Error detection and correction
A locally testable code is a type of error-correcting code for which it can be determined if a string is a word in that code by looking at a small (frequently constant) number of bits of the string. In some situations, it is useful to know if the data is corrupted without decoding all of it so that appropriate action can be taken in response. For example, in communication, if the receiver encounters a corrupted code, it can request the data be re-sent, which could increase the accuracy of said data. Similarly, in data storage, these codes can allow for damaged data to be recovered and rewritten properly. In contrast, locally decodable codes use a small number of bits of the codeword to probabilistically recover the original information. The fraction of errors determines how likely it is that the decoder correctly recovers the original bit; however, not all locally decodable codes are locally testable. Clearly, any valid codeword should be accepted as a codeword, but strings that are not codewords could be only one bit off, which would require many (certainly more than a constant number) probes. To account for this, testing failure is only defined if the string is off by at least a set fraction of its bits. This implies words of the code must be longer than the input strings by adding some redundancy. (Wikipedia).
Locally testable codes with constant rate, distance, and locality, Part I - Irit Dinur
Computer Science/Discrete Mathematics Seminar I Topic: Locally testable codes with constant rate, distance, and locality, Part I Speaker: Irit Dinur Affiliation: Weizmann Institute Date: October 25, 2021 A locally testable code (LTC) is an error correcting code that admits a very efficie
From playlist Mathematics
Locally testable codes with constant rate, distance, and locality, Part II - Irit Dinur
Computer Science/Discrete Mathematics Seminar II Topic: Locally testable codes with constant rate, distance, and locality, Part II Speaker: Irit Dinur Affiliation: Weizmann Institute Date: October 26, 2021 A locally testable code (LTC) is an error correcting code that admits a very effic
From playlist Mathematics
Using the vertical line test to determine if a graph is a function or not
๐ Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
How to determine if a set of points is a function, onto, one to one, domain, range
๐ Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Determine the domain, range and if a relation is a function
๐ Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Determine if the equation represents a function
๐ Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Importing and Manipulating Data Sets
Get a Free Trial: https://goo.gl/C2Y9A5 Get Pricing Info: https://goo.gl/kDvGHt Ready to Buy: https://goo.gl/vsIeA5 Import test data for estimating the model and validating results. For more videos, visit http://www.mathworks.com/products/sysid/examples.html
From playlist Control System Design and Analysis
How to determine if an ordered pair is a function or not
๐ Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Lifting small locally testable codes (LTCs) to large LTCs via HDXs - Prahladh Harsha
Computer Science/Discrete Mathematics Seminar I Topic: Lifting small locally testable codes (LTCs) to large LTCs via HDXs Speaker: Prahladh Harsha Affiliation: Tata Institute of Fundamental Research Date: November 25, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Locally testable and locally correctable codes approaching the GV bound - Shubhangi Saraf
Computer Science/Discrete Mathematics Seminar I Topic: Locally testable and locally correctable codes approaching the Gilbert-Varshamov bound Speaker: Shubhangi Sara Affiliation: Rutgers University Date: November 27, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
2 Minute Quickie - How to make your own QR code using Mathematica
In this two minute quickie I am going to show you how to make your own QR code using Mathematica. Here is what I type: b = BarcodeImage["http://www.partridgegetslucky.com/", "QR"] r = BarcodeRecognize[b]; SystemOpen[r] For information on private tutoring, see the about section of my c
From playlist Mathematica Programming
Stability and testability - a computational perspectiveJonathan Mosheiff
Stability and Testability Topic: Stability and testability - a computational perspective Speaker: Jonathan Mosheiff Affiliation: Carnegie Mellon University Date: October 21, 2020 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - A.Harrow
Aram Harrow (MIT) / 15.09.17 Title: Local Hamiltonians Whose Ground States are Hard to Approximate Abstract: Ground states of local Hamiltonians are typically highly entangled: any quantum circuit that generates them (even approximately) must be sufficiently deep to allow coupling (entan
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
New Locally Decodable Codes from Lifting - Madhu Sudan
Madhu Sudan Microsoft Research March 25, 2013 Locally decodable codes (LDCs) are error-correcting codes that allow for highly-efficient recovery of "pieces" of information even after arbitrary corruption of a codeword. Locally testable codes (LTCs) are those that allow for highly-efficient
From playlist Mathematics
The PCP theorem, locally testable codes, and property testing - Irit Dinur
Stability and Testability Topic: The PCP theorem, locally testable codes, and property testing Speaker: Irit Dinur Affiliation: Weizmann Institute of Science Date: January 13, 2021 For more video please visit http://video.ias.edu
From playlist Stability and Testability
High Dimensional Expansion and Error Correcting Codes - Irit Dinur
Hermann Weyl Lectures Topic: High Dimensional Expansion and Error Correcting Codes Speaker: Irit Dinur Affiliation: Weizmann Institute of Science; Visiting Professor, School of Mathematics Date: November 19, 2019 For more video please visit http://video.ias.edu
From playlist Hermann Weyl Lectures
Constant Rate PCPs for Circuit-SAT with Sublinear Query Complexity - Eli Ben-Sasson
Eli Ben-Sasson Technion; Massachusetts Institute of Technology March 18, 2013 The PCP theorem (Arora et. al., J. ACM 45(1,3)) says that every NP-proof can be encoded to another proof, namely, a probabilistically checkable proof (PCP), which can be tested by a verifier that queries only a s
From playlist Mathematics
Learn how to determine the domain and range from a table and from a graph
๐ functions are the possible output values (y-values) of the function. To find the domain of a function from a table we list out the set of the input values and for the range we list out the set of output values. To find the domain and the range of a function from a graph, we use the behav
From playlist What is the Domain and Range of the Function