The document describes a programming project to solve the Instant Insanity problem using a recursive approach in Python. It takes a general approach that checks every pair on every line to find solutions. The algorithm has a time complexity of O(n^4). Distributed computing methods like Hadoop and RabbitMQ could solve it faster. The program found 3 solutions within the limited time and resources. Further optimizations using dynamic programming could reduce the time required.
Given presentation tell us about string, string matching and the navie method of string matching. Well this method has O((n-m+1)*m) time complexicity. It also tells the problem with naive approach and gives list of approaches which can be applied to reduce the time complexicity
In this approach, the pattern is made to slide over text one by one and test for a match. If a match is found while testing, then it returns the starting index number from where the pattern is found in the text and then slides by 1 again to check for subsequent matches of the pattern in the text. Copy the link given below and paste it in new browser window to get more information on Naive String Matching Algorithm:- http://www.transtutors.com/homework-help/computer-science/naive-string-matching-algorithm.aspx
Matching the String with a pattern is known as String Match”. Now, what are these strings and patterns? Alright, the string is that which is to be checked entered by the user and is matched with the pattern which is already in the database. Copy the link given below and paste it in new browser window to get more information on String Match:- www.transtutors.com/homework-help/computer-science/string-match.aspx
Probabilistic breakdown of assembly graphsc.titus.brown
1. The document describes a new technique for storing and analyzing k-mers from large DNA datasets in a memory and computationally efficient manner using probabilistic data structures.
2. It allows for querying whether a k-mer is present, traversing the k-mer graph, and partitioning the graph into smaller disconnected components in a way that guarantees correct "no" answers.
3. This technique has been implemented in a Python package that can partition and assemble datasets of up to 50 Gb in under a week using only 70gb of RAM, providing a 10x speed improvement over existing assemblers.
Spike sorting: What is it? Why do we need it? Where does it come from? How is...NeuroMat
This document discusses spike sorting and stochastic modeling of spike trains. It proposes using a more realistic model that accounts for the log-normal distribution of inter-spike intervals and the exponential relaxation of spike amplitudes over time. This model is formulated within a Bayesian framework, where the spike sorting problem amounts to estimating the configuration of neuron identities for each spike. Computing the posterior configuration probability is challenging due to combinatorial explosion, but can be addressed using Markov chain Monte Carlo methods like the Metropolis-Hastings algorithm.
The second quantum revolution: the world beyond binary 0 and 1Bruno Fedrici, PhD
Our active application of quantum
mechanics has previously been constrained by our
ability to engineer and control systems at the small
scales where quantum effects predominate. This has
now changed. Scientists have reached first base on a
set of enabling technologies that allow us to
routinely manipulate atoms of matter and photons of
light at individual level. This has unlocked our ability
to create a new generation of devices that deliver
unique capabilities directly tied to properties of quantum mechanics such as superposition and entanglement.
Quantum Computing - Challenges in the field of securityNavin Pai
Presented by Navin "M@dmAx" Pai at NullCon 2010, Goa, India on the implications of Quantum computing on the field of security.
This was a half hour presentation.
Given presentation tell us about string, string matching and the navie method of string matching. Well this method has O((n-m+1)*m) time complexicity. It also tells the problem with naive approach and gives list of approaches which can be applied to reduce the time complexicity
In this approach, the pattern is made to slide over text one by one and test for a match. If a match is found while testing, then it returns the starting index number from where the pattern is found in the text and then slides by 1 again to check for subsequent matches of the pattern in the text. Copy the link given below and paste it in new browser window to get more information on Naive String Matching Algorithm:- http://www.transtutors.com/homework-help/computer-science/naive-string-matching-algorithm.aspx
Matching the String with a pattern is known as String Match”. Now, what are these strings and patterns? Alright, the string is that which is to be checked entered by the user and is matched with the pattern which is already in the database. Copy the link given below and paste it in new browser window to get more information on String Match:- www.transtutors.com/homework-help/computer-science/string-match.aspx
Probabilistic breakdown of assembly graphsc.titus.brown
1. The document describes a new technique for storing and analyzing k-mers from large DNA datasets in a memory and computationally efficient manner using probabilistic data structures.
2. It allows for querying whether a k-mer is present, traversing the k-mer graph, and partitioning the graph into smaller disconnected components in a way that guarantees correct "no" answers.
3. This technique has been implemented in a Python package that can partition and assemble datasets of up to 50 Gb in under a week using only 70gb of RAM, providing a 10x speed improvement over existing assemblers.
Spike sorting: What is it? Why do we need it? Where does it come from? How is...NeuroMat
This document discusses spike sorting and stochastic modeling of spike trains. It proposes using a more realistic model that accounts for the log-normal distribution of inter-spike intervals and the exponential relaxation of spike amplitudes over time. This model is formulated within a Bayesian framework, where the spike sorting problem amounts to estimating the configuration of neuron identities for each spike. Computing the posterior configuration probability is challenging due to combinatorial explosion, but can be addressed using Markov chain Monte Carlo methods like the Metropolis-Hastings algorithm.
The second quantum revolution: the world beyond binary 0 and 1Bruno Fedrici, PhD
Our active application of quantum
mechanics has previously been constrained by our
ability to engineer and control systems at the small
scales where quantum effects predominate. This has
now changed. Scientists have reached first base on a
set of enabling technologies that allow us to
routinely manipulate atoms of matter and photons of
light at individual level. This has unlocked our ability
to create a new generation of devices that deliver
unique capabilities directly tied to properties of quantum mechanics such as superposition and entanglement.
Quantum Computing - Challenges in the field of securityNavin Pai
Presented by Navin "M@dmAx" Pai at NullCon 2010, Goa, India on the implications of Quantum computing on the field of security.
This was a half hour presentation.
The document summarizes the design of renovating the first two floors and rooftop of the Transcontinental Hotel in Oakland, CA. It includes a design statement focusing on incorporating industrial elements representing the area's railroad history. It also includes an analysis of the site noting the location in downtown Oakland near public transportation and cultural attractions, as well as details about the climate, demographics of the area, and logistics of the building site.
El documento describe el papel del ingeniero como solucionador de problemas. Los ingenieros identifican necesidades y carencias para desarrollar dispositivos, estructuras o procesos que las satisfagan de manera original, confiable y económica. Trabajan con especialistas de diversas áreas para crear y supervisar proyectos mediante el uso de su ingenio, juicio y capacidad creativa. Además, los ingenieros realizan la mayor parte de su trabajo de manera abstracta, por ejemplo, con el diseño y supervisión de una construcción.
This document advertises a two-day corporate training program on making successful presentations. It notes that 95% of presentations currently "suck" but can be improved by mastering three things: message, visual storytelling, and delivery method. The training will help attendees transform bad presentations into good ones by learning key elements of presentation design and ecosystem. Those who sign up will get skills to effectively present tasks, understand design principles, and receive early bird discounts by calling now.
Esquema comparativo del rol del docente y el estudiante tradicional y actual.Fe Maria Holguin Bencosme
En este trabajo presento dos esquemas comparativos del rol del docente tradicional y el actual y otro sobre el rol del estudiante tradicional y el actual
This document introduces the concept of NP-completeness. It discusses that while some problems like shortest paths, minimum spanning trees, and bipartite matching have efficient polynomial time algorithms, other problems like satisfiability (SAT), the travelling salesman problem (TSP), integer linear programming (ILP), and set cover have only exponential time algorithms. It defines the class NP as problems that can be solved by a non-deterministic Turing machine in polynomial time. It states that if any NP-complete problem could be solved in polynomial time, then P would equal NP. Problems are NP-hard if all problems in NP can be reduced to them in polynomial time, and NP-complete if they are both in NP and NP-
This document discusses the limits of computation. It distinguishes between intractable problems that take an impractical amount of time to solve versus truly unsolvable problems. It describes different complexity classes based on how fast the number of operations grows with input size. Hard problems like the traveling salesman problem are inherently difficult even with faster computers. Reductions show relationships between problem difficulties. The halting problem and incompleteness theorems prove certain logical and mathematical questions cannot be answered algorithmically.
This document discusses the limits of computation. It distinguishes between intractable problems that take an impractical amount of time to solve versus truly unsolvable problems. It describes different complexity classes based on how fast the number of operations grows with input size. Hard problems like the traveling salesman problem are in NP and are inherently difficult even with faster computers or quantum computing. Reductions show relationships between problem difficulties. The halting problem and Godel's incompleteness theorems establish fundamental limits of computation and logical systems.
This document discusses time and space complexity analysis of algorithms. It analyzes the time complexity of bubble sort, which is O(n^2) as each pass through the array requires n-1 comparisons and there are n passes needed. Space complexity is typically a secondary concern to time complexity. Time complexity analysis allows comparison of algorithms to determine efficiency and whether an algorithm will complete in a reasonable time for a given input size. NP-complete problems cannot be solved in polynomial time but can be verified in polynomial time.
This document summarizes various algorithms topics including pattern matching, matrix multiplication, graph algorithms, algebraic problems, and NP-hard and NP-complete problems. It provides details on pattern matching techniques in computer science including exact string matching and applications. It also describes how to find the most efficient way to multiply a sequence of matrices by considering different orders of operations. Graph algorithms are introduced including directed and undirected graphs. Popular design approaches for algebraic problems such as divide-and-conquer, greedy techniques, and dynamic programming are outlined. Finally, the key differences between NP, NP-hard, and NP-complete problems are defined.
P, NP, NP-Complete, and NP-Hard
Reductionism in Algorithms
NP-Completeness and Cooks Theorem
NP-Complete and NP-Hard Problems
Travelling Salesman Problem (TSP)
Travelling Salesman Problem (TSP) - Approximation Algorithms
PRIMES is in P - (A hope for NP problems in P)
Millennium Problems
Conclusions
Solomonoff's theory of inductive inference is Ray Solomonoff's mathematical formalization of Occam's razor. It explains observations of the world by the smallest computer program that outputs those observations. Solomonoff proved that this explanation is the most likely one, by assuming the world is generated by an unknown computer program. That is to say the probability distribution of all computer programs that output the observations favors the shortest one.
Prediction is done using a completely Bayesian framework. The universal prior is calculated for all computable sequences—this is the universal a priori probability distribution; no computable hypothesis will have a zero probability. This means that Bayes rule of causation can be used in predicting the continuation of any particular computable sequence.
This document discusses solving NP-complete problems using graph embodiment on a quantum computation paradigm. It proposes a method for solving relational database queries by transforming the query problem and results into a labeled directed graph, where the results are derived as the maximum clique of the graph. The document suggests that if this method can be used to solve queries on both classical and quantum computers using graph embodiment, then P could equal NP. However, if it cannot be solved on both paradigms, then the P vs NP problem cannot be resolved with current computation models and new mathematical axioms would be needed.
This document provides an overview of asymptotic analysis and Landau notation. It discusses justifying algorithm analysis mathematically rather than experimentally. Examples are given to show that two functions may appear different but have the same asymptotic growth rate. Landau symbols like O, Ω, o and Θ are introduced to describe asymptotic upper and lower bounds between functions. Big-Q represents asymptotic equivalence between functions, meaning one can be improved over the other with a faster computer.
The document discusses the halting problem, which asks if there are problems for which no algorithm exists. Alan Turing proved that non-computable problems exist by introducing the halting problem - determining if a given program will ever finish running. The document shows that no procedure can solve the halting problem by considering a paradoxical program: if it says the program halts, it leads to a contradiction, and if it says the program doesn't halt, it also leads to a contradiction. This proves the halting problem is non-computable, as any procedure to solve it would have to either give the wrong answer or not terminate. A formal model of computation is needed to give a rigorous proof.
This document provides an introduction to probabilistic programming using PyMC3 and Edward. It discusses the differences between frequentist and Bayesian approaches. Bayesian inference is well-suited for problems with small datasets, where frequentist estimates have high variance. The document covers Markov chain Monte Carlo (MCMC) techniques like Metropolis-Hastings and Gibbs sampling that are used to perform Bayesian inference. It also discusses variational inference as an alternative to MCMC. Real-life examples of probabilistic modeling of climate data and education metrics are presented. The document concludes with tips for getting started with probabilistic programming.
The document provides an overview of the topics covered in a discrete mathematics course, including methods of proof, algorithms, growth of functions, complexity of algorithms, integers and division, and number theory applications. It discusses different methods of proof like direct proof, proof by contradiction, and proof by equivalence. It also describes algorithms for finding the maximum element in a sequence, linear search, binary search, and sorting algorithms like bubble sort and insertion sort. It provides pseudocode and sample programs for these algorithms.
This document provides an overview of NP-completeness and polynomial time reductions. It defines the classes P and NP, and explains that the core question is whether P=NP. NP-complete problems are the hardest problems in NP, and to prove a problem is NP-complete it must be shown to be in NP and there must be a polynomial time reduction from a known NP-complete problem like 3-SAT. Examples of NP-complete problems discussed include Clique, Independent Set, and Minesweeper. The document outlines the method for proving a problem is NP-complete using a reduction from 3-SAT.
1. Exact inference in Bayesian networks is NP-hard in the worst case, so approximation techniques are needed for large networks.
2. Major approximation techniques include variational methods like mean-field approximation, sampling methods like Monte Carlo Markov Chain, and bounded cutset conditioning.
3. Variational methods introduce variational parameters to minimize the distance between the approximate and true distributions. Sampling methods draw random samples to estimate probabilities. Bounded cutset conditioning breaks loops by instantiating subsets of variables.
The document summarizes the design of renovating the first two floors and rooftop of the Transcontinental Hotel in Oakland, CA. It includes a design statement focusing on incorporating industrial elements representing the area's railroad history. It also includes an analysis of the site noting the location in downtown Oakland near public transportation and cultural attractions, as well as details about the climate, demographics of the area, and logistics of the building site.
El documento describe el papel del ingeniero como solucionador de problemas. Los ingenieros identifican necesidades y carencias para desarrollar dispositivos, estructuras o procesos que las satisfagan de manera original, confiable y económica. Trabajan con especialistas de diversas áreas para crear y supervisar proyectos mediante el uso de su ingenio, juicio y capacidad creativa. Además, los ingenieros realizan la mayor parte de su trabajo de manera abstracta, por ejemplo, con el diseño y supervisión de una construcción.
This document advertises a two-day corporate training program on making successful presentations. It notes that 95% of presentations currently "suck" but can be improved by mastering three things: message, visual storytelling, and delivery method. The training will help attendees transform bad presentations into good ones by learning key elements of presentation design and ecosystem. Those who sign up will get skills to effectively present tasks, understand design principles, and receive early bird discounts by calling now.
Esquema comparativo del rol del docente y el estudiante tradicional y actual.Fe Maria Holguin Bencosme
En este trabajo presento dos esquemas comparativos del rol del docente tradicional y el actual y otro sobre el rol del estudiante tradicional y el actual
This document introduces the concept of NP-completeness. It discusses that while some problems like shortest paths, minimum spanning trees, and bipartite matching have efficient polynomial time algorithms, other problems like satisfiability (SAT), the travelling salesman problem (TSP), integer linear programming (ILP), and set cover have only exponential time algorithms. It defines the class NP as problems that can be solved by a non-deterministic Turing machine in polynomial time. It states that if any NP-complete problem could be solved in polynomial time, then P would equal NP. Problems are NP-hard if all problems in NP can be reduced to them in polynomial time, and NP-complete if they are both in NP and NP-
This document discusses the limits of computation. It distinguishes between intractable problems that take an impractical amount of time to solve versus truly unsolvable problems. It describes different complexity classes based on how fast the number of operations grows with input size. Hard problems like the traveling salesman problem are inherently difficult even with faster computers. Reductions show relationships between problem difficulties. The halting problem and incompleteness theorems prove certain logical and mathematical questions cannot be answered algorithmically.
This document discusses the limits of computation. It distinguishes between intractable problems that take an impractical amount of time to solve versus truly unsolvable problems. It describes different complexity classes based on how fast the number of operations grows with input size. Hard problems like the traveling salesman problem are in NP and are inherently difficult even with faster computers or quantum computing. Reductions show relationships between problem difficulties. The halting problem and Godel's incompleteness theorems establish fundamental limits of computation and logical systems.
This document discusses time and space complexity analysis of algorithms. It analyzes the time complexity of bubble sort, which is O(n^2) as each pass through the array requires n-1 comparisons and there are n passes needed. Space complexity is typically a secondary concern to time complexity. Time complexity analysis allows comparison of algorithms to determine efficiency and whether an algorithm will complete in a reasonable time for a given input size. NP-complete problems cannot be solved in polynomial time but can be verified in polynomial time.
This document summarizes various algorithms topics including pattern matching, matrix multiplication, graph algorithms, algebraic problems, and NP-hard and NP-complete problems. It provides details on pattern matching techniques in computer science including exact string matching and applications. It also describes how to find the most efficient way to multiply a sequence of matrices by considering different orders of operations. Graph algorithms are introduced including directed and undirected graphs. Popular design approaches for algebraic problems such as divide-and-conquer, greedy techniques, and dynamic programming are outlined. Finally, the key differences between NP, NP-hard, and NP-complete problems are defined.
P, NP, NP-Complete, and NP-Hard
Reductionism in Algorithms
NP-Completeness and Cooks Theorem
NP-Complete and NP-Hard Problems
Travelling Salesman Problem (TSP)
Travelling Salesman Problem (TSP) - Approximation Algorithms
PRIMES is in P - (A hope for NP problems in P)
Millennium Problems
Conclusions
Solomonoff's theory of inductive inference is Ray Solomonoff's mathematical formalization of Occam's razor. It explains observations of the world by the smallest computer program that outputs those observations. Solomonoff proved that this explanation is the most likely one, by assuming the world is generated by an unknown computer program. That is to say the probability distribution of all computer programs that output the observations favors the shortest one.
Prediction is done using a completely Bayesian framework. The universal prior is calculated for all computable sequences—this is the universal a priori probability distribution; no computable hypothesis will have a zero probability. This means that Bayes rule of causation can be used in predicting the continuation of any particular computable sequence.
This document discusses solving NP-complete problems using graph embodiment on a quantum computation paradigm. It proposes a method for solving relational database queries by transforming the query problem and results into a labeled directed graph, where the results are derived as the maximum clique of the graph. The document suggests that if this method can be used to solve queries on both classical and quantum computers using graph embodiment, then P could equal NP. However, if it cannot be solved on both paradigms, then the P vs NP problem cannot be resolved with current computation models and new mathematical axioms would be needed.
This document provides an overview of asymptotic analysis and Landau notation. It discusses justifying algorithm analysis mathematically rather than experimentally. Examples are given to show that two functions may appear different but have the same asymptotic growth rate. Landau symbols like O, Ω, o and Θ are introduced to describe asymptotic upper and lower bounds between functions. Big-Q represents asymptotic equivalence between functions, meaning one can be improved over the other with a faster computer.
The document discusses the halting problem, which asks if there are problems for which no algorithm exists. Alan Turing proved that non-computable problems exist by introducing the halting problem - determining if a given program will ever finish running. The document shows that no procedure can solve the halting problem by considering a paradoxical program: if it says the program halts, it leads to a contradiction, and if it says the program doesn't halt, it also leads to a contradiction. This proves the halting problem is non-computable, as any procedure to solve it would have to either give the wrong answer or not terminate. A formal model of computation is needed to give a rigorous proof.
This document provides an introduction to probabilistic programming using PyMC3 and Edward. It discusses the differences between frequentist and Bayesian approaches. Bayesian inference is well-suited for problems with small datasets, where frequentist estimates have high variance. The document covers Markov chain Monte Carlo (MCMC) techniques like Metropolis-Hastings and Gibbs sampling that are used to perform Bayesian inference. It also discusses variational inference as an alternative to MCMC. Real-life examples of probabilistic modeling of climate data and education metrics are presented. The document concludes with tips for getting started with probabilistic programming.
The document provides an overview of the topics covered in a discrete mathematics course, including methods of proof, algorithms, growth of functions, complexity of algorithms, integers and division, and number theory applications. It discusses different methods of proof like direct proof, proof by contradiction, and proof by equivalence. It also describes algorithms for finding the maximum element in a sequence, linear search, binary search, and sorting algorithms like bubble sort and insertion sort. It provides pseudocode and sample programs for these algorithms.
This document provides an overview of NP-completeness and polynomial time reductions. It defines the classes P and NP, and explains that the core question is whether P=NP. NP-complete problems are the hardest problems in NP, and to prove a problem is NP-complete it must be shown to be in NP and there must be a polynomial time reduction from a known NP-complete problem like 3-SAT. Examples of NP-complete problems discussed include Clique, Independent Set, and Minesweeper. The document outlines the method for proving a problem is NP-complete using a reduction from 3-SAT.
1. Exact inference in Bayesian networks is NP-hard in the worst case, so approximation techniques are needed for large networks.
2. Major approximation techniques include variational methods like mean-field approximation, sampling methods like Monte Carlo Markov Chain, and bounded cutset conditioning.
3. Variational methods introduce variational parameters to minimize the distance between the approximate and true distributions. Sampling methods draw random samples to estimate probabilities. Bounded cutset conditioning breaks loops by instantiating subsets of variables.
1. Exact inference in Bayesian networks is NP-hard in the worst case, so approximation techniques are needed for large networks.
2. Major approximation techniques include variational methods like mean-field approximation, sampling methods like Monte Carlo Markov Chain, and bounded cutset conditioning.
3. Variational methods introduce variational parameters to minimize the distance between the approximate and true distributions. Sampling methods draw random samples to estimate probabilities. Bounded cutset conditioning breaks loops by instantiating subsets of variables.
The document discusses topics in discrete mathematics including methods of proof, algorithms, and number theory. It provides overviews and examples of different types of proofs like direct proof, proof by contradiction, and proof by equivalence. It also discusses algorithms like searching algorithms, sorting algorithms, analyzing their properties, and providing pseudocode examples. Specific algorithms discussed include linear search, binary search, bubble sort, and insertion sort.
The document discusses an introduction to basic concepts in computational complexity theory presented by a PhD student. It covers definitions of algorithms, asymptotic analysis using Big O notation, and computational models including Turing machines, multi-tape Turing machines, non-deterministic Turing machines, and oracle Turing machines. It also introduces complexity classes such as P, NP, NTIME and discusses how different computational models are equivalent in computational power.
This document discusses the complexity of primality testing. It begins by explaining what prime and composite numbers are, and why primality testing is important for applications like public-key cryptography that rely on the assumption that factoring large composite numbers is computationally difficult. It then covers algorithms for primality testing like the Monte Carlo algorithm and discusses their runtime complexities. It shows that while testing if a number is composite can be done in polynomial time, general number factoring is believed to require exponential time, making primality testing an important problem.
Similar to InstantInsanityProgrammingAssignment (20)
3. Python implementation of pseudocode:
1. def compareIt(arr, genList):
2. for i in xrange(len(arr[0])):
3. genList[i] = arr[0][i] #store the first pair
4. print("First stored pair:",genList[i])
5. recurse(arr, 1, genList) # recurse to the next line
6.
7. def recurse(arr, ind, genList):
8. if ind == 40:
9. print ("Solution is: ",genList)
10. else:
11. #print("hit else")
12. for i in xrange(len(arr[ind])):
13. #print("i is ",i)
14. #print ("array pair: ",arr[ind][i])
15. pair = arr[ind][i] #select a pair
16. for i in xrange(ind): #select each previous line in genList
17. #print("current genList is: ")
18. for r in xrange(ind):
19. print(genList[r])
20. #print("pair[0] is ", pair[0], "genList[i][0] is: ", genList[i][0])
21. if pair[0] != genList[i][0]:
22. #no problem, check other item
23. if pair[1] != genList[i][1]:
24. #no problem, add pair
25. genList[i+1] = pair
26. #print("Recursed")
27. recurse(arr, ind+1, genList)
28. else:
29. #problem, don't add
30. c = 0
31. #endif
32. else:
33. #problem, don't add
34. c = 0
35. #endif
36. #endfor
37. #endfor
38. #endif
39.#end recurse
Analysis
The time complexity of this algorithm is O(n^4). In order to reduce the actual execution
time of the program, a Hadoop cluster could be used with an advanced message queue
protocol such as RabbitMQ. RabbitMQ can be used to distribute bits and pieces of the required
computation to separate machines in each cluster. Hadoop is used for distributing processing
power and computations of a large data set throughout multiple clusters of computers. The
execution time of an optimized algorithm then relies heavily on how much computational