sort by: Relevancy | Title try advanced search for more options
This course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM m...more
This course is the second of a two-term sequence. The focus is on coding techniques for approaching the Shannon limit of additive white Gaussian noise (AWGN) channels, their performance analysis, and design principles. After a review of Principles of Digital Communication I and the Shannon limit for AWGN channels, the course begins by discussing small signal constellations, performance analysis and coding gain, and hard-decision and soft-d...more
The current Holocene epoch is considered to be a time period of relatively stable climate compared to earlier geological periods. Still, some significant changes in temperature and sea level did occur. These climatic fluctuations include the Medieval Warm Period and the Little Ice Age, and more recently global warming. Temperature data for the 20th century shows a strong warming from about 1970 to the present day, typically associated with...more
This lecture continues our theme of cache-oblivious data structures.First we'll finally cover the black box we used last lecture to obtain cache-oblivious B-trees: maintain an ordered file with O(1)-size gaps in O(lg2 N) moves per insert/delete in the middle of the file. As an extra bonus, we'll see how to maintain a linked list subject to order queries in O(1) time per insert/delete, which is a black box we used back in Lecture 1 to linea...more
Heap Management - How Information about Allocations are Stored in the Heap, Result of Freeing Memory Improperly, Actual Sizes of Heap Allocations - Nearest Power of 2, Management of Free Blocks on the Heap by Storing Addresses in the Blocks of Free Memory, Algorithms for Choosing Which Free Block to Allocate, How the Heap's Free List Can Be Updated When Memory is Freed, How Adjacent Free Blocks Are Combined To Avoid Fragmentation, Compacti...more
The topic of the next three lectures is cache-efficient data structures. A classic result here is that B-trees are good at exploiting that data is transferred in blocks between cache and main memory, and between main memory and disk, and so on. B-trees achieve O(logB N) insert/delete/predecessor/ successor for N items and memory block transfers of size B. What's more recent and surprising is that you can achieve the same performance even i...more
Jeff Housenbold, CEO of Shutterfly, recalls how he learned that merging community with commerce was the winning ticket in business online. He recounts his days at Raging Bull, an upstart financial vehicle that knocked the larger, more established players out of the ring. It's secret? The site was bullish on building community and responsive to its users, resulting in millions of users in just a few short months. Furthermore, Housenbold cre...more
Jordan Canonical Form, Generalized Modes, Cayley-Hamilton Theorem, Proof Of C-H Theorem, Linear Dynamical Systems With Inputs & Outputs, Block Diagram, Transfer Matrix, Impulse Matrix, Step Matrix
Least-Norm Solution, Least-Norm Solution Via QR Factorization, Derivation Via Langrange Multipliers, Example: Transferring Mass Unit Distance, Relation To Regularized Least-Squares, General Norm Minimization With Equality Constraints, Autonomous Linear Dynamical Systems, Block Diagram
Linearization (Continued), Navigation By Range Measurement, Broad Categories Of Applications, Matrix Multiplication As Mixture Of Columns, Block Diagram Representation, Linear Algebra Review, Basis And Dimension, Nullspace Of A Matrix
Learn how to find the Least Common Multiple of two integers. It's an important building block for many number properties questions on the GMAT.
In this lecture Processor Lewin introduces elasticity and Young's modulus. The fractional length deformation of a material (the strain) depends on the force per unit area (the stress). The stress vs. strain dependence is described conceptually, then explored empirically. The speed of sound in a material depends on the stiffness and density of the material; from this follows the fundamental frequency at which a rod resonates. Professor Lewi...more
