1. Cook's theorem shows that the satisfiability problem (SAT) is NP-complete. SAT is the problem of determining if there exists an assignment of true/false values to variables in a boolean formula that makes the formula evaluate to true.
2. The document outlines Cook's proof, which constructs a polynomial-time reduction from any NP language to SAT. It does this by encoding the computation of a non-deterministic Turing machine as a boolean formula.
3. The proof shows that restricted versions of SAT, where the boolean formulas are in conjunctive normal form (CSAT) or 3-conjunctive normal form (3SAT), are also NP-complete.
The document defines equivalence relation and provides two examples. It then proves some properties about equivalence relations on real numbers. It proves mathematical induction for a formula relating sums and cubes. It proves properties about spanning trees and connectivity in graphs. It also proves that congruence modulo m is an equivalence relation by showing it satisfies the properties of reflexivity, symmetry, and transitivity. Finally, it explains the concepts of transition graphs and transition tables for representing finite state automata.
The document discusses minterms, maxterms, and their representation using shorthand notation in digital logic. It also covers the steps to obtain the shorthand notation for minterms and maxterms. Standard forms such as SOP and POS are introduced along with methods to simplify boolean functions into canonical forms using Karnaugh maps. The implementation of boolean functions using NAND and NOR gates is also described through examples.
I am Martin J. I am a Stochastic Processes Assignment Expert at excelhomeworkhelp.com. I hold a Ph.D. in Stochastic Processes, from Minnesota, USA. I have been helping students with their homework for the past 7 years. I solve assignments related to Stochastic Processes. Visit excelhomeworkhelp.com or email info@excelhomeworkhelp.com. You can also call on +1 678 648 4277 for any assistance with Stochastic Processes Assignments.
This document provides an overview of modular arithmetic and its applications. It begins with definitions of modular equivalence and congruence classes. Applications discussed include hashing to store records efficiently, generating pseudorandom numbers, and calculating ISBN numbers and Easter dates. The Chinese Remainder Theorem and solving linear congruences are also covered. The document concludes with a method for performing arithmetic on large integers using modular arithmetic.
1) Sorting algorithms are useful for keeping data ordered to aid other algorithms like searching. Finding the optimal order for matrix multiplication can greatly reduce computation time when transformations don't need to be performed immediately.
2) The inverse of a matrix is unique. The product of two lower triangular matrices is lower triangular. The inverse of a lower triangular matrix is also lower triangular.
3) Gaussian elimination preserves the inverse of a matrix up to row operations on the inverse. If a matrix has only real elements, then its inverse and cofactors must also be real.
A Stochastic Limit Approach To The SAT ProblemValerie Felton
This document proposes using quantum adaptive stochastic systems to solve NP-complete problems like SAT in polynomial time. It summarizes the SAT problem, discusses existing quantum algorithms for it, and introduces the concept of using channels instead of just unitary operators to model more realistic quantum computations. It argues that combining a quantum SAT algorithm with a stochastic limit approach using channels could provide a method to distinguish computation results that existing algorithms cannot, potentially solving NP-complete problems efficiently.
Boolean algebra is an algebra of logic developed by George Boole between 1815-1864 to represent logical statements as an algebra of true and false. It is used to perform logical operations in digital computers by representing true as 1 and false as 0. The fundamental logical operators are AND, OR, and NOT. Boolean algebra expressions can be represented in sum of products (SOP) form or product of sums (POS) form and minimized using algebraic rules or Karnaugh maps. Minterms and maxterms are used to derive Boolean functions from truth tables in canonical SOP or POS form.
I am Martin J. I am a Stochastic Processes Assignment Expert at statisticshomeworkhelper.com. I hold a Ph.D. in Stochastic Processes, from Minnesota, USA. I have been helping students with their homework for the past 7 years. I solve assignments related to Stochastic Processes. Visit statisticshomeworkhelper.com or email info@statisticshomeworkhelper.com. You can also call on +1 678 648 4277 for any assistance with Stochastic Processes Assignments.
The document defines equivalence relation and provides two examples. It then proves some properties about equivalence relations on real numbers. It proves mathematical induction for a formula relating sums and cubes. It proves properties about spanning trees and connectivity in graphs. It also proves that congruence modulo m is an equivalence relation by showing it satisfies the properties of reflexivity, symmetry, and transitivity. Finally, it explains the concepts of transition graphs and transition tables for representing finite state automata.
The document discusses minterms, maxterms, and their representation using shorthand notation in digital logic. It also covers the steps to obtain the shorthand notation for minterms and maxterms. Standard forms such as SOP and POS are introduced along with methods to simplify boolean functions into canonical forms using Karnaugh maps. The implementation of boolean functions using NAND and NOR gates is also described through examples.
I am Martin J. I am a Stochastic Processes Assignment Expert at excelhomeworkhelp.com. I hold a Ph.D. in Stochastic Processes, from Minnesota, USA. I have been helping students with their homework for the past 7 years. I solve assignments related to Stochastic Processes. Visit excelhomeworkhelp.com or email info@excelhomeworkhelp.com. You can also call on +1 678 648 4277 for any assistance with Stochastic Processes Assignments.
This document provides an overview of modular arithmetic and its applications. It begins with definitions of modular equivalence and congruence classes. Applications discussed include hashing to store records efficiently, generating pseudorandom numbers, and calculating ISBN numbers and Easter dates. The Chinese Remainder Theorem and solving linear congruences are also covered. The document concludes with a method for performing arithmetic on large integers using modular arithmetic.
1) Sorting algorithms are useful for keeping data ordered to aid other algorithms like searching. Finding the optimal order for matrix multiplication can greatly reduce computation time when transformations don't need to be performed immediately.
2) The inverse of a matrix is unique. The product of two lower triangular matrices is lower triangular. The inverse of a lower triangular matrix is also lower triangular.
3) Gaussian elimination preserves the inverse of a matrix up to row operations on the inverse. If a matrix has only real elements, then its inverse and cofactors must also be real.
A Stochastic Limit Approach To The SAT ProblemValerie Felton
This document proposes using quantum adaptive stochastic systems to solve NP-complete problems like SAT in polynomial time. It summarizes the SAT problem, discusses existing quantum algorithms for it, and introduces the concept of using channels instead of just unitary operators to model more realistic quantum computations. It argues that combining a quantum SAT algorithm with a stochastic limit approach using channels could provide a method to distinguish computation results that existing algorithms cannot, potentially solving NP-complete problems efficiently.
Boolean algebra is an algebra of logic developed by George Boole between 1815-1864 to represent logical statements as an algebra of true and false. It is used to perform logical operations in digital computers by representing true as 1 and false as 0. The fundamental logical operators are AND, OR, and NOT. Boolean algebra expressions can be represented in sum of products (SOP) form or product of sums (POS) form and minimized using algebraic rules or Karnaugh maps. Minterms and maxterms are used to derive Boolean functions from truth tables in canonical SOP or POS form.
I am Martin J. I am a Stochastic Processes Assignment Expert at statisticshomeworkhelper.com. I hold a Ph.D. in Stochastic Processes, from Minnesota, USA. I have been helping students with their homework for the past 7 years. I solve assignments related to Stochastic Processes. Visit statisticshomeworkhelper.com or email info@statisticshomeworkhelper.com. You can also call on +1 678 648 4277 for any assistance with Stochastic Processes Assignments.
Skiena algorithm 2007 lecture21 other reductionzukun
This document discusses reductions and NP-completeness. It summarizes how reductions can be used to prove that one problem is at least as hard as another by translating instances of one problem into instances of the other. It then gives examples of reductions between several problems like vertex cover, integer partition, satisfiability, and integer programming to prove them NP-complete.
I am George P. I am a Stochastic Processes Assignment Expert at statisticsassignmenthelp.com. I hold a Master's in Statistics, Malacca, Malaysia. I have been helping students with their homework for the past 8 years. I solve assignments related to Stochastic Processes.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Stochastic Processes Assignments.
Boolean algebra is a system of logical operations developed by George Boole in the 19th century. It represents logical statements as expressions of binary variables, where true is represented by 1 and false by 0. The fundamental logical operations are AND, OR, and NOT. Boolean algebra finds application in digital circuits, where it is used to perform logical operations using electrical switches representing 1s and 0s. Boolean functions can be expressed in canonical forms such as Sum of Products (SOP) or Product of Sum (POS) and simplified using algebraic rules or Karnaugh maps to minimize the number of logic gates required.
I am Charles B. I am a Programming Exam Expert at programmingexamhelp.com. I hold a Ph.D. in Programming Texas University, USA. I have been helping students with their exams for the past 9 years. You can hire me to take your exam in Programming.
Visit programmingexamhelp.com or email support@programmingexamhelp.com. You can also call on +1 678 648 4277 for any assistance with the Programming Exam.
George Boole developed Boolean algebra between 1815-1864 as an algebra of logic to represent logical statements as algebraic expressions. Boolean algebra uses two values, True and False (represented by 1 and 0 respectively) and logical operators like AND, OR, and NOT to represent logical statements and perform operations on them. Boolean algebra finds application in digital circuits where it is used to perform logical operations. Canonical forms and Karnaugh maps are techniques used to simplify Boolean expressions into their minimal forms.
This topic on matrix theory and linear algebra is fundamental. The focus is on subjects like systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices that will be helpful in other fields.
Visit mathsassignmenthelp.com or email info@mathsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with linear algebra assignment.
I am Martina J. I am a Signals and Systems Assignment Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, from the University of Maryland. I have been helping students with their assignments for the past 9 years. I solve assignments related to Signals and Systems.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Signals and Systems assignments.
The document discusses the theory of NP-completeness. It begins by classifying problems as solvable, unsolvable, tractable, or intractable. It then defines deterministic and nondeterministic algorithms, and how nondeterministic algorithms can be expressed. The document introduces the complexity classes P and NP. It discusses reducing one problem to another to prove NP-completeness via transitivity. Several classic NP-complete problems are proven to be NP-complete, such as 3SAT, 3-coloring, and subset sum. The document also discusses how to cope with NP-complete problems in practice by sacrificing optimality, generality, or efficiency.
This document discusses recursive functions and growth functions. It defines recursive functions as functions defined in terms of previous values using initial conditions and recurrence relations. Examples of recursively defined sequences like Fibonacci are provided. Growth functions are defined using big-O notation to analyze how functions grow relative to each other. Common proof techniques like direct proof, indirect proof, proof by contradiction and induction are described. Walks and paths in trees are defined as sequences of alternating vertices and edges that begin and end at vertices. Deterministic finite automata are defined as 5-tuples with states, input alphabet, transition function, start state, and set of accepting/final states.
I am Grey Nolan. Currently associated with matlabassignmentexperts.com as an assignment helper. After completing my master's from the University of British Columbia, I was in search for an opportunity that expands my area of knowledge hence I decided to help students with their Signals and Systems assignments. I have written several assignments till date to help students overcome numerous difficulties they face in Signals and Systems Assignments.
This dissertation defense presentation summarizes Sawinder Pal Kaur's PhD dissertation on the existence and properties of positive solutions to certain nonlinear eigenvalue problems involving multi-dimensional arrays. The presentation outlines Kaur's work on proving the existence of a unique positive solution for nonlinear transformations in two and three variables, including the discretization of the Gross-Pitaevskii equation. It also summarizes the properties of these solutions, such as continuity and asymptotic behavior. The proofs utilize tools like Kronecker products, Perron-Frobenius theory, and the Kantorovich fixed point theorem.
I am Ben R. I am a Statistics Assignment Expert at statisticshomeworkhelper.com. I hold a Ph.D. in Statistics, from University of Denver, USA. I have been helping students with their homework for the past 5 years. I solve assignments related to Statistics.
Visit statisticshomeworkhelper.com or email info@statisticshomeworkhelper.com.
You can also call on +1 678 648 4277 for any assistance with Statistics Assignment.
This document contains exercises related to dynamical systems and periodic points. It includes the following summaries:
1. The doubling map on the circle has 2n-1 periodic points of period n. Its periodic points are dense.
2. The map f(x)=|x-2| has a fixed point at x=1. Other periodic and pre-periodic points are [0,2]\{1\} of period 2 and (-∞,0)∪(2,+∞) which are pre-periodic.
3. Expanding maps of the circle are topologically mixing since intervals get longer under iteration, eventually covering the entire circle.
I am Falid B. I am a Mathematical Statistics Assignment Expert at excelhomeworkhelp.com. I hold a Master's in Statistics, from George Town, Malaysia. I have been helping students with their assignments for the past 6 years. I solved an assignment related to Mathematical Statistics.
Visit excelhomeworkhelp.com or email info@excelhomeworkhelp.com. You can also call on +1 678 648 4277 for any assistance with Mathematical Statistics Assignment.
The mobius function and the mobius inversion formulaBenjJamiesonDuag
This document discusses the Mobius function and the Mobius inversion formula. It defines the Mobius function μ(n) which investigates integers in terms of their prime decomposition. It then defines the Mobius inversion formula which determines the values of a function f at an integer in terms of its summatory function F. It proves several theorems about the Mobius function and Mobius inversion formula, including that the Mobius function is multiplicative and that the Mobius inversion formula can be used to invert summatory functions and retrieve the original function.
1) Interpolation is a process that defines a function to connect data points by determining a unique polynomial curve that passes through the specified points.
2) Cubic spline interpolation fits piecewise cubic polynomials to pass through given control points, with the curves matching positions and derivatives at the points.
3) Hermite interpolation also uses piecewise cubics but specifies the tangent at each control point, allowing local control of the curve sections. Boundary conditions define the curves to match positions and specified tangent derivatives at endpoints.
1. The document discusses basic probability concepts like sample spaces, events, and probability laws. It also covers random variables, probability distributions, and functions of random variables.
2. Stochastic processes are discussed, including Poisson processes where arrivals follow an exponential distribution. Continuous-time Markov chains are modeled where the future is independent of the past given the present state.
3. Key concepts covered include moments, transforms, special distributions like binomial and normal, and steady-state probabilities for Markov chains in the long run.
This document provides an overview of maximum likelihood estimation (MLE). It discusses why MLE is needed for nonlinear models, the general steps for obtaining MLEs, and some key properties. The document also includes an example of calculating the MLE for a Poisson distribution in R. Key points covered include deriving the likelihood function, taking derivatives to find the MLE, and measuring uncertainty around the MLE estimate.
Best 20 SEO Techniques To Improve Website Visibility In SERPPixlogix Infotech
Boost your website's visibility with proven SEO techniques! Our latest blog dives into essential strategies to enhance your online presence, increase traffic, and rank higher on search engines. From keyword optimization to quality content creation, learn how to make your site stand out in the crowded digital landscape. Discover actionable tips and expert insights to elevate your SEO game.
Skiena algorithm 2007 lecture21 other reductionzukun
This document discusses reductions and NP-completeness. It summarizes how reductions can be used to prove that one problem is at least as hard as another by translating instances of one problem into instances of the other. It then gives examples of reductions between several problems like vertex cover, integer partition, satisfiability, and integer programming to prove them NP-complete.
I am George P. I am a Stochastic Processes Assignment Expert at statisticsassignmenthelp.com. I hold a Master's in Statistics, Malacca, Malaysia. I have been helping students with their homework for the past 8 years. I solve assignments related to Stochastic Processes.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Stochastic Processes Assignments.
Boolean algebra is a system of logical operations developed by George Boole in the 19th century. It represents logical statements as expressions of binary variables, where true is represented by 1 and false by 0. The fundamental logical operations are AND, OR, and NOT. Boolean algebra finds application in digital circuits, where it is used to perform logical operations using electrical switches representing 1s and 0s. Boolean functions can be expressed in canonical forms such as Sum of Products (SOP) or Product of Sum (POS) and simplified using algebraic rules or Karnaugh maps to minimize the number of logic gates required.
I am Charles B. I am a Programming Exam Expert at programmingexamhelp.com. I hold a Ph.D. in Programming Texas University, USA. I have been helping students with their exams for the past 9 years. You can hire me to take your exam in Programming.
Visit programmingexamhelp.com or email support@programmingexamhelp.com. You can also call on +1 678 648 4277 for any assistance with the Programming Exam.
George Boole developed Boolean algebra between 1815-1864 as an algebra of logic to represent logical statements as algebraic expressions. Boolean algebra uses two values, True and False (represented by 1 and 0 respectively) and logical operators like AND, OR, and NOT to represent logical statements and perform operations on them. Boolean algebra finds application in digital circuits where it is used to perform logical operations. Canonical forms and Karnaugh maps are techniques used to simplify Boolean expressions into their minimal forms.
This topic on matrix theory and linear algebra is fundamental. The focus is on subjects like systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices that will be helpful in other fields.
Visit mathsassignmenthelp.com or email info@mathsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with linear algebra assignment.
I am Martina J. I am a Signals and Systems Assignment Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, from the University of Maryland. I have been helping students with their assignments for the past 9 years. I solve assignments related to Signals and Systems.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Signals and Systems assignments.
The document discusses the theory of NP-completeness. It begins by classifying problems as solvable, unsolvable, tractable, or intractable. It then defines deterministic and nondeterministic algorithms, and how nondeterministic algorithms can be expressed. The document introduces the complexity classes P and NP. It discusses reducing one problem to another to prove NP-completeness via transitivity. Several classic NP-complete problems are proven to be NP-complete, such as 3SAT, 3-coloring, and subset sum. The document also discusses how to cope with NP-complete problems in practice by sacrificing optimality, generality, or efficiency.
This document discusses recursive functions and growth functions. It defines recursive functions as functions defined in terms of previous values using initial conditions and recurrence relations. Examples of recursively defined sequences like Fibonacci are provided. Growth functions are defined using big-O notation to analyze how functions grow relative to each other. Common proof techniques like direct proof, indirect proof, proof by contradiction and induction are described. Walks and paths in trees are defined as sequences of alternating vertices and edges that begin and end at vertices. Deterministic finite automata are defined as 5-tuples with states, input alphabet, transition function, start state, and set of accepting/final states.
I am Grey Nolan. Currently associated with matlabassignmentexperts.com as an assignment helper. After completing my master's from the University of British Columbia, I was in search for an opportunity that expands my area of knowledge hence I decided to help students with their Signals and Systems assignments. I have written several assignments till date to help students overcome numerous difficulties they face in Signals and Systems Assignments.
This dissertation defense presentation summarizes Sawinder Pal Kaur's PhD dissertation on the existence and properties of positive solutions to certain nonlinear eigenvalue problems involving multi-dimensional arrays. The presentation outlines Kaur's work on proving the existence of a unique positive solution for nonlinear transformations in two and three variables, including the discretization of the Gross-Pitaevskii equation. It also summarizes the properties of these solutions, such as continuity and asymptotic behavior. The proofs utilize tools like Kronecker products, Perron-Frobenius theory, and the Kantorovich fixed point theorem.
I am Ben R. I am a Statistics Assignment Expert at statisticshomeworkhelper.com. I hold a Ph.D. in Statistics, from University of Denver, USA. I have been helping students with their homework for the past 5 years. I solve assignments related to Statistics.
Visit statisticshomeworkhelper.com or email info@statisticshomeworkhelper.com.
You can also call on +1 678 648 4277 for any assistance with Statistics Assignment.
This document contains exercises related to dynamical systems and periodic points. It includes the following summaries:
1. The doubling map on the circle has 2n-1 periodic points of period n. Its periodic points are dense.
2. The map f(x)=|x-2| has a fixed point at x=1. Other periodic and pre-periodic points are [0,2]\{1\} of period 2 and (-∞,0)∪(2,+∞) which are pre-periodic.
3. Expanding maps of the circle are topologically mixing since intervals get longer under iteration, eventually covering the entire circle.
I am Falid B. I am a Mathematical Statistics Assignment Expert at excelhomeworkhelp.com. I hold a Master's in Statistics, from George Town, Malaysia. I have been helping students with their assignments for the past 6 years. I solved an assignment related to Mathematical Statistics.
Visit excelhomeworkhelp.com or email info@excelhomeworkhelp.com. You can also call on +1 678 648 4277 for any assistance with Mathematical Statistics Assignment.
The mobius function and the mobius inversion formulaBenjJamiesonDuag
This document discusses the Mobius function and the Mobius inversion formula. It defines the Mobius function μ(n) which investigates integers in terms of their prime decomposition. It then defines the Mobius inversion formula which determines the values of a function f at an integer in terms of its summatory function F. It proves several theorems about the Mobius function and Mobius inversion formula, including that the Mobius function is multiplicative and that the Mobius inversion formula can be used to invert summatory functions and retrieve the original function.
1) Interpolation is a process that defines a function to connect data points by determining a unique polynomial curve that passes through the specified points.
2) Cubic spline interpolation fits piecewise cubic polynomials to pass through given control points, with the curves matching positions and derivatives at the points.
3) Hermite interpolation also uses piecewise cubics but specifies the tangent at each control point, allowing local control of the curve sections. Boundary conditions define the curves to match positions and specified tangent derivatives at endpoints.
1. The document discusses basic probability concepts like sample spaces, events, and probability laws. It also covers random variables, probability distributions, and functions of random variables.
2. Stochastic processes are discussed, including Poisson processes where arrivals follow an exponential distribution. Continuous-time Markov chains are modeled where the future is independent of the past given the present state.
3. Key concepts covered include moments, transforms, special distributions like binomial and normal, and steady-state probabilities for Markov chains in the long run.
This document provides an overview of maximum likelihood estimation (MLE). It discusses why MLE is needed for nonlinear models, the general steps for obtaining MLEs, and some key properties. The document also includes an example of calculating the MLE for a Poisson distribution in R. Key points covered include deriving the likelihood function, taking derivatives to find the MLE, and measuring uncertainty around the MLE estimate.
Best 20 SEO Techniques To Improve Website Visibility In SERPPixlogix Infotech
Boost your website's visibility with proven SEO techniques! Our latest blog dives into essential strategies to enhance your online presence, increase traffic, and rank higher on search engines. From keyword optimization to quality content creation, learn how to make your site stand out in the crowded digital landscape. Discover actionable tips and expert insights to elevate your SEO game.
HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-und-domino-lizenzkostenreduzierung-in-der-welt-von-dlau/
DLAU und die Lizenzen nach dem CCB- und CCX-Modell sind für viele in der HCL-Community seit letztem Jahr ein heißes Thema. Als Notes- oder Domino-Kunde haben Sie vielleicht mit unerwartet hohen Benutzerzahlen und Lizenzgebühren zu kämpfen. Sie fragen sich vielleicht, wie diese neue Art der Lizenzierung funktioniert und welchen Nutzen sie Ihnen bringt. Vor allem wollen Sie sicherlich Ihr Budget einhalten und Kosten sparen, wo immer möglich. Das verstehen wir und wir möchten Ihnen dabei helfen!
Wir erklären Ihnen, wie Sie häufige Konfigurationsprobleme lösen können, die dazu führen können, dass mehr Benutzer gezählt werden als nötig, und wie Sie überflüssige oder ungenutzte Konten identifizieren und entfernen können, um Geld zu sparen. Es gibt auch einige Ansätze, die zu unnötigen Ausgaben führen können, z. B. wenn ein Personendokument anstelle eines Mail-Ins für geteilte Mailboxen verwendet wird. Wir zeigen Ihnen solche Fälle und deren Lösungen. Und natürlich erklären wir Ihnen das neue Lizenzmodell.
Nehmen Sie an diesem Webinar teil, bei dem HCL-Ambassador Marc Thomas und Gastredner Franz Walder Ihnen diese neue Welt näherbringen. Es vermittelt Ihnen die Tools und das Know-how, um den Überblick zu bewahren. Sie werden in der Lage sein, Ihre Kosten durch eine optimierte Domino-Konfiguration zu reduzieren und auch in Zukunft gering zu halten.
Diese Themen werden behandelt
- Reduzierung der Lizenzkosten durch Auffinden und Beheben von Fehlkonfigurationen und überflüssigen Konten
- Wie funktionieren CCB- und CCX-Lizenzen wirklich?
- Verstehen des DLAU-Tools und wie man es am besten nutzt
- Tipps für häufige Problembereiche, wie z. B. Team-Postfächer, Funktions-/Testbenutzer usw.
- Praxisbeispiele und Best Practices zum sofortigen Umsetzen
leewayhertz.com-AI in predictive maintenance Use cases technologies benefits ...alexjohnson7307
Predictive maintenance is a proactive approach that anticipates equipment failures before they happen. At the forefront of this innovative strategy is Artificial Intelligence (AI), which brings unprecedented precision and efficiency. AI in predictive maintenance is transforming industries by reducing downtime, minimizing costs, and enhancing productivity.
Generating privacy-protected synthetic data using Secludy and MilvusZilliz
During this demo, the founders of Secludy will demonstrate how their system utilizes Milvus to store and manipulate embeddings for generating privacy-protected synthetic data. Their approach not only maintains the confidentiality of the original data but also enhances the utility and scalability of LLMs under privacy constraints. Attendees, including machine learning engineers, data scientists, and data managers, will witness first-hand how Secludy's integration with Milvus empowers organizations to harness the power of LLMs securely and efficiently.
5th LF Energy Power Grid Model Meet-up SlidesDanBrown980551
5th Power Grid Model Meet-up
It is with great pleasure that we extend to you an invitation to the 5th Power Grid Model Meet-up, scheduled for 6th June 2024. This event will adopt a hybrid format, allowing participants to join us either through an online Mircosoft Teams session or in person at TU/e located at Den Dolech 2, Eindhoven, Netherlands. The meet-up will be hosted by Eindhoven University of Technology (TU/e), a research university specializing in engineering science & technology.
Power Grid Model
The global energy transition is placing new and unprecedented demands on Distribution System Operators (DSOs). Alongside upgrades to grid capacity, processes such as digitization, capacity optimization, and congestion management are becoming vital for delivering reliable services.
Power Grid Model is an open source project from Linux Foundation Energy and provides a calculation engine that is increasingly essential for DSOs. It offers a standards-based foundation enabling real-time power systems analysis, simulations of electrical power grids, and sophisticated what-if analysis. In addition, it enables in-depth studies and analysis of the electrical power grid’s behavior and performance. This comprehensive model incorporates essential factors such as power generation capacity, electrical losses, voltage levels, power flows, and system stability.
Power Grid Model is currently being applied in a wide variety of use cases, including grid planning, expansion, reliability, and congestion studies. It can also help in analyzing the impact of renewable energy integration, assessing the effects of disturbances or faults, and developing strategies for grid control and optimization.
What to expect
For the upcoming meetup we are organizing, we have an exciting lineup of activities planned:
-Insightful presentations covering two practical applications of the Power Grid Model.
-An update on the latest advancements in Power Grid -Model technology during the first and second quarters of 2024.
-An interactive brainstorming session to discuss and propose new feature requests.
-An opportunity to connect with fellow Power Grid Model enthusiasts and users.
This presentation provides valuable insights into effective cost-saving techniques on AWS. Learn how to optimize your AWS resources by rightsizing, increasing elasticity, picking the right storage class, and choosing the best pricing model. Additionally, discover essential governance mechanisms to ensure continuous cost efficiency. Whether you are new to AWS or an experienced user, this presentation provides clear and practical tips to help you reduce your cloud costs and get the most out of your budget.
Taking AI to the Next Level in Manufacturing.pdfssuserfac0301
Read Taking AI to the Next Level in Manufacturing to gain insights on AI adoption in the manufacturing industry, such as:
1. How quickly AI is being implemented in manufacturing.
2. Which barriers stand in the way of AI adoption.
3. How data quality and governance form the backbone of AI.
4. Organizational processes and structures that may inhibit effective AI adoption.
6. Ideas and approaches to help build your organization's AI strategy.
A Comprehensive Guide to DeFi Development Services in 2024Intelisync
DeFi represents a paradigm shift in the financial industry. Instead of relying on traditional, centralized institutions like banks, DeFi leverages blockchain technology to create a decentralized network of financial services. This means that financial transactions can occur directly between parties, without intermediaries, using smart contracts on platforms like Ethereum.
In 2024, we are witnessing an explosion of new DeFi projects and protocols, each pushing the boundaries of what’s possible in finance.
In summary, DeFi in 2024 is not just a trend; it’s a revolution that democratizes finance, enhances security and transparency, and fosters continuous innovation. As we proceed through this presentation, we'll explore the various components and services of DeFi in detail, shedding light on how they are transforming the financial landscape.
At Intelisync, we specialize in providing comprehensive DeFi development services tailored to meet the unique needs of our clients. From smart contract development to dApp creation and security audits, we ensure that your DeFi project is built with innovation, security, and scalability in mind. Trust Intelisync to guide you through the intricate landscape of decentralized finance and unlock the full potential of blockchain technology.
Ready to take your DeFi project to the next level? Partner with Intelisync for expert DeFi development services today!
Monitoring and Managing Anomaly Detection on OpenShift.pdfTosin Akinosho
Monitoring and Managing Anomaly Detection on OpenShift
Overview
Dive into the world of anomaly detection on edge devices with our comprehensive hands-on tutorial. This SlideShare presentation will guide you through the entire process, from data collection and model training to edge deployment and real-time monitoring. Perfect for those looking to implement robust anomaly detection systems on resource-constrained IoT/edge devices.
Key Topics Covered
1. Introduction to Anomaly Detection
- Understand the fundamentals of anomaly detection and its importance in identifying unusual behavior or failures in systems.
2. Understanding Edge (IoT)
- Learn about edge computing and IoT, and how they enable real-time data processing and decision-making at the source.
3. What is ArgoCD?
- Discover ArgoCD, a declarative, GitOps continuous delivery tool for Kubernetes, and its role in deploying applications on edge devices.
4. Deployment Using ArgoCD for Edge Devices
- Step-by-step guide on deploying anomaly detection models on edge devices using ArgoCD.
5. Introduction to Apache Kafka and S3
- Explore Apache Kafka for real-time data streaming and Amazon S3 for scalable storage solutions.
6. Viewing Kafka Messages in the Data Lake
- Learn how to view and analyze Kafka messages stored in a data lake for better insights.
7. What is Prometheus?
- Get to know Prometheus, an open-source monitoring and alerting toolkit, and its application in monitoring edge devices.
8. Monitoring Application Metrics with Prometheus
- Detailed instructions on setting up Prometheus to monitor the performance and health of your anomaly detection system.
9. What is Camel K?
- Introduction to Camel K, a lightweight integration framework built on Apache Camel, designed for Kubernetes.
10. Configuring Camel K Integrations for Data Pipelines
- Learn how to configure Camel K for seamless data pipeline integrations in your anomaly detection workflow.
11. What is a Jupyter Notebook?
- Overview of Jupyter Notebooks, an open-source web application for creating and sharing documents with live code, equations, visualizations, and narrative text.
12. Jupyter Notebooks with Code Examples
- Hands-on examples and code snippets in Jupyter Notebooks to help you implement and test anomaly detection models.
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2. 2
Boolean Expressions
Boolean, or propositional-logic
expressions are built from variables and
constants using the operators AND, OR,
and NOT.
Constants are true and false, represented
by 1 and 0, respectively.
We’ll use concatenation (juxtaposition) for
AND, + for OR, - for NOT, unlike the text.
3. 3
Example: Boolean expression
(x+y)(-x + -y) is true only when
variables x and y have opposite truth
values.
Note: parentheses can be used at will,
and are needed to modify the
precedence order NOT (highest), AND,
OR.
4. 4
The Satisfiability Problem (SAT )
Study of boolean functions generally is
concerned with the set of truth
assignments (assignments of 0 or 1 to
each of the variables) that make the
function true.
NP-completeness needs only a simpler
question (SAT): does there exist a truth
assignment making the function true?
5. 5
Example: SAT
(x+y)(-x + -y) is satisfiable.
There are, in fact, two satisfying truth
assignments:
1. x=0; y=1.
2. x=1; y=0.
x(-x) is not satisfiable.
6. 6
SAT as a Language/Problem
An instance of SAT is a boolean
function.
Must be coded in a finite alphabet.
Use special symbols (, ), +, - as
themselves.
Represent the i-th variable by symbol x
followed by integer i in binary.
7. 7
Example: Encoding for SAT
(x+y)(-x + -y) would be encoded by
the string (x1+x10)(-x1+-x10)
8. 8
SAT is in NP
There is a multitape NTM that can decide if a
Boolean formula of length n is satisfiable.
The NTM takes O(n2) time along any path.
Use nondeterminism to guess a truth
assignment on a second tape.
Replace all variables by guessed truth values.
Evaluate the formula for this assignment.
Accept if true.
9. 9
Cook’s Theorem
SAT is NP-complete.
Really a stronger result: formulas may be
in conjunctive normal form (CSAT) – later.
To prove, we must show how to
construct a polytime reduction from
each language L in NP to SAT.
Start by assuming the most resticted
possible form of NTM for L (next slide).
10. 10
Assumptions About NTM for L
1. One tape only.
2. Head never moves left of the initial
position.
3. States and tape symbols are disjoint.
Key Points: States can be named
arbitrarily, and the constructions
many-tapes-to-one and two-way-
infinite-tape-to-one at most square
the time.
11. 11
More About the NTM M for L
Let p(n) be a polynomial time bound
for M.
Let w be an input of length n to M.
If M accepts w, it does so through a
sequence I0⊦I1⊦…⊦Ip(n) of p(n)+1 ID’s.
Assume trivial move from a final state.
Each ID is of length at most p(n)+1,
counting the state.
12. 12
From ID Sequences to
Boolean Functions
The Boolean function that the
transducer for L will construct from w
will have (p(n)+1)2 “variables.”
Let variable Xij represent the j-th
position of the i-th ID in the accepting
sequence for w, if there is one.
i and j each range from 0 to p(n).
13. 13
Picture of Computation as an Array
Initial ID X00 X01 … X0p(n)
X10 X11 … X1p(n)
I1
Ip(n)
Xp(n)0 Xp(n)1 … Xp(n)p(n)
.
.
.
.
.
.
14. 14
Intuition
From M and w we construct a boolean
formula that forces the X’s to represent
one of the possible ID sequences of
NTM M with input w, if it is to be
satisfiable.
It is satisfiable iff some sequence leads
to acceptance.
15. 15
From ID’s to Boolean Variables
The Xij’s are not boolean variables; they
are states and tape symbols of M.
However, we can represent the value of
each Xij by a family of Boolean variables
yijA, for each possible state or tape
symbol A.
yijA is true if and only if Xij = A.
16. 16
Points to Remember
1. The boolean function has components that
depend on n.
These must be of size polynomial in n.
2. Other pieces depend only on M.
No matter how many states/symbols m has,
these are of constant size.
3. Any logical formula about a set of
variables whose size is independent of n
can be written somehow.
17. 17
Designing the Function
We want the Boolean function that
describes the Xij’s to be satisfiable if
and only if the NTM M accepts w.
Four conditions:
1. Unique: only one symbol per position.
2. Starts right: initial ID is q0w.
3. Moves right: each ID follows from the
next by a move of M.
4. Finishes right: M accepts.
18. 18
Unique
Take the AND over all i, j, Y, and Z of
(-yijY+ -yijZ).
That is, it is not possible for Xij to be
both symbols Y and Z.
19. 19
Starts Right
The Boolean Function needs to assert
that the first ID is the correct one with
w = a1…an as input.
1. X00 = q0.
2. X0i = ai for i = 1,…, n.
3. X0i = B (blank) for i = n+1,…, p(n).
Formula is the AND of y0iZ for all i,
where Z is the symbol in position i.
20. 20
Finishes Right
Somewhere, there must be an
accepting state.
Form the OR of Boolean variables yijq,
where i and j are arbitrary and q is an
accepting state.
Note: differs from text.
21. 21
Running Time So Far
Unique requires O(p2(n)) symbols be
written.
Parentheses, signs, propositional variables.
Algorithm is easy, so it takes no more
time than O(p2(n)).
Starts Right takes O(p(n)) time.
Finishes Right takes O(p2(n)) time.
Variation
over i and j
Variation over symbols Y
and Z is independent of n,
so covered by constant.
22. 22
Running Time – (2)
Caveat: Technically, the propositions
that are output of the transducer must
be coded in a fixed alphabet, e.g.,
x10011 rather than yijA.
Thus, the time and output length have
an additional factor O(log n) because
there are O(p2(n)) variables.
But log factors do not affect polynomials
23. 23
Moves Right
Xij = Xi-1,j whenever the state is none of
Xi-1,j-1, Xi-1,j, or Xi-1,j+1.
For each i and j, construct a formula
that says (in propositional variables) the
OR of “Xij = Xi-1,j” and all yi-1,k,A where A
is a state symbol (k = i-1, i, or i+1).
Note: Xij = Xi-1,j is the OR of yijA.yi-1,jA for all
symbols A.
Works because
Unique assures
only one yijX true.
24. 24
Constraining the Next Symbol
… A B C …
B
Easy case;
must be B
… A q C …
? ? ?
Hard case; all
three may depend
on the move of M
25. 25
Moves Right – (2)
In the case where the state is nearby,
we need to write an expression that:
1. Picks one of the possible moves of the
NTM M.
2. Enforces the condition that when Xi-1,j is
the state, the values of Xi,j-1, Xi,j, and
Xi,j+1. are related to Xi-1,j-1, Xi-1,j, and
Xi-1,j+1 in a way that reflects the move.
26. 26
Example: Moves Right
Suppose δ(q, A) contains (p, B, L).
Then one option for any i, j, and C is:
C q A
p C B
If δ(q, A) contains (p, B, R), then an
option for any i, j, and C is:
C q A
C B p
27. 27
Moves Right – (3)
For each possible move, express the
constraints on the six X’s by a Boolean
formula.
For each i and j, take the OR over all
possible moves.
Take the AND over all i and j.
Small point: for edges (e.g., state at 0),
assume invisible symbols are blank.
28. 28
Running Time
We have to generate O(p2(n)) Boolean
formulas, but each is constructed from
the moves of the NTM M, which is fixed
in size, independent of the input w.
Takes time O(p2(n)) and generates an
output of that length.
Times log n, because variables must be
coded in a fixed alphabet.
29. 29
Cook’s Theorem – Finale
In time O(p2(n) log n) the transducer
produces a boolean formula, the AND of
the four components: Unique, Starts,
Finishes, and Moves Right.
If M accepts w, the ID sequence gives
us a satisfying truth assignment.
If satisfiable, the truth values tell us an
accepting computation of M.
30. 30
Picture So Far
We have one NP-complete problem: SAT.
In the future, we shall do polytime
reductions of SAT to other problems,
thereby showing them NP-complete.
Why? If we polytime reduce SAT to X,
and X is in P, then so is SAT, and
therefore so is all of NP.
31. 31
Conjunctive Normal Form
A Boolean formula is in Conjunctive
Normal Form (CNF) if it is the AND of
clauses.
Each clause is the OR of literals.
A literal is either a variable or the
negation of a variable.
Problem CSAT : is a Boolean formula in
CNF satisfiable?
33. 33
NP-Completeness of CSAT
The proof of Cook’s theorem can be
modified to produce a formula in CNF.
Unique is already the AND of clauses.
Starts Right is the AND of clauses, each
with one variable.
Finishes Right is the OR of variables,
i.e., a single clause.
34. 34
NP-Completeness of CSAT – (2)
Only Moves Right is a problem, and not
much of a problem.
It is the product of formulas for each i
and j.
Those formulas are fixed, independent
of n.
35. 35
NP-Completeness of CSAT – (3)
You can convert any formula to CNF.
It may exponentiate the size of the
formula and therefore take time to write
down that is exponential in the size of
the original formula, but these numbers
are all fixed for a given NTM M and
independent of n.
36. 36
k-SAT
If a boolean formula is in CNF and
every clause consists of exactly k
literals, we say the boolean formula is
an instance of k-SAT.
Say the formula is in k-CNF.
Example: 3-SAT formula
(x + y + z)(x + -y + z)(x + y + -z)(x + -y + -z)
37. 37
k-SAT Facts
Every boolean formula has an
equivalent CNF formula.
But the size of the CNF formula may be
exponential in the size of the original.
Not every boolean formula has a k-SAT
equivalent.
2SAT is in P; 3SAT is NP-complete.
38. 38
Proof: 2SAT is in P (Sketch)
Pick an assignment for some variable,
say x = true.
Any clause with –x forces the other
literal to be true.
Example: (-x + -y) forces y to be false.
Keep seeing what other truth values
are forced by variables with known
truth values.
39. 39
Proof – (2)
One of three things can happen:
1. You reach a contradiction (e.g., z is
forced to be both true and false).
2. You reach a point where no more
variables have their truth value forced,
but some clauses are not yet made true.
3. You reach a satisfying truth assignment.
40. 40
Proof – (3)
Case 1: (Contradiction) There can only
be a satisfying assignment if you use
the other truth value for x.
Simplify the formula by replacing x by this
truth value and repeat the process.
Case 3: You found a satisfying
assignment, so answer “yes.”
41. 41
Proof – (4)
Case 2: (You force values for some
variables, but other variables and
clauses are not affected).
Adopt these truth values, eliminate the
clauses that they satisfy, and repeat.
In Cases 1 and 2 you have spent O(n2)
time and have reduced the length of
the formula by > 1, so O(n3) total.
42. 42
3SAT
This problem is NP-complete.
Clearly it is in NP, since SAT is.
It is not true that every Boolean
formula can be converted to an
equivalent 3-CNF formula, even if we
exponentiate the size of the formula.
43. 43
3SAT – (2)
But we don’t need equivalence.
We need to reduce every CNF formula
F to some 3-CNF formula that is
satisfiable if and only if F is.
Reduction involves introducing new
variables into long clauses, so we can
split them apart.
44. 44
Reduction of CSAT to 3SAT
Let (x1+…+xn) be a clause in some
CSAT instance, with n > 4.
Note: the x’s are literals, not variables; any
of them could be negated variables.
Introduce new variables y1,…,yn-3 that
appear in no other clause.
45. 45
CSAT to 3SAT – (2)
Replace (x1+…+xn) by
(x1+x2+y1)(x3+y2+ -y1) … (xi+yi-1+ -yi-2)
… (xn-2+yn-3+ -yn-4)(xn-1+xn+ -yn-3)
If there is a satisfying assignment of
the x’s for the CSAT instance, then one
of the literals xi must be made true.
Assign yj = true if j < i-1 and yj = false
for larger j.
46. 46
CSAT to 3SAT – (3)
We are not done.
We also need to show that if the
resulting 3SAT instance is satisfiable,
then the original CSAT instance was
satisfiable.
47. 47
CSAT to 3SAT – (4)
Suppose (x1+x2+y1)(x3+y2+ -y1) …
(xn-2+yn-3+ -yn-4)(xn-1+xn+ -yn-3)
is satisfiable, but none of the x’s is true.
The first clause forces y1 = true.
Then the second clause forces y2 = true.
And so on … all the y’s must be true.
But then the last clause is false.
48. 48
CSAT to 3SAT – (5)
There is a little more to the reduction,
for handling clauses of 1 or 2 literals.
Replace (x) by (x+y1+y2) (x+y1+ -y2)
(x+ -y1+y2) (x+ -y1+ -y2).
Replace (w+x) by (w+x+y)(w+x+ -y).
Remember: the y’s are different
variables for each CNF clause.
49. 49
CSAT to 3SAT Running Time
This reduction is surely polynomial.
In fact it is linear in the length of the
CSAT instance.
Thus, we have polytime-reduced CSAT
to 3SAT.
Since CSAT is NP-complete, so is 3SAT.