Approximations - PowerPoint PPT Presentation


Approaches for Approximating Non-Linear Equations

Techniques for approximating solutions to non-linear algebraic equations involve converting the problem into a root-finding one. Seven methods such as Newton's method, bisection method, and linear interpolation are utilized with specific halting conditions. Tangent and secant lines, as well as Taylo

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A Unified Approach to Interpreting Model Predictions

Unified methodology for interpreting model predictions through additive explanations and Shapley values. It discusses the relationship between Additive Explanations and LIME, introduces Shapley values, approximations, experiments, and extensions in model interpretation. The approach unifies various

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Optimization Methods: Understanding Gradient Descent and Second Order Techniques

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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Fundamentals of Applying the Method of Fundamental Solutions to Algid Soil Freezing Fronts

Explore the application of the Method of Fundamental Solutions (MFS) in modeling 2-D advancing freezing for algid soil, aiming to enhance technology for estimating heat flux and locating freezing fronts in roadway embankments. The project emphasizes the adaptive and convenient nature of MFS compared

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Microwave Filter Design Using Transmission Lines

Explore the design of microwave filters using transmission lines, starting with lumped-element designs and transitioning to transmission line approximations. Learn how to realize series inductors and shunt capacitors using narrow and wide sections of microstrip lines. Discover techniques such as Ric

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Advancements in Program Analysis Beyond Deductive Methods

Explore the evolution of program analysis beyond deductive methods with innovative tools like static analyzers and data-driven analysis design. Discover the challenges faced, such as undecidable analysis questions and scalability issues, and the strategies employed to address them. Learn about the s

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Learning-Based Low-Rank Approximations and Linear Sketches

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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Sketching Techniques for Efficient Numerical Linear Algebra on Massive Data Sets

Explore how sketching methods can be applied in numerical linear algebra to handle massive data sets efficiently. David Woodruff of IBM Almaden discusses using randomized approximations for algorithms aiming for nearly linear time complexity. Applications include analyzing internet traffic logs, fin

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Pseudodeterministic Algorithms and Their Application in Search Problems

Pseudodeterministic algorithms provide a unique approach to the search problem associated with binary relations, offering an error reduction technique while sacrificing the ability to approximate the average value of a function. By introducing m-pseudodeterministic and pseudo-pseudodeterministic alg

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Approximability and Proof Complexity in Constraint Satisfaction Problems

Explore the realm of constraint satisfaction problems, from Max-Cut to Unique Games, delving into approximation algorithms and NP-hardness. Dive into open questions surrounding the Unique Games Conjecture, the hardness of Max-Cut approximations, and the quest to approximate the Balanced Separator pr

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Accuracy-Aware Program Transformations for Energy-Efficient Computing

Explore the concept of accuracy-aware program transformations led by Sasa Misailovic and collaborators at MIT CSAIL. The research focuses on trading accuracy for energy and performance, harnessing approximate computing, and applying automated transformations in program optimization. Discover how to

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Mixed Learning Resource Allocation in Decision Analytics

Explore the concept of mixed learning resource allocation in decision analytics, focusing on scenarios like using drones for oil detection, responding to natural disasters like Hurricane Sandy, and managing information states for optimal decision-making. The discussion also delves into the developme

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Sequential Decision Analytics Framework Overview

This content discusses a unified framework for sequential decision analytics presented at Olin Business School, University of Washington. Topics include guidelines for choosing policies, policy function approximations, cost function approximations, value function approximations, and direct lookahead

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Tackling Store Buffers in TSO Analysis

The discussion revolves around the management of store buffers in Total Store Ordering (TSO) analysis, contrasting Sequential Consistency (SC) memory model. Different protocols and approaches like Dekker's mutual exclusion and verification techniques for TSO are explored. An innovative method of red

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The Need for Approximations in Computer Science

Exploring the concept of approximations in computer science, despite the inherent challenges in proving them, as discussed by Professor Gary T. Leavens. The content covers the background of problems and algorithms, defining effective procedures through examples and intriguing programs. Delve into th

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ACCEPT: A Programmer-Guided Compiler Framework for Practical Approximate Computing

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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Strategy-Proof Voting: Approximations and Possibilities

Explore the concept of approximately strategy-proof voting through models and constructions, aiming to prevent manipulation while ensuring fair outcomes. Discuss the challenges and potential methods to circumvent manipulations based on Gibbard-Satterthwaite theorems. Delve into defining approximatio

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Improved Truthful Mechanisms for Subadditive Combinatorial Auctions

This research paper discusses strategies to maximize welfare in combinatorial auctions. It explores mechanisms for handling strategic bidders with private valuations, aiming to design truthful and optimal welfare mechanisms while considering polytime constraints. The study presents advancements in a

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Flower Pollination Algorithm: Nature-Inspired Optimization

Real-world design problems often require multi-objective optimization, and the Flower Pollination Algorithm (FPA) developed by Xin-She Yang in 2012 mimics the pollination process of flowering plants to efficiently solve such optimization tasks. FPA has shown promising results in extending to multi-o

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Challenges in Model-Based Nonlinear Bandit and Reinforcement Learning

Delving into advanced topics of provable model-based nonlinear bandit and reinforcement learning, this content explores theories, complexities, and state-of-the-art analyses in deep reinforcement learning and neural net approximation. It highlights the difficulty of statistical learning with even on

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Evolution of Survival Sample Size Methods and Considerations in Survival Analysis

Survival analysis sample size determination is crucial for estimating the expected duration of time to an event accurately. Over time, methods have evolved from simple approximations to more complex models, offering greater flexibility and accuracy in study design. Considerations such as expected su

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Riemann Sums and Area Approximations in Calculus

Explore the concepts of Riemann sums, different types of approximations like left, right, and midpoint sums, trapezoidal rule, and interpreting area in real-life scenarios with examples. Learn how to apply these methods to approximate irregular areas and calculate distances and average speeds. Dive

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Coalescence Times at Two Loci under Markovian Coalescent Models

This presentation discusses coalescence times at two loci using Markovian coalescent approximations and pedigree models. The speaker, Shai Carmi from The Hebrew University of Jerusalem, presents joint work with other researchers, focusing on the ARG, SMC, and the effect of shared pedigree on estimat

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Quasi-Interpolation for Scattered Data in High Dimensions: Methods and Applications

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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Sequential Approximate Inference with Limited Resolution Measurements

Delve into the world of sequential approximate inference through sequential measurements of likelihoods, accounting for Hick's Law. Explore optimal inference strategies implemented by Bayes rule and tackle the challenges of limited resolution measurements. Discover the central question of refining a

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Optical Potentials and Resonances at Lower Energies

Investigating the accuracy of common approximations in linking optical potentials to resonances at lower energies. The study focuses on neutron reactions with 14N as a test case, transitioning from R-matrix theory to Hauser-Feshbach models and evaluating known levels and level densities. Key topics

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Approximation Employed in Spontaneous Emission Theory / D.F. Walls and C.W. Gardiner (Physics Letters 41A (1972))

Examining the approximations utilized in Spontaneous Emission Theory by Walls and Gardiner in 1972. Discusses the motivation, Hamiltonian derivation, and comparisons between R.W.A and the Ladder approximations.

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Systematic Observation on Rear Leakage Correction

Different behavior observed between Data and Monte Carlo simulations in terms of rear leakage correction, with details on the lack of dependence on energy in initial approximations, comparisons between TB and MC data, fits and approximations at different energy levels, and systematic analysis of Cle

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Trigonometry Small Angle Approximations and Identities

Delve into the use of small angle approximations in trigonometry, deriving and applying identities for sine, cosine, and tangent functions. Understand the significance of small angles in accurate calculations and explore the practical applications in physics fields. Discover adjusted trigonometric i

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Algorithms for Big Data: Special Topics on CSCE 689

This course covers advanced algorithms for handling big data, focusing on topics such as Euclidean space, CountSketch, ?2 estimation, moment estimation, Johnson-Lindenstrauss lemma, and algorithm implementation. Dive into the intricacies of Euclidean space, distance functions, heavy-hitters problems

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Principled Approximations in Probabilistic Programming and Hardware Fault Tolerance

Explore the world of probabilistic programming with advancements in principled approximations. Delve into robustness to hardware faults in sampler clustering using DPMM. Discover the concept of approximating compilers and the implementation of probabilistic programs. This collection covers a range o

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Signals and Systems: Fourier Series, Square Wave Approximations, and Orthogonality

Explore the concepts of Fourier series, square wave approximations, and signal orthogonality in the context of signals and systems. Learn how square waves, trigonometric series, and exponential decay can be represented and analyzed using mathematical approaches. Understand the significance of signal

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Gabor Transform: Definitions, Approximations, and Applications

Explore the Gabor Transform, including its definitions, approximations, and applications in signal processing and time-frequency analysis. Learn about the Gaussian function, uncertainty principle, and more in this comprehensive guide.

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Environmental Data Analysis: Linear Approximations and Nonlinear Least Squares

Explore the application of linear approximations to error estimation and least squares in environmental data analysis. Learn how to make linear approximations of nonlinear functions and apply them effectively. Dive into polynomial approximations and Taylor series to enhance your understanding of dat

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Effective Environmental Data Analysis Techniques

Explore advanced methods in environmental data analysis using MATLAB or Python, with topics ranging from linear approximations to hypothesis testing. Gain insights into making linear approximations of non-linear functions, error estimation, and applying least squares in data analysis. Delve into pol

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Exploring JPEG Image Approximations and Outer Product Calculations

Dive into the world of JPEG image approximations with 8x8 pixel blocks and explore outer product calculations within the images for data analysis. Learn about different levels of approximation and how they affect the final image quality.

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Exploring Mathematical Approximations and Artistic Ratios

Uncover the world of mathematical approximations and artistic ratios through images and explanations, including the Vitruvian Man, the Golden Rectangle, and more. Dive into mathematical concepts and their visual representation, alongside insights into order approximations and first-order approximati

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Understanding Binomial Probability Approximations in Data Analysis

Explore how normal approximations are used to estimate binomial probabilities in data analysis. Learn about the process of converting discrete probabilities to continuous distributions for accurate predictions in statistical modeling.

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Understanding Thin Layer Interfaces in COMSOL Simulation

Explore the concept of thin layer interfaces in COMSOL simulation, including different approximations such as solid, membrane, and spring. Learn how these approximations affect displacement and stress fields, and when to use each for optimal results in your simulations.

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Fast Approximations to Edit and Dyck Edit Distances

Explore simple, deterministic, and fast approximations to edit distance and Dyck edit distance, including dynamic programming approaches and reductions between the two distance metrics.

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