High order approximation - PowerPoint PPT Presentation

Approximation algorithms aim to find near-optimal solutions for optimization problems, with the performance ratio indicating how close the algorithm's solution is to the optimal solution. The terminology used in approximation algorithms includes P (optimization problem), C (approximation algorithm),

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Delve into the fascinating world of the particle-on-a-ring approximation in chemistry, exploring concepts like quantum quantization of energy levels, De Broglie approach, Schrödinger equation, and its relevance to the electronic structure of molecules. Discover how confining particles to a ring lea

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This content delves into the concepts of gradient descent and second-order methods in optimization. Gradient descent is a first-order method utilizing the first-order Taylor expansion, while second-order methods consider the first three terms of the multivariate Taylor series. Second-order methods l

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Exploring learning-based low-rank approximations and linear sketches in matrices, including techniques like dimensionality reduction, regression, and streaming algorithms. Discusses the use of random matrices, sparse matrices, and the concept of low-rank approximation through singular value decompos

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Grigory Yaroslavtsev and collaborators present an improved approximation for the Directed Spanner Problem, exploring the concept of k-Spanner in directed graphs. The research delves into finding the sparsest k-spanner, preserving distances and discussing applications, including simulating synchroniz

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Structural components subjected to multi-axial cyclic loading can be analyzed for low-cycle fatigue using notch approximation. By transforming elastic response into an elastoplastic state, the computation time is reduced, and fatigue evaluation is done based on the Smith-Watson-Topper model. Strain-

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This paper proposes a method for dimensionality reduction based on functional approximation using Gaussian basis functions. Nonlinear Gauss weights are utilized to train a least squares support vector machine (LS-SVM) model, with further variable selection using forward-backward methodology. The met

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Explore the intricate relationship between demand planning and order management, crucial for optimizing customer order fulfillment cycles. Learn key principles, tools, and techniques to enhance communication and manage demand effectively, along with contemporary approaches and e-commerce fulfillment

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This piece discusses approximation algorithms for stochastic optimization problems, focusing on modeling uncertainty in inputs, adapting to stochastic predictions, and exploring different optimization themes. It covers topics such as weakening the adversary in online stochastic optimization, two-sta

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Push beyond traditional NLP models like logistic regression and PCFG with approximation-aware training. Explore factor graphs, BP algorithm, and fancier models to improve predictions. Learn how to tweak algorithms, tune parameters, and build custom models for machine learning in NLP.

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Strategies for dealing with engineering-to-order product/system configuration including assemble-to-order, make-to-order, configure-to-order, and engineer-to-order approaches. Highlights different levels of diversity, challenges, and solutions in personalized system configurations.

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ACCEPT is an Approximate C Compiler framework that allows programmers to designate which parts of the code can be approximated for energy and performance trade-offs. It automatically determines the best approximation parameters, identifies safe approximation areas, and can utilize FPGA for hardware

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Regret-bounded vehicle routing problems aim to minimize client delays by considering client-centric views and bounded client regret measures. This involves measuring waiting times relative to shortest-path distances from the starting depot. Additive and multiplicative regret measures are used to add

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This research explores regret-bounded vehicle routing problems (VRPs) where the focus is on minimizing client delays based on their distances from the starting depot. The study introduces a client-centric view to measure regret and devises algorithms for both additive and multiplicative regret-based

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Mitigating memory and bandwidth walls, this research extends rollback-free value prediction to GPUs, achieving up to 2x improvement in energy and performance while maintaining 10% quality degradation. Utilizing microarchitecturally-triggered approximation to predict missed loads, this work focuses o

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This research presents LP-Based Algorithms for the Capacitated Facility Location problem, aiming to choose facilities to open and assign clients to these facilities efficiently. It discusses solving the problem using metric costs, client and facility sets, capacities, and opening costs. The research

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The content covers iterative root approximation using natural logarithm in solving equations. It explores finding roots by iterative formulas and demonstrates calculations to reach approximate values. The process involves selecting intervals to show correct values and ensuring continuity for accurat

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This research discusses hierarchy-based algorithms for minimizing makespan in scheduling problems with precedence and communication constraints. Various approximation techniques, open questions in scheduling theory, and QPTAS for different settings are explored, including the possibility of beating

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Explore correlation clustering, a powerful clustering method using qualitative similarities. Learn about LP rounding techniques, approximation algorithms, NP-hardness, and practical applications like document deduplication. Discover insights from leading researchers and tutorials on theory and pract

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This research explores the use of quasi-interpolation techniques to approximate functions from scattered data points in high dimensions. It discusses the interpretation of Moving Least Squares (MLS) for direct pointwise approximation of differential operators, handling singularities, and improving a

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Explore characteristics and properties of good approximation operators, such as quasi-interpolation and Moving Least-Squares (MLS), for approximating functions with singularities and near boundaries. Learn about direct approximation of local functionals and high-order approximation methods for non-s

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Vortex transport by uniform flow case study presented at the First International High-Order CFD Workshop in 2012. It focuses on assessing the efficiency of high-order methods for LES/DES of turbulent flows and comparing them with state-of-the-art 2nd order FV algorithms. The case involves a very low

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The research discusses LP-based approximation algorithms for solving Multi-Vehicle Minimum Latency Problems, focusing on minimizing waiting times for vehicles visiting clients starting from a depot. Various cases, including single- and multi-depot scenarios, are explored, and significant improvement

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Uncover the world of approximation algorithms in the realm of Design & Analysis of Algorithms. Delve into topics like 7/8 approximation for Max-3-SAT, Quick Sort with random pivot, and the 7/8 approximation for Max-3-CNF with in-depth explanations and proofs of the algorithms involved.

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Discussed are stochastic optimization problems, including convex-concave saddle point problems. Solutions like stochastic approximation and sample average approximation are analyzed. Theoretical assumptions and notations are explained, along with classical SA algorithms. Further discussions delve in

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Delve into the fundamentals of Density Functional Theory (DFT) and Time-Dependent Density Functional Theory (TDDFT) through the works of Hardy Gross, a prominent researcher at Max-Planck Institute of Microstructure Physics. Explore the Hamiltonian of condensed matter systems, including atoms, molecu

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Delve into the realm of approximation algorithms to solve NP-hard optimization problems efficiently and effectively. Explore the concept of NP-hardness, approximation ratios, and strategies for finding near-optimal solutions. Understand the trade-offs between accuracy and complexity in algorithm des

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Dive into the world of approximation algorithms for NP-complete problems like Min Vertex Cover with a focus on providing good but not optimal solutions. Explore various approximation techniques and algorithms to tackle these challenging computational problems efficiently.

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In the study of approximation theory, interpolation plays a crucial role in representing data points using polynomials and splines. This content discusses the concepts of interpolation polynomials, including Newton's Divided Difference and Lagrange Polynomials, as well as spline interpolation techni

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Delve into the world of approximate computing with insights from "Programming Abstractions for Approximate Computing" by Michael Carbin and team. Discover the challenges of specifying approximations, verifying program results, reproducing failures, and adapting to changing assumptions. Learn fundame

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The Group Steiner Tree Problem involves finding a tree rooted at a central vertex that connects transistors located at different ports in a VLSI circuit. Various approximation methods and degree bounds have been explored, with a focus on low degrees for efficient layout and routing. Known approximat

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Dive into Sturm-Liouville equations, exploring eigenvalues, eigenfunctions, and approximation techniques such as Rayleigh-Ritz and Green's function solutions. Learn about the properties, orthogonality, and completeness of eigenfunctions. Discover various boundary conditions and the formal completene

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Explore the comparison of Rayleigh-Jeans law, Wien approximation, and Planck's law at 8 mK temperature. Understand how classical physics and quantum mechanics intersect in describing black-body radiation.

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Explore the challenges and solutions of network design problems through approximation algorithms for non-uniform buy-at-bulk scenarios. Discover the complexities of connecting nodes efficiently while minimizing costs associated with cables and bandwidth demands.

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Learn about the concept of low-rank matrix approximation in text mining, including solving with Latent Semantic Analysis (LSA) using Singular Value Decomposition (SVD) and understanding the challenges of Natural Language Processing (NLP) due to ambiguities and common sense reasoning.

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Learn about Adaptive CSMA under the SINR model and its fast convergence method through Bethe Approximation. This study presents a scalable approach for computing CSMA parameters to achieve desired service rates with implications on convergence rate, accuracy, and robustness to network changes.

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Learn about approximation methods for higher-order transfer functions in control systems, including first-order plus time delay (FOPTD) and second-order plus time delay (SOPTD) models. Discover techniques such as Taylor series expansion, pad approximations, and Skogestad's half rule for simplifying

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Delve into the concept of compulsory approximation in various technology domains highlighted by Adrian Sampson. Discover the benefits, challenges, and application of compulsory approximation techniques in machine learning and parallel computing methods like Hogwild. Uncover how existing approximatio

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Explore the efficient computation of multiple functions over distributed streams in a dynamic data environment to avoid centralizing and re-running costs. This research highlights the challenges and solutions for processing distributed streams, emphasizing the importance of simultaneous approximatio

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Explore the evolution and current status of approximation algorithms, from past popularity to present challenges in acceptance. Delve into open problems in various fields, including graph coloring, scheduling, and minimum Steiner forest, shedding light on unresolved complexities in the realm of comp

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