SC_notes_0.pdf
// a2 A + B // / // / / / A// // / / / / / / // / / / / a1 + b1 a2 + b2 a2 a1 A B b1 a2 − b2 A − B a1 − b1 b2 − − −−→ → → For two points P and Q the vector PQ = Q − P i.e., PQ is the displacement from P to Q. −−→ y y O •Q = (q1, q2) −−→ PQ •P = (p1, p1) Q P x Vectors in three dimensions We represent a...	https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/38223d6ec70b12de9d01446438100b9d_MIT18_02SC_notes_0.pdf
:105), k = (cid:104)0, 0, 1(cid:105). Using them Then, for A = (cid:104)a1, a2, a3(cid:105) and B = (cid:104)b1, b2, b3(cid:105) we have (cid:104)a1, a2, a3(cid:105) = a1i + a2j + a3k. (cid:104)a1, a2, a3(cid:105) + (cid:104)b1, b2, b3(cid:105) = (cid:104)a1 + b1, a2 + b2, a3 + b3(cid:105). exactly as in the two dimens...	https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/38223d6ec70b12de9d01446438100b9d_MIT18_02SC_notes_0.pdf
(a1, a2, a3) a3 a1 y (cid:116)(cid:116)(cid:116)(cid:116)(cid:116)(cid:116)(cid:116)(cid:116)(cid:116)(cid:116) a 2 (cid:116) x Unit vectors A unit vector is any vector with unit length. When we want to indicate that a vector is a unit vector we put a hat (circumﬂex) above it, e.g., u. (cid:98) The special vectors i, j...	https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/38223d6ec70b12de9d01446438100b9d_MIT18_02SC_notes_0.pdf
6.837 Computer Graphics Curve Properties & Conversion, Surface Representations vectorportal.com 6.837 – Matusik 1 Cubic Bezier Splines • P(t) = (1-t)³ P1 + 3t(1-t)² P2 + 3t²(1-t) P3 + P4 t³ 2 Bernstein Polynomials • For Bézier curves, the basis polynomials/vectors are Bernstein polynomia...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
– Tensor Product Splines – Subdivision Surfaces – Procedural Surfaces – Other 10Differential Properties of Curves • Motivation – Compute normal for surfaces – Compute velocity for animation – Analyze smoothness Image courtesy of Kristian Molhave on Wikimedia Commons. License: CC- BY-SA. This content is exclud...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
t)/\|\|P’(t)\|\| – normalized velocity, \|\|T(t)\|\| = 1 • This provides us with one orientation for swept surfaces later Courtesy of Seth Teller. 15Curvature Vector • Derivative of unit tangent – K(t)=T’(t) – Magnitude \|\|K(t)\|\| is constant for a circle – Zero for a straight line • Always orthogonal to tangent, ie. ...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
subcurves? 23Questions? 24Cubic B-Splines • ≥ 4 control points • Locally cubic – Cubics chained together, again. Courtesy of Seth Teller. 25 Cubic B-Splines • ≥ 4 control points • Locally cubic – Cubics chained together, again. Courtesy of Seth Teller. 26 Cubic B-Splines • ≥ 4 control points • Locally...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
other! 35Converting between Bézier & BSpline • Simple with the basis matrices! – Note that this only works for a single segment of 4 control points • P(t) = G B1 T(t) = G B1 (B2-1B2) T(t)= (G B1 B2-1) B2 T(t) • G B1 B2-1 are the control points for the segment in new basis. 36 Converting between Bézier & B...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
: Wikimedia Commons. 41 Smooth Surfaces? • P(t) = (1-t)³ P1 + 3t(1-t)² P2 + 3t²(1-t) P3 + P4 t³ What’s the dimensionality of a curve? 1D! What about a surface? 42 How to Build Them? Here’s an Idea • P(u) = (1-u)³ P1 + 3u(1-u)² P2 + 3u²(1-u) P3 + u³ P4 (Note! We relabeled t to u) 43...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
+ 3u(1-u)² P2(v) + 3u²(1-u) P3(v) P4(v) + u³ • Let’s make the Pis move along curves! A 2D surface patch! v=0 v=1/3 v=2/3 v=1 52 Tensor Product Bézier Patches • In the previous, Pis were just some curves • What if we make them Bézier curves? 53Tensor Product Bézier Patches • In the previou...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
Bicubics, Tensor Product • P(u,v) = B1(u) * P1(v) + B2(u) * P2(v) + B3(u) * P3(v) + B4(u) * P4(v) • Pi(v) = B1(v) * Pi,1 + B2(v) * Pi,2 + B3(v) * Pi,3 + B4(v) * Pi,4 58 Bicubics, Tensor Product • P(u,v) = B1(u) * P1(v) + B2(u) * P2(v) + B3(u) * P3(v) + B4(u) * P4(v) • Pi(v) = B1(v) * Pi...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
to surface at P © Addison-Wesley. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/. 62 Tangents and Normals for Patches • P(u,v) is a 3D point specified by u, v • The partial derivatives and are 3D vectors • Both are ...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
atches • Bézier and B-Spline curves are both cubics – Can change between representations using matrices • Consequently, you can build tensor product surface patches out of B-Splines just as well – Still 4x4 control points for each patch – 2D basis functions are pairwise products of B-Spline basis functions – Ye...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
w.mit.edu/help/faq-fair-use/. 73Displacement Mapping Example This image is in the public domain. Source: Wikimedia Commons. Smooth base surface Displaced Surface 74Questions? 75Subdivision Surfaces • Start with polygonal mesh • Subdivide into larger number of polygons, smooth result after each subdivision – ...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
– Numerical stability, well-behaved meshes – Code simplicity • Little disadvantage: – Procedural definition – Not parametric – Tricky at special vertices 89 Flavors of Subdivision Surfaces • Catmull-Clark – Quads and triangles – Generalizes bicubics to arbitrary topology! • Loop, Butterfly – Triangl...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
be seen as a special case where trajectory is a circle s s(u,v)=M(c(v))q(u) where M is a matrix that depends on the trajectory c c q 95General Swept Surfaces • How do we get M? – Translation is easy, given by c(v) – What about orientation? • Orientation options: – Align profile curve with an axis. – Bett...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
is in the public domain. Source: Wikimedia Commons. 102Implicit Surfaces • Pros: – Efficient check whether point is inside – Efficient Boolean operations – Can handle weird topology for animation – Easy to do sketchy modeling • Cons: – Does not allow us to easily generate a point on the surface Image courtesy...	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
– Buss, Chapters 7 & 8 • Subvision curves and surfaces – http://www.cs.nyu.edu/~dzorin/sig00course/ 6.837 – Durand 0 9 109 MIT OpenCourseWare http://ocw.mit.edu 6.837 Computer Graphics Fall 2012 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.	https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/38682e92015a39734867853f57ccf55b_MIT6_837F12_Lec02.pdf
3.225 Electrical,Optical, and Magnetic Properties of Materials • Professor Eugene Fitzgerald • Purpose: connect atoms and structure to properties • Semi-historical context – What was understood first from the micro to the macro? – What was missing to explain other materials? Origin of Conduction Range of Resi...	https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/386e36fc0277bd2f6cb8e49e14d0882d_lecture_1.pdf
mic behavior Microscopic origin? Remove geometry of material V L I W V=IR=IR/L R=L/(σA) J=σE In general, r ~ r J = E σ All material info In cubic material, Isotropic material E Anisotropic material E J J J ⎛ ⎜ J ⎜ y ⎜ J z ⎝ ⎞ x ⎟ ⎟ ⎟ ⎠ = σ ⎛ ⎜ σ ⎜ ⎜ σ ⎝ xx xy xz σ σ σ xy yy yz σ σ σ ⎞ E ⎛ xz ...	https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/386e36fc0277bd2f6cb8e49e14d0882d_lecture_1.pdf
p t( ) τ + F t( ) + F ( )t +... 2 1 Response (ma) Drag Driving Force Restoring Force... dp t ( ) dt ≈ − p t( ) τ − eE Add a drag term, i.e. the electrons have many collisions during drift 1/τ represents a ‘viscosity’ in mechanical terms In steady state, dp t ( ) dt = 0 −t p t( ) = p∞ (1− e τ ) p∞ = −...	https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/386e36fc0277bd2f6cb8e49e14d0882d_lecture_1.pdf
(5 K) Rb (5 K) Cs (5 K) Cu Ag Au Be Mg Ca Sr Ba Nb Fe Mn (a) Zn Cd Hg (78 K) Al Ga In Tl Sn Pb Bi Sb 1 1 1 1 1 1 1 1 2 2 2 2 2 1 2 2 2 2 2 3 3 3 3 4 4 5 5 4.70 2.65 1.40 1.15 0.91 8.47 5.86 5.90 24.7 8.61 4.61 3.55 3.15 5.56 17.0 16.5 13.2 9.27 8.65 18.1 15.4 11.5 10.5 14.8 13.2 14.1 16.5 o rs(A) 1.72 2.08 2.57 2.75 2....	https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/386e36fc0277bd2f6cb8e49e14d0882d_lecture_1.pdf
7 3.57 3.71 3.07 2.12 2.14 2.30 2.59 2.65 2.07 2.19 2.41 2.48 2.22 2.30 2.25 2.14 Table by MIT OpenCourseWare. Extracting Typical τ for Metals • τ~10-14 sec for metals in Drude model Element 77 K 273 K Li Na K Rb Cs Cu Ag Au Be Mg Ca Sr Ba Nb Fe Zn Cd Hg Al Ga In Tl Sn Pb Bi Sb 7.3 17 18 14 8.6 21 20 12 6.7 1.4 0...	https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/386e36fc0277bd2f6cb8e49e14d0882d_lecture_1.pdf
.25 0.15 0.15 0.099 0.016 0.036 Drude relaxation times in units of 10-14 second Table by MIT OpenCourseWare. Thermal Velocity • So far we have discussed drift velocity vD and scattering time τ related to the applied electric field • Thermal velocity vth is much greater than vD x x L=vDt 3 2 kT 1 2 mvth 2 =...	https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/386e36fc0277bd2f6cb8e49e14d0882d_lecture_1.pdf
OS includes conductivity engineering • One example: as devices shrink… – vertical field increases – τ decreases due to increased scattering at SiO2/Si interface – increased doping in channel need for electrostatic integrity: ionized impurity scattering – τSiO2<τimpurity if scaling continues ‘properly’ S Evert ...	https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/386e36fc0277bd2f6cb8e49e14d0882d_lecture_1.pdf
Today's plan: [Any questions about lock server lab?] Reviewing event driven programming Outline structure of the remaining labs Common libasync/libarpc/nfsloop programming idioms: writing rpc client code writing async functions that call RPCs writing rpc server code Flash Event driven programming Ach...	https://ocw.mit.edu/courses/6-824-distributed-computer-systems-engineering-spring-2006/38dc024fe5e0b8fe7115d4e19d2476ba_lec3_events.pdf
aclnt handles all bookkeeping/formatting/etc for us: e.g. which cb gets called write servers (asrv/svccb) Asynchronous RPC: needs a callback! [Example 3] Note: Cite as: Robert Morris, course materials for 6.824 Distributed Computer Systems Engineering, Spring 2006. MIT OpenCourseWare (http://ocw.mit.edu/), M...	https://ocw.mit.edu/courses/6-824-distributed-computer-systems-engineering-spring-2006/38dc024fe5e0b8fe7115d4e19d2476ba_lec3_events.pdf
kernel->ccfs->lockserver/blockserver] Not unlike how we might operate: get an e-mail from friend: can you make it to my wedding? check class calendar on web, check research deadlines send IM to wife, research ticket prices, reply Or Amazon.com login... [Example 6] An aside on locking: No locking etc need...	https://ocw.mit.edu/courses/6-824-distributed-computer-systems-engineering-spring-2006/38dc024fe5e0b8fe7115d4e19d2476ba_lec3_events.pdf
MASSACHUSETTS INSTITUTE OF TECHNOLOGY SLOAN SCHOOL OF MANAGEMENT 15.565 Integrating Information Systems: Technology, Strategy, and Organizational Factors 15.578 Global Information Systems: Communications & Connectivity Among Information Systems Spring 2002 Lecture 11 EMERGING TECHNOLOGIES “THE LAST MILE” (xDSL / C...	https://ocw.mit.edu/courses/15-565j-integrating-esystems-global-information-systems-spring-2002/3903d757ddd00703e1d0fa181da78ae6_lecture11.pdf
ADSL = Asymmetric digital subscriber line, HDSL = High-speed digital subscriber line, T1 = 1.544 M 2 Customer must have cable service 4 CABLE MODEMS COAX FIBER CABLE HEAD A B C SUBSCRIBERS NETWORK SOURCE • HOW SIMILAR TO AND DIFFER FROM ETHERNET – IMPACT ON PERFORMANCE / PRIVACY • WHY ASYMMETRIC (NORMALLY) ...	https://ocw.mit.edu/courses/15-565j-integrating-esystems-global-information-systems-spring-2002/3903d757ddd00703e1d0fa181da78ae6_lecture11.pdf
USES SINGLE WIRE PAIR AND SHORTER DISTANCES • VDSL : VERY HIGH BIT-RATE DSL – ASYMMETRIC AND FASTEST (13-52M DOWN, 1.5-2.3M UP) – SHORTEST DISTANCE (1000-4500 FEET) 7 APPLICATIONS (with differing needs) • Internet / Intranet Access • Web browsing vs hosting • E-mail • Remote LAN • Video conferencing • Tran...	https://ocw.mit.edu/courses/15-565j-integrating-esystems-global-information-systems-spring-2002/3903d757ddd00703e1d0fa181da78ae6_lecture11.pdf
In this lecture, we continue (and finish) the theme of geometric data structures. First, we'll finish our coverage of fractional cascading from Lecture 3 by illustrating a really cool application: 3D orthogonal range searching in O(log n) time. This gives us the second log factor improvement mentioned in Lecture 3, ...	https://ocw.mit.edu/courses/6-851-advanced-data-structures-spring-2012/396340161b7bd4c5cfc8820210a9743a_MIT6_851S12_Lecture4.pdf
6.826—Principles of Computer Systems 2002 6.826—Principles of Computer Systems 2002 9. Atomic Semantics of Spec This handout defines the semantics of the atomic part of the Spec language fairly carefully. It tries to be precise about all difficult points, but is sloppy about some things that seem obvious in orde...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
machines you should be able to understand all this without any trouble. One reason for doing this is to make sure that we really do know what we are talking about. In general, descriptions of programming languages are not in that state of grace. If you read the Pascal manual or the C manual carefully you will come ...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
the job. And there is a lot to be said for just having one notation you can use over and over again, as opposed to picking up a new one each time. There are many pitfalls in devising a new notation. Those are the two themes of this lecture. We are going to get down to the foundations of Spec, and we are going to se...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
les of Computer Systems 2002 standard one for a situation where you have things that are made up out of smaller things: structural induction. The idea of structural induction is this. If you have something which is made up of an A and a B, and you know the meaning of each, and have a way to put them together, you ...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
names have two parts, the module name and the simple name. When referring to a variable in another module, you need both parts. MODULE M VAR x MODULE N M.x := 3 x := 3 ... M.x := 3 To simplify the semantics, we will use M.x as the name everywhere. In other words, to apply the semantics you first must go throu...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
do not affect state. Question: What about assignments? Assignments are not expressions. If you have been programming in C, you have the weird idea that assignments are expressions. Spec, however, takes a hard line that expressions must be deterministic or functional; that is, their values depend only on the state. ...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
a function T -> U, the correct type of its meaning is (T, S) -> U, since the function can read the state but not modify it. Next, how are we going to attach a meaning to an invocation f(x)? Remember the rule of structural induction. In order to explain the meaning of a complicated thing, you are supposed to build it...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
S -> S ? This is good for a subset of commands. But what about this one? x := 1 [] x := 2 Is its meaning a function from states to states? No, from states to sets of states. It can’t just be a function. It has to be a relation. Of course, there are lots of ways to code relations as functions. The way we use is: C...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
5 Handout 9. Atomic Semantics of Spec 6 6.826—Principles of Computer Systems 2002 6.826—Principles of Computer Systems 2002 or in general variable := expression What we have to come up with for the meaning is an expression of the form (\ s, o \| ...) So when does the relation hold for x := exp? Well, perhaps...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
programs. You could write everything just as predicates. (Of course, you could also write everything in the ugly o = s{...} form, but that would look pretty awful. The predicates don’t look so bad.) Sometimes it’s actually nice to do this. Say you want to write the predicate that says you can have any value at all ...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
’t so nested and might be clearer, would be to introduce an intermediate state s'. Now we have to use LAMBDA: (LAMBDA (s, o)->Bool = VAR s' = s{"$a" -> ME(e)(s)} \| RET ME(p)(s)(s', o)) These two are exactly the same thing. The invocation relates s to o iff the routine relates s' to o, where s' is just s with the ar...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
), the meaning of p. This is no longer a transition but a function from argument values to transitions, because the idea is that for every possible argument value, we are going to get a different meaning for the routine, namely what that routine does when given that particular argument value. So we pass it the argum...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
what the meaning of a function is. The latter is more elegant, but we use the former because it is less confusing. Stepping back from these technical details, what the meaning function is doing is taking an expression and producing its meaning. The expression is a piece of syntax, and there are a lot of possible wa...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
Spec 10 6.826—Principles of Computer Systems 2002 6.826—Principles of Computer Systems 2002 MC(c1)(s, o) \/ … But what next? One possibility is ~ MC(c1)(s, o) /\ ... ) \/ IsX(o') /\ o'("$x") IN xs) /\ MC(c2)(o'{"$x" -> ""}, o) So, with this semantics for handling exceptions, the meaning of: (c1 EXCEPT xs ...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
do c2, do c3 if exception and not handled do c1, no c2, no c3 Commands — VAR id: T \| c0 The idea is “there exists a value for id such that c0 succeeds”. This intuition suggests something like (EXISTS v :IN T \| MC(c0)(s{"id" -> v}, o)) However, if we look carefully, we see that id is left defined in the output s...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
semicolon case. If there’s an exception, then do c2. If there’s no exception, do not do c2. We also need to include an additional check to insure that the exception considered is an element of the exception set—that is to say, that it is a handled exception. (EXISTS o' \| MC(cl)(s, o') /\ ( ((~IsX(o') \/ ~o'("$x")...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
atomic commands (treated in handout 17 on formal concurrency). For the first two there is no concurrency: expressions and atomic commands are atomic. This makes it possible to give their meanings quite simply: Expressions as functions from states to results, that is, values or exceptions. Atomic commands as relatio...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
code for Spec, that is, to a compiler or interpreter. It does look a lot like an interpreter. As with other specs written in Spec, however, this one is not practical code because it uses existential quantifiers and other forms of non-determinism too freely. Most of these quantifiers are just there for clarity and co...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
Name -> V WITH {isX:=OIsX} = O SUCHTHAT (\ o \| ~ o.isX) = (S, O) -> Bool % eXception Set % Outcome % State % Atomic Transition X XS O S ATr CONST letter digit ids globals noX retX loopX typeX trueV := "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz".rng := "0123456789".rng := {id \| true} ...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
Handout 9. Atomic Semantics of Spec 13 Handout 9. Atomic Semantics of Spec 14 6.826—Principles of Computer Systems 2002 6.826—Principles of Computer Systems 2002 The meaning of an id or var is just the string, of an exceptionSet the set of strings that are the exceptions in the set, of a type the set of val...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
An assignment var := e requires that the value of e have the type of var. If the type of e is not equal to the type of var because it involves a union or a SUCHTHAT, this check can’t be done statically. To take account of this and to ensure that the meaning of expressions is independent of the static type checking, ...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
)} MC(C« e1(e2); var := $a »)(s, o) e => c0 c1 [] c2 c1 [*] c2 c1 ; c2 ME(e)(s) = trueV /\ MC(c0)(s, o) MC(c2)(s, o) MC(c1)(s, o) \/ MC(c1)(s, o) \/ ( MC(c2)(s, o) /\ ~(EXISTS o' \| MC(c1)(s, o')) ) \/ ( EXISTS o' \| MC(c1)(s, o) /\ o .isX MC(c1)(s, o') /\ ~ o'.isX /\ MC(c2)(o',o ) ) c1 EXCEPT xs => c2 \/...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
, and $havoc is false. Handout 9. Atomic Semantics of Spec 15 Handout 9. Atomic Semantics of Spec 16 6.826—Principles of Computer Systems 2002 6.826—Principles of Computer Systems 2002 Atomic commands An atomic command relates a state to an outcome; in other words, it is defined by an ATr (atomic transition...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
simple to give the definition of the function MC. It has the form FUNC MC(c) -> ATr = IF ... [] VAR var, e \| c = «var := e» => RET (\ o, s \| full predicate for this case ) ... [] VAR c1, c2 \| c = «c1 ; c2» => RET (\ o, s \| full predicate for this case ) ... FI Now to explain the predicates. First we do the ...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
composition c1 ; c2 relates s to o if there is a suitable intermediate state, or if o is an exceptional outcome of c1. c1 EXCEPT xs=>c2 is the same as c1 for a normal outcome or an exceptional outcome not in the exception set xs. For an exceptional outcome o' in xs, c2 must relate o' as a normal state to o. This is...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
6.826—Principles of Computer Systems 2002 command, we can get its meaning from MC. The idea is that the meaning of the routine should be a relation of states to outcomes just like the meaning of a command. In this relation, the pseudo- name $a holds the argument in the initial state and the result in the outcome. Fo...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
-local variables or call procedures. FUNC ME(e) -> (S -> (V + X)) = IF ... [] VAR e1, e2 \| e = E« e1(e2) » => % if E is an invocation its meaning is this function from states to values VAR aTr := MC(C« e1(e2) ») \| RET ( LAMBDA (s) -> V = % the command must have a unique outcome, that is, aTr must be a % funct...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
( o'("$a") IN t2 => noX % retX means normal outcome [] typeX ) [] o'("$x") = noX => typeX [*] o'("$x) % if result typechecks; % normal outcome means typeX; % pass on exceptions ) } \/ ~ s("$a") IN t1 /\ o = s{"$x" -> typeX} ) ) % argument doesn't typecheck % end of the two lambdas We leave the meaning o...	https://ocw.mit.edu/courses/6-826-principles-of-computer-systems-spring-2002/39afa4d7545639c4a282d63b8f9978a0_9.pdf
3.15 Displays C.A. Ross, DMSE, MIT References: Braithwaite and Weaver chapter 6.4 Displays can work by -emitting light, eg. Incandescence (light from heating a filament) Cathodoluminescence (light from electron bombardment) ZnS +Ag (blue), (Zn,Cd)S +Cu (green), Y2O2S +Eu,Tb (red) –excited by three 20kV electron gun...	https://ocw.mit.edu/courses/3-15-electrical-optical-magnetic-materials-and-devices-fall-2006/39b18424818b1face2ad6579a915e34b_lecture14.pdf
3V) between the front and back plates aligns the nematic and light can no longer pass, so the display is dark. Colors come from dyes or filters. Response time limited by viscosity. Electrode patterns are made from thin film transistors (TFTs) made on glass – these use a-Si to make the channel region, with p-type source...	https://ocw.mit.edu/courses/3-15-electrical-optical-magnetic-materials-and-devices-fall-2006/39b18424818b1face2ad6579a915e34b_lecture14.pdf
Genesis of Friction between Macroscale contacts • Reference: Chapter 3 of the text books What is friction? F = ∂W ∂s µ varies as a function of the sliding distance. 1 0.6 0.2 0 0 20 40 60 80 D i stan ce slid ( m ) Scale issues in tribology Table 3.1 Scales in Tribology and Typical alues Adapte...	https://ocw.mit.edu/courses/2-800-tribology-fall-2004/39bee0a6dd75b805338d29c25b8a0810_ch3_friction.pdf
3 1E-3 1E-3 1E-3 1E-3 1E-3 0.1 0.1 0.1 0.1 0.1 0.1 ta-C Si wafer Si-DLC a-C:H Sputtered DLC Optimized DLC 1 1 1 1 1 1 10 10 10 10 10 10 100 100 100 100 100 100 Relative friction forces in MEMS of two flat and smooth surfaces as functions of the distance between the two surfaces 103 100 h-1 Capillary at ...	https://ocw.mit.edu/courses/2-800-tribology-fall-2004/39bee0a6dd75b805338d29c25b8a0810_ch3_friction.pdf

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.