The document discusses Hidden Markov Models (HMMs). It defines HMMs as a popular statistical tool that can model time series data through an underlying probabilistic process. HMMs have been successfully applied to natural language processing tasks like part-of-speech tagging. The document provides formal definitions of HMMs and describes algorithms like the forward algorithm that allow evaluating the probability of an observation sequence given an HMM model.
The document discusses the double modal transformation technique for analyzing the dynamic response of linear structures subjected to stochastic loading. It proposes a method called double modal transformation that simultaneously transforms the equations of motion and the loading process. This allows the structural response to be obtained through a double series expansion where structural and loading modal contributions are superimposed. The effectiveness of this technique is illustrated through two classic wind engineering problems: alongwind response and vortex-induced crosswind response of slender structures.
Steerable Filters generated with the Hypercomplex Dual-Tree Wavelet Transform...Jan Wedekind
The use of wavelets in the image processing domain is still in its infancy, and largely associated with image compression. With the advent of the dual-tree hypercomplex wavelet transform (DHWT) and its improved shift invariance and directional selectivity, applications in other areas of image processing are more conceivable. This paper discusses the problems and solutions in developing the DHWT and its inverse. It also offers a practical implementation of the algorithms involved. The aim of this work is to apply the DHWT in machine vision.
Tentative work on a possible new way of feature extraction is presented. The paper shows that 2-D hypercomplex basis wavelets can be used to generate steerable filters which allow rotation as well as translation.
Transverse vibration of slender sandwich beams with viscoelastic inner layer ...Evangelos Ntotsios
This document presents a model for analyzing the transverse vibration of slender sandwich beams with a viscoelastic inner layer. A Galerkin-type approximation is used to derive state-space equations of motion for the composite beam system from its kinetic and potential energies. Numerical examples are presented to validate the model, which can be used to study the dynamic behavior of structural sandwich panels and continuous dynamic vibration absorbers.
The document discusses hidden Markov models (HMM) and their application. It begins with an introduction to HMM and covers three key algorithms: model evaluation, most probable path decoding, and model training. Successful applications of HMM include handwriting recognition, speech recognition, and gene sequence analysis. The document then provides details on Markov models as the basis for HMM, including state transition probabilities, sequence probabilities, and efficient algorithms for calculating state probabilities over time.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Predictive analytics have long lived in the domain of statistical tools like R. Increasingly, however, as companies struggle to deal with exploding volumes of data not easily analyzed by small data tools, they are looking at ways of doing predictive analytics directly inside the primary data store.
This approach, called in-database predictive analytics, eliminates the need to sample data and perform a separate ETL process into a statistical tool, which can decrease total cost, improve the quality of predictive models, and dramatically shorten development time. In this class, you will learn the pros and cons of doing in-database predictive analytics, highlights of its limitations, and survey the tools and technologies necessary to head down the path.
The document summarizes two models:
1. The Lo-Zivot Threshold Cointegration Model, which uses a threshold vector error correction model (TVECM) to analyze the dynamic adjustment of cointegrated time series variables to their long-run equilibrium. It allows for nonlinear and asymmetric adjustment speeds.
2. A bivariate vector error correction model (VECM) and band-threshold vector error correction model (BAND-TVECM) that extend the VECM to allow for nonlinear and discontinuous adjustments to long-run equilibrium across multiple regimes defined by thresholds on a variable. This captures asymmetric adjustment speeds and dynamic behavior.
The BAND-TVECM allows modeling of
The document discusses the double modal transformation technique for analyzing the dynamic response of linear structures subjected to stochastic loading. It proposes a method called double modal transformation that simultaneously transforms the equations of motion and the loading process. This allows the structural response to be obtained through a double series expansion where structural and loading modal contributions are superimposed. The effectiveness of this technique is illustrated through two classic wind engineering problems: alongwind response and vortex-induced crosswind response of slender structures.
Steerable Filters generated with the Hypercomplex Dual-Tree Wavelet Transform...Jan Wedekind
The use of wavelets in the image processing domain is still in its infancy, and largely associated with image compression. With the advent of the dual-tree hypercomplex wavelet transform (DHWT) and its improved shift invariance and directional selectivity, applications in other areas of image processing are more conceivable. This paper discusses the problems and solutions in developing the DHWT and its inverse. It also offers a practical implementation of the algorithms involved. The aim of this work is to apply the DHWT in machine vision.
Tentative work on a possible new way of feature extraction is presented. The paper shows that 2-D hypercomplex basis wavelets can be used to generate steerable filters which allow rotation as well as translation.
Transverse vibration of slender sandwich beams with viscoelastic inner layer ...Evangelos Ntotsios
This document presents a model for analyzing the transverse vibration of slender sandwich beams with a viscoelastic inner layer. A Galerkin-type approximation is used to derive state-space equations of motion for the composite beam system from its kinetic and potential energies. Numerical examples are presented to validate the model, which can be used to study the dynamic behavior of structural sandwich panels and continuous dynamic vibration absorbers.
The document discusses hidden Markov models (HMM) and their application. It begins with an introduction to HMM and covers three key algorithms: model evaluation, most probable path decoding, and model training. Successful applications of HMM include handwriting recognition, speech recognition, and gene sequence analysis. The document then provides details on Markov models as the basis for HMM, including state transition probabilities, sequence probabilities, and efficient algorithms for calculating state probabilities over time.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Predictive analytics have long lived in the domain of statistical tools like R. Increasingly, however, as companies struggle to deal with exploding volumes of data not easily analyzed by small data tools, they are looking at ways of doing predictive analytics directly inside the primary data store.
This approach, called in-database predictive analytics, eliminates the need to sample data and perform a separate ETL process into a statistical tool, which can decrease total cost, improve the quality of predictive models, and dramatically shorten development time. In this class, you will learn the pros and cons of doing in-database predictive analytics, highlights of its limitations, and survey the tools and technologies necessary to head down the path.
The document summarizes two models:
1. The Lo-Zivot Threshold Cointegration Model, which uses a threshold vector error correction model (TVECM) to analyze the dynamic adjustment of cointegrated time series variables to their long-run equilibrium. It allows for nonlinear and asymmetric adjustment speeds.
2. A bivariate vector error correction model (VECM) and band-threshold vector error correction model (BAND-TVECM) that extend the VECM to allow for nonlinear and discontinuous adjustments to long-run equilibrium across multiple regimes defined by thresholds on a variable. This captures asymmetric adjustment speeds and dynamic behavior.
The BAND-TVECM allows modeling of
The document discusses Eulerian circuits in graphs. It begins by defining an Eulerian circuit as a path that uses each edge exactly once and returns to the starting point. For an undirected graph to have an Eulerian circuit, every vertex must have an even degree. It then explains how to construct an Eulerian circuit using a stack data structure and outlines pseudocode. The document also discusses extending the concept to directed graphs and provides examples of applications involving finding circuits in graphs modeling necklaces.
The document summarizes Christophe Paul's work on algorithms for modular decomposition. It discusses Ehrenfeucht et al's modular decomposition algorithm which computes the modular partition M(G,v) of a graph G with respect to a vertex v. It then computes the modular decomposition of the quotient graph G/M(G,v) and the induced subgraphs G[X] for each module X in M(G,v). The document also discusses Gallai's theorem on the decomposition of graphs into parallel, series, or prime modules and algorithms for recognizing cographs and computing the modular decomposition tree.
Model-based analysis using generative embeddingkhbrodersen
This document describes using generative models to analyze brain imaging data and distinguish between disease states. It discusses:
1. Developing neural models of pathophysiological processes and validating them with experimental data.
2. Inverting these models on imaging data from individual subjects to obtain subject-specific representations in a generative score space.
3. Using these representations to train classifiers that can distinguish patient groups, with the goal of inferring pathophysiological mechanisms in patients.
4. An example application where this framework is able to accurately diagnose stroke patients based on speech-related brain regions.
The document discusses scalar quantization and the Lloyd-Max algorithm. It provides examples of using the Lloyd-Max algorithm to design scalar quantizers for Gaussian and Laplacian distributed signals. The algorithm works by iteratively calculating decision thresholds and representative levels to minimize mean squared error. At high rates, the distortion-rate function of a Lloyd-Max quantizer is approximated. The document also discusses entropy-constrained scalar quantization and an iterative algorithm to design those quantizers.
The document discusses quantization in analog-to-digital conversion. It describes the three processes of A/D conversion as sampling, quantization, and binary encoding. Quantization involves mapping amplitude values into a set of discrete values using a quantization interval or step size. The document discusses uniform quantization and how the range is divided into equal intervals. It also discusses non-uniform quantization which has smaller intervals near zero to better match real audio signals. Examples and MATLAB code demonstrations are provided to illustrate quantization of audio signals at different bit rates.
This document discusses Hidden Markov Models (HMMs). It begins with an introduction to HMMs, explaining that they are statistical tools that can model generative sequences with an underlying probabilistic process. It then covers the key calculations involved in HMMs - evaluation, decoding, and learning. Evaluation calculates the probability of an observation sequence given a model. Decoding finds the most likely hidden state sequence. Learning estimates model parameters from training data using maximum likelihood. The document also discusses extensions like multi-dimensional observations and addressing floating point underflow during implementation.
This document summarizes the shape context algorithm for shape matching and object recognition. It discusses computing shape contexts, which describe the distribution of relative positions of points around a shape. Shape contexts are represented as histograms of distances and angles between points. The algorithm finds correspondences between points on two shapes by matching their shape contexts and minimizing the total cost. Additional cost terms can be added, such as color or texture differences. The algorithm is shown to be robust to noise and inexact rotations.
This document provides an overview of three-dimensional displays, from physiological depth cues to electronic holograms. It discusses depth cues our eyes use to perceive depth, including psychological cues like occlusion and physiological cues like binocular disparity. Examples of 3D displays that provide some depth cues, like lenticular sheets, are described. The document also covers holograms, including how they can provide all depth cues by reconstructing the original wavefront. It discusses challenges like the large amount of information in holograms and methods to reduce it, like rainbow and multiplex holograms. Computer generated and electronic holograms using dynamic modulators are also summarized.
Bayesian Inference on a Stochastic Volatility model Using PMCMC methodspaperbags
This document summarizes a Bayesian inference method called particle Markov chain Monte Carlo (PMCMC) for estimating parameters in a stochastic volatility model of financial time series. PMCMC combines sequential Monte Carlo (SMC) methods and Markov chain Monte Carlo (MCMC) to sample the parameter posterior distribution. SMC is used to estimate likelihoods and simulate state trajectories, while MCMC proposals are accepted or rejected based on a Metropolis-Hastings ratio involving the estimated likelihoods. The document outlines the stochastic volatility model, parameter estimation using Gibbs sampling, SMC methods for simulation and filtering, and the particle MCMC algorithm for joint simulation of parameters and states.
The document describes methods for image registration and transformation. It discusses several transformation models (Tθ) and metrics (M) to measure misalignment. It defines compositions of multiple transformations and how to calculate the dice similarity between images after applying sequential transformations. Finally, it shows graphs comparing dice similarity for different numbers of atlas images and target images.
This document discusses techniques for visualizing high-dimensional data, including t-Distributed Stochastic Neighbor Embedding (t-SNE). t-SNE is used to visualize molecular data with thousands of features and won a Kaggle competition by mapping the data based on activity and time. The document also discusses limitations of single maps and introduces multiple maps t-SNE to better model relationships between different concepts.
Why we don’t know how many colors there areJan Morovic
There is no definitive answer to how many colors exist because the concept of color depends on factors like the illumination, viewing conditions, and human perception. Computational models can predict color gamuts under different scenarios, but the largest gamut volume estimated is around 6.6 million colors using real measured light sources, which still may not capture all possible colors perceivable by humans. Determining all possible colors ultimately requires a color appearance model that more closely mimics the complexities of human vision.
The Origin of Diversity - Thinking with Chaotic WalkTakashi Iba
We will show that diverse complex patterns can emerge even in the universe governed by deterministic laws. See the details of this study on our paper: Iba, T. & Shimonishi, K. (2011), "The Origin of Diversity: Thinking with Chaotic Walk," in Unifying Themes in Complex Systems Volume VIII: Proceedings of the Eighth International Conference on Complex Systems, New England Complex Systems Institute Series on Complexity (Sayama, H., Minai, A. A., Braha, D. and Bar-Yam, Y. eds., NECSI Knowledge Press, 2011), pp.447-461.
Amth250 octave matlab some solutions (3)asghar123456
The document contains solutions to 6 questions on interpolation and curve fitting.
Question 1 estimates life expectancies in 1977, 1983 and 1988 for two countries using polynomial interpolation and cubic spline interpolation.
Question 2 finds an interpolating function that fits given data points by solving a linear system.
Question 3 compares errors between polynomial, cubic spline and pchip cubic interpolation on a dataset and analyzes properties of cubic spline and pchip interpolants.
Question 4 plots a cubic spline interpolant and its derivatives, showing it satisfies properties of being cubic on subintervals with continuous derivatives.
Question 5 uses linear least squares to fit a linear model to some data.
Question 6 fits quadratic, exponential and power
The document discusses Eulerian circuits in graphs. It begins by defining an Eulerian circuit as a path that uses each edge exactly once and returns to the starting point. For an undirected graph to have an Eulerian circuit, every vertex must have an even degree. It then explains how to construct an Eulerian circuit using a stack data structure and outlines pseudocode. The document also discusses extending the concept to directed graphs and provides examples of applications involving finding circuits in graphs modeling necklaces.
The document summarizes Christophe Paul's work on algorithms for modular decomposition. It discusses Ehrenfeucht et al's modular decomposition algorithm which computes the modular partition M(G,v) of a graph G with respect to a vertex v. It then computes the modular decomposition of the quotient graph G/M(G,v) and the induced subgraphs G[X] for each module X in M(G,v). The document also discusses Gallai's theorem on the decomposition of graphs into parallel, series, or prime modules and algorithms for recognizing cographs and computing the modular decomposition tree.
Model-based analysis using generative embeddingkhbrodersen
This document describes using generative models to analyze brain imaging data and distinguish between disease states. It discusses:
1. Developing neural models of pathophysiological processes and validating them with experimental data.
2. Inverting these models on imaging data from individual subjects to obtain subject-specific representations in a generative score space.
3. Using these representations to train classifiers that can distinguish patient groups, with the goal of inferring pathophysiological mechanisms in patients.
4. An example application where this framework is able to accurately diagnose stroke patients based on speech-related brain regions.
The document discusses scalar quantization and the Lloyd-Max algorithm. It provides examples of using the Lloyd-Max algorithm to design scalar quantizers for Gaussian and Laplacian distributed signals. The algorithm works by iteratively calculating decision thresholds and representative levels to minimize mean squared error. At high rates, the distortion-rate function of a Lloyd-Max quantizer is approximated. The document also discusses entropy-constrained scalar quantization and an iterative algorithm to design those quantizers.
The document discusses quantization in analog-to-digital conversion. It describes the three processes of A/D conversion as sampling, quantization, and binary encoding. Quantization involves mapping amplitude values into a set of discrete values using a quantization interval or step size. The document discusses uniform quantization and how the range is divided into equal intervals. It also discusses non-uniform quantization which has smaller intervals near zero to better match real audio signals. Examples and MATLAB code demonstrations are provided to illustrate quantization of audio signals at different bit rates.
This document discusses Hidden Markov Models (HMMs). It begins with an introduction to HMMs, explaining that they are statistical tools that can model generative sequences with an underlying probabilistic process. It then covers the key calculations involved in HMMs - evaluation, decoding, and learning. Evaluation calculates the probability of an observation sequence given a model. Decoding finds the most likely hidden state sequence. Learning estimates model parameters from training data using maximum likelihood. The document also discusses extensions like multi-dimensional observations and addressing floating point underflow during implementation.
This document summarizes the shape context algorithm for shape matching and object recognition. It discusses computing shape contexts, which describe the distribution of relative positions of points around a shape. Shape contexts are represented as histograms of distances and angles between points. The algorithm finds correspondences between points on two shapes by matching their shape contexts and minimizing the total cost. Additional cost terms can be added, such as color or texture differences. The algorithm is shown to be robust to noise and inexact rotations.
This document provides an overview of three-dimensional displays, from physiological depth cues to electronic holograms. It discusses depth cues our eyes use to perceive depth, including psychological cues like occlusion and physiological cues like binocular disparity. Examples of 3D displays that provide some depth cues, like lenticular sheets, are described. The document also covers holograms, including how they can provide all depth cues by reconstructing the original wavefront. It discusses challenges like the large amount of information in holograms and methods to reduce it, like rainbow and multiplex holograms. Computer generated and electronic holograms using dynamic modulators are also summarized.
Bayesian Inference on a Stochastic Volatility model Using PMCMC methodspaperbags
This document summarizes a Bayesian inference method called particle Markov chain Monte Carlo (PMCMC) for estimating parameters in a stochastic volatility model of financial time series. PMCMC combines sequential Monte Carlo (SMC) methods and Markov chain Monte Carlo (MCMC) to sample the parameter posterior distribution. SMC is used to estimate likelihoods and simulate state trajectories, while MCMC proposals are accepted or rejected based on a Metropolis-Hastings ratio involving the estimated likelihoods. The document outlines the stochastic volatility model, parameter estimation using Gibbs sampling, SMC methods for simulation and filtering, and the particle MCMC algorithm for joint simulation of parameters and states.
The document describes methods for image registration and transformation. It discusses several transformation models (Tθ) and metrics (M) to measure misalignment. It defines compositions of multiple transformations and how to calculate the dice similarity between images after applying sequential transformations. Finally, it shows graphs comparing dice similarity for different numbers of atlas images and target images.
This document discusses techniques for visualizing high-dimensional data, including t-Distributed Stochastic Neighbor Embedding (t-SNE). t-SNE is used to visualize molecular data with thousands of features and won a Kaggle competition by mapping the data based on activity and time. The document also discusses limitations of single maps and introduces multiple maps t-SNE to better model relationships between different concepts.
Why we don’t know how many colors there areJan Morovic
There is no definitive answer to how many colors exist because the concept of color depends on factors like the illumination, viewing conditions, and human perception. Computational models can predict color gamuts under different scenarios, but the largest gamut volume estimated is around 6.6 million colors using real measured light sources, which still may not capture all possible colors perceivable by humans. Determining all possible colors ultimately requires a color appearance model that more closely mimics the complexities of human vision.
The Origin of Diversity - Thinking with Chaotic WalkTakashi Iba
We will show that diverse complex patterns can emerge even in the universe governed by deterministic laws. See the details of this study on our paper: Iba, T. & Shimonishi, K. (2011), "The Origin of Diversity: Thinking with Chaotic Walk," in Unifying Themes in Complex Systems Volume VIII: Proceedings of the Eighth International Conference on Complex Systems, New England Complex Systems Institute Series on Complexity (Sayama, H., Minai, A. A., Braha, D. and Bar-Yam, Y. eds., NECSI Knowledge Press, 2011), pp.447-461.
Amth250 octave matlab some solutions (3)asghar123456
The document contains solutions to 6 questions on interpolation and curve fitting.
Question 1 estimates life expectancies in 1977, 1983 and 1988 for two countries using polynomial interpolation and cubic spline interpolation.
Question 2 finds an interpolating function that fits given data points by solving a linear system.
Question 3 compares errors between polynomial, cubic spline and pchip cubic interpolation on a dataset and analyzes properties of cubic spline and pchip interpolants.
Question 4 plots a cubic spline interpolant and its derivatives, showing it satisfies properties of being cubic on subintervals with continuous derivatives.
Question 5 uses linear least squares to fit a linear model to some data.
Question 6 fits quadratic, exponential and power
The document discusses Markov models, which are mathematical models used to predict dependent random events based on previously observed events. Specifically, it provides an example of using a Markov model to predict tomorrow's weather based on today's weather. Key aspects covered include the definition of a Markov process, examples of Markov and non-Markov systems, and calculating the probability of future weather events given the current weather.
Natalia Restrepo-Coupe_Remotely-sensed photosynthetic phenology and ecosystem...TERN Australia
This document discusses using remotely sensed data and tower eddy covariance CO2 flux measurements to study phenology and ecosystem productivity. It notes that flux tower data can help validate remote sensing phenology products by determining if they correctly capture dates of green-up, peak growing season, end of season, and season length. The document also aims to better understand what vegetation indices mean quantitatively and their biome-specific relationships to in-situ ecosystem behavior and capacity. Improving this understanding could lead to more robust land surface models informed by remote sensing.
This document provides an overview of wavelet processing and wavelet transforms. It begins by reviewing Fourier transforms and introducing 1D multiresolutions and wavelet transforms. It describes the filter constraints for approximation and detail filters. It then discusses 2D multiresolutions and wavelet transforms, including anisotropic, separable, and isotropic transforms. It also covers fast wavelet transforms, discrete wavelet coefficients, and inverting the transform. The document concludes with examples of wavelet decompositions.
1. The document discusses the Discrete Cosine Transform (DCT), which is commonly used in image and video processing applications to decorrelate pixel data and reduce redundancy.
2. A typical image/video transmission system first applies a transformation like the DCT in the source encoder to decorrelate pixel values, followed by quantization and entropy encoding to further compress the data.
3. The DCT maps the spatially correlated pixel data into transformed coefficients that are decorrelated. This decorrelation reduces interpixel redundancy and allows more efficient compression of image and video data.
1. The document discusses the Discrete Cosine Transform (DCT), which is commonly used in image and video processing applications to decorrelate pixel data and reduce redundancy.
2. A typical image/video transmission system first applies a transformation like the DCT in the source encoder to decorrelate pixels, followed by quantization and entropy encoding to further compress the data.
3. The DCT maps the spatially correlated pixel data into transformed coefficients that are largely uncorrelated, allowing more efficient compression by reducing the number of bits needed to represent the image information.
1. The document discusses the Discrete Cosine Transform (DCT), which is commonly used in image and video processing applications to decorrelate pixel data and reduce redundancy.
2. A typical image/video transmission system first applies a transformation like the DCT in the source encoder to decorrelate pixels, followed by quantization, entropy encoding, and channel encoding for transmission.
3. The DCT aims to map spatially correlated pixel data into uncorrelated transform coefficients to exploit the fact that pixel values can be predicted from neighbors, allowing for better data compression compared to the original spatial domain representation.
1. The document contains definitions, examples, and properties of infinite sequences and series. It includes limits of specific sequences as well as proofs of the convergence or divergence of sequences using various tests.
2. Key topics covered include the limit definition of convergence of a sequence, tests for convergence such as direct comparison test, limit comparison test, ratio test, root test, alternating series test, and tests involving logarithms.
3. Various examples calculate the limits of sequences directly or use standard tests to determine convergence or divergence of sequences.
1. The document discusses various infinite sequences and their limits as n approaches infinity.
2. Several examples of sequences are analyzed, such as 1/n^3, sqrt(n)/n, and (2n+1)/n, and their behavior is described as n increases without bound.
3. It is shown that sequences like 1/n^3 converge to 0 as their terms approach 0 as n increases, while sequences like (2n+1)/n converge to a non-zero limit of 2.
This document discusses an upcoming summer school presentation on modeling correlated risks using copulas. It will include a short introduction to copulas, quantifying dependence, statistical inference of copulas, and properties of aggregating risks. The presentation will define copulas and discuss their use in modeling multivariate distributions and quantifying dependence between random variables. It will also provide references on applying copulas in finance and insurance to model large correlated risks.
This new release is features-rich, as we added several new functionality: trend analysis (for linear, polynomial, logarithmic, and exponential trends), histograms, spectral analysis (discrete Fourier transform), and more. We also revised the existing correlation function (XCF) to extend support for new methods (e.g. Kendall, Spearman, etc.), and added a statistical test for examining its significance. Finally, NumXL now includes a new unit-root and stationarity test: the Augmented Dickey-Fuller (ADF) test.
http://www.spiderfinancial.com/products/numxl
The document provides an overview of the course EC533: Digital Signal Processing including the instructor and TA contact details, textbook references, assessment system, course outline covering topics such as real-time DSP systems, discrete-time signals and systems, Z-transform, digital filter design, DFT and FFT. It also gives introductions to digital signal processing, real-time DSP systems, sampling theorem, anti-aliasing filtering, and considerations in selecting the sampling frequency and filter design.
[OReilly Superstream] Occupy the Space: A grassroots guide to engineering (an...Jason Yip
The typical problem in product engineering is not bad strategy, so much as “no strategy”. This leads to confusion, lack of motivation, and incoherent action. The next time you look for a strategy and find an empty space, instead of waiting for it to be filled, I will show you how to fill it in yourself. If you’re wrong, it forces a correction. If you’re right, it helps create focus. I’ll share how I’ve approached this in the past, both what works and lessons for what didn’t work so well.
zkStudyClub - LatticeFold: A Lattice-based Folding Scheme and its Application...Alex Pruden
Folding is a recent technique for building efficient recursive SNARKs. Several elegant folding protocols have been proposed, such as Nova, Supernova, Hypernova, Protostar, and others. However, all of them rely on an additively homomorphic commitment scheme based on discrete log, and are therefore not post-quantum secure. In this work we present LatticeFold, the first lattice-based folding protocol based on the Module SIS problem. This folding protocol naturally leads to an efficient recursive lattice-based SNARK and an efficient PCD scheme. LatticeFold supports folding low-degree relations, such as R1CS, as well as high-degree relations, such as CCS. The key challenge is to construct a secure folding protocol that works with the Ajtai commitment scheme. The difficulty, is ensuring that extracted witnesses are low norm through many rounds of folding. We present a novel technique using the sumcheck protocol to ensure that extracted witnesses are always low norm no matter how many rounds of folding are used. Our evaluation of the final proof system suggests that it is as performant as Hypernova, while providing post-quantum security.
Paper Link: https://eprint.iacr.org/2024/257
Driving Business Innovation: Latest Generative AI Advancements & Success StorySafe Software
Are you ready to revolutionize how you handle data? Join us for a webinar where we’ll bring you up to speed with the latest advancements in Generative AI technology and discover how leveraging FME with tools from giants like Google Gemini, Amazon, and Microsoft OpenAI can supercharge your workflow efficiency.
During the hour, we’ll take you through:
Guest Speaker Segment with Hannah Barrington: Dive into the world of dynamic real estate marketing with Hannah, the Marketing Manager at Workspace Group. Hear firsthand how their team generates engaging descriptions for thousands of office units by integrating diverse data sources—from PDF floorplans to web pages—using FME transformers, like OpenAIVisionConnector and AnthropicVisionConnector. This use case will show you how GenAI can streamline content creation for marketing across the board.
Ollama Use Case: Learn how Scenario Specialist Dmitri Bagh has utilized Ollama within FME to input data, create custom models, and enhance security protocols. This segment will include demos to illustrate the full capabilities of FME in AI-driven processes.
Custom AI Models: Discover how to leverage FME to build personalized AI models using your data. Whether it’s populating a model with local data for added security or integrating public AI tools, find out how FME facilitates a versatile and secure approach to AI.
We’ll wrap up with a live Q&A session where you can engage with our experts on your specific use cases, and learn more about optimizing your data workflows with AI.
This webinar is ideal for professionals seeking to harness the power of AI within their data management systems while ensuring high levels of customization and security. Whether you're a novice or an expert, gain actionable insights and strategies to elevate your data processes. Join us to see how FME and AI can revolutionize how you work with data!
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.
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.
AppSec PNW: Android and iOS Application Security with MobSFAjin Abraham
Mobile Security Framework - MobSF is a free and open source automated mobile application security testing environment designed to help security engineers, researchers, developers, and penetration testers to identify security vulnerabilities, malicious behaviours and privacy concerns in mobile applications using static and dynamic analysis. It supports all the popular mobile application binaries and source code formats built for Android and iOS devices. In addition to automated security assessment, it also offers an interactive testing environment to build and execute scenario based test/fuzz cases against the application.
This talk covers:
Using MobSF for static analysis of mobile applications.
Interactive dynamic security assessment of Android and iOS applications.
Solving Mobile app CTF challenges.
Reverse engineering and runtime analysis of Mobile malware.
How to shift left and integrate MobSF/mobsfscan SAST and DAST in your build pipeline.
Ivanti’s Patch Tuesday breakdown goes beyond patching your applications and brings you the intelligence and guidance needed to prioritize where to focus your attention first. Catch early analysis on our Ivanti blog, then join industry expert Chris Goettl for the Patch Tuesday Webinar Event. There we’ll do a deep dive into each of the bulletins and give guidance on the risks associated with the newly-identified vulnerabilities.
How information systems are built or acquired puts information, which is what they should be about, in a secondary place. Our language adapted accordingly, and we no longer talk about information systems but applications. Applications evolved in a way to break data into diverse fragments, tightly coupled with applications and expensive to integrate. The result is technical debt, which is re-paid by taking even bigger "loans", resulting in an ever-increasing technical debt. Software engineering and procurement practices work in sync with market forces to maintain this trend. This talk demonstrates how natural this situation is. The question is: can something be done to reverse the trend?
What is an RPA CoE? Session 1 – CoE VisionDianaGray10
In the first session, we will review the organization's vision and how this has an impact on the COE Structure.
Topics covered:
• The role of a steering committee
• How do the organization’s priorities determine CoE Structure?
Speaker:
Chris Bolin, Senior Intelligent Automation Architect Anika Systems
Your One-Stop Shop for Python Success: Top 10 US Python Development Providersakankshawande
Simplify your search for a reliable Python development partner! This list presents the top 10 trusted US providers offering comprehensive Python development services, ensuring your project's success from conception to completion.
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Lambda, Elastic Beanstalk, Lightsail, Amplify, S3 (and more!) can each host websites + APIs. But which one should we choose?
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For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/temporal-event-neural-networks-a-more-efficient-alternative-to-the-transformer-a-presentation-from-brainchip/
Chris Jones, Director of Product Management at BrainChip , presents the “Temporal Event Neural Networks: A More Efficient Alternative to the Transformer” tutorial at the May 2024 Embedded Vision Summit.
The expansion of AI services necessitates enhanced computational capabilities on edge devices. Temporal Event Neural Networks (TENNs), developed by BrainChip, represent a novel and highly efficient state-space network. TENNs demonstrate exceptional proficiency in handling multi-dimensional streaming data, facilitating advancements in object detection, action recognition, speech enhancement and language model/sequence generation. Through the utilization of polynomial-based continuous convolutions, TENNs streamline models, expedite training processes and significantly diminish memory requirements, achieving notable reductions of up to 50x in parameters and 5,000x in energy consumption compared to prevailing methodologies like transformers.
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How to Interpret Trends in the Kalyan Rajdhani Mix Chart.pdfChart Kalyan
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1. Hidden Markov Models
Phil Blunsom pcbl@cs.mu.oz.au
August 19, 2004
Abstract
The Hidden Markov Model (HMM) is a popular statistical tool for modelling a wide
range of time series data. In the context of natural language processing(NLP), HMMs have
been applied with great success to problems such as part-of-speech tagging and noun-phrase
chunking.
1 Introduction
The Hidden Markov Model(HMM) is a powerful statistical tool for modeling generative se-
quences that can be characterised by an underlying process generating an observable sequence.
HMMs have found application in many areas interested in signal processing, and in particular
speech processing, but have also been applied with success to low level NLP tasks such as
part-of-speech tagging, phrase chunking, and extracting target information from documents.
Andrei Markov gave his name to the mathematical theory of Markov processes in the early
twentieth century[3], but it was Baum and his colleagues that developed the theory of HMMs
in the 1960s[2].
Markov Processes Diagram 1 depicts an example of a Markov process. The model
presented describes a simple model for a stock market index. The model has three states, Bull,
Bear and Even, and three index observations up, down, unchanged. The model is a finite state
automaton, with probabilistic transitions between states. Given a sequence of observations,
example: up-down-down we can easily verify that the state sequence that produced those
observations was: Bull-Bear-Bear, and the probability of the sequence is simply the product
of the transitions, in this case 0.2 × 0.3 × 0.3.
Hidden Markov Models Diagram 2 shows an example of how the previous model can
be extended into a HMM. The new model now allows all observation symbols to be emitted
from each state with a finite probability. This change makes the model much more expressive
0.3
0.6
0.2
Bull Bear
0.5
0.4 0.1
up 0.2 0.2 down
Even
unchanged
0.5
Figure 1: Markov process example[1]
1
2. up 0.3 up
0.6
0.7 0.2 0.1
down 0.1 Bull Bear 0.6 down
0.2 0.5
0.3
unchanged 0.4 0.1 unchanged
0.2 0.2
up
0.3
Even
0.3
down
0.4
0.5
unchanged
Figure 2: Hidden Markov model example[1]
and able to better represent our intuition, in this case, that a bull market would have both
good days and bad days, but there would be more good ones. The key difference is that
now if we have the observation sequence up-down-down then we cannot say exactly what
state sequence produced these observations and thus the state sequence is ‘hidden’. We can
however calculate the probability that the model produced the sequence, as well as which
state sequence was most likely to have produced the observations. The next three sections
describe the common calculations that we would like to be able to perform on a HMM.
The formal definition of a HMM is as follows:
λ = (A, B, π) (1)
S is our state alphabet set, and V is the observation alphabet set:
S = (s1 , s2 , · · · , sN ) (2)
V = (v1 , v2 , · · · , vM ) (3)
We define Q to be a fixed state sequence of length T, and corresponding observations O:
Q = q 1 , q2 , · · · , q T (4)
O = o1 , o2 , · · · , oT (5)
A is a transition array, storing the probability of state j following state i . Note the state
transition probabilities are independent of time:
A = [aij ] , aij = P (qt = sj |qt−1 = si ) . (6)
B is the observation array, storing the probability of observation k being produced from
the state j, independent of t:
B = [bi (k)] , bi (k) = P (xt = vk |qt = si ) . (7)
π is the initial probability array:
π = [πi ] , πi = P (q1 = si ) . (8)
Two assumptions are made by the model. The first, called the Markov assumption, states
that the current state is dependent only on the previous state, this represents the memory of
the model:
t−1
P (qt |q1 ) = P (qt |qt−1 ) (9)
The independence assumption states that the output observation at time t is dependent
only on the current state, it is independent of previous observations and states:
P (ot |ot−1 , q1 ) = P (ot |qt )
1
t
(10)
2
3. 1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
t=1 t=2 t=3 t=4
Figure 3: A trellis algorithm
2 Evaluation
Given a HMM, and a sequence of observations, we’d like to be able to compute P (O|λ), the
probability of the observation sequence given a model. This problem could be viewed as one
of evaluating how well a model predicts a given observation sequence, and thus allow us to
choose the most appropriate model from a set.
The probability of the observations O for a specific state sequence Q is:
T
P (O|Q, λ) = P (ot |qt , λ) = bq1 (o1 ) × bq2 (o2 ) · · · bqT (oT ) (11)
t=1
and the probability of the state sequence is:
P (Q|λ) = πq1 aq1 q2 aq2 q3 · · · aqT −1 qT (12)
so we can calculate the probability of the observations given the model as:
P (O|λ) = P (O|Q, λ)P (Q|λ) = πq1 bq1 (o1 )aq1 q2 bq2 (o2 ) · · · aqT −1 qT bqT (oT ) (13)
Q q1 ···qT
This result allows the evaluation of the probability of O, but to evaluate it directly would be
exponential in T.
A better approach is to recognise that many redundant calculations would be made by
directly evaluating equation 13, and therefore caching calculations can lead to reduced com-
plexity. We implement the cache as a trellis of states at each time step, calculating the cached
valued (called α) for each state as a sum over all states at the previous time step. α is the
probability of the partial observation sequence o1 , o2 · · · ot and state si at time t. This can be
visualised as in figure 3. We define the forward probability variable:
αt (i) = P (o1 o2 · · · ot , qt = si |λ) (14)
so if we work through the trellis filling in the values of α the sum of the final column of the
trellis will equal the probability of the observation sequence. The algorithm for this process
is called the forward algorithm and is as follows:
1. Initialisation:
α1 (i) = πi bi (o1 ), 1 ≤ i ≤ N. (15)
2. Induction:
N
αt+1 (j) = [ αt (i)aij ]bj (ot+1 ), 1 ≤ t ≤ T − 1, 1 ≤ j ≤ N. (16)
i=1
3
4. S1
S1
α1(t)
a1j
S2
α2(t) a2j
Sj
αj(t+1)
a3j
S3
α3(t)
aNj
SN
SN
αN(t)
t t+1
Figure 4: The induction step of the forward algorithm
3. Termination:
N
P (O|λ) = αT (i). (17)
i=1
The induction step is the key to the forward algorithm and is depicted in figure 4. For each
state sj , αj (t) stores the probability of arriving in that state having observed the observation
sequence up until time t.
It is apparent that by caching α values the forward algorithm reduces the complexity of
calculations involved to N 2 T rather than 2T N T . We can also define an analogous backwards
algorithm which is the exact reverse of the forwards algorithm with the backwards variable:
βt (i) = P (ot+1 ot+2 · · · oT |qt = si , λ) (18)
as the probability of the partial observation sequence from t + 1 to T , starting in state si .
3 Decoding
The aim of decoding is to discover the hidden state sequence that was most likely to have
produced a given observation sequence. One solution to this problem is to use the Viterbi
algorithm to find the single best state sequence for an observation sequence. The Viterbi
algorithm is another trellis algorithm which is very similar to the forward algorithm, except
that the transition probabilities are maximised at each step, instead of summed. First we
define:
δt (i) = max P (q1 q2 · · · qt = si , o1 , o2 · · · ot |λ) (19)
q1 ,q2 ,···,qt−1
as the probability of the most probable state path for the partial observation sequence.
The Viterbi algorithm and is as follows:
1. Initialisation:
δ1 (i) = πi bi (o1 ), 1 ≤ i ≤ N, ψ1 (i) = 0. (20)
2. Recursion:
δt (j) = max [δt−1 (i)aij ]bj (ot ), 2 ≤ t ≤ T, 1 ≤ j ≤ N, (21)
1≤i≤N
ψt (j) = arg max [δt−1 (i)aij ], 2 ≤ t ≤ T, 1 ≤ j ≤ N. (22)
1≤i≤N
4
5. S1
S1
δt(1)
a1j
S2
δt(2)
a2j Sj
δ (j) =
t+1
S3 a3j δt(2)bj(ot+1)
δt(3) ψt+1(j) = 2
aNj
SN
SN
δt(N)
t t+1
Figure 5: The recursion step of the viterbi algorithm
1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
4 3 3 3
Figure 6: The backtracing step of the viterbi algorithm
3. Termination:
P ∗ = max [δT (i)] (23)
1≤i≤N
∗
qT = arg max [δT (i)]. (24)
1≤i≤N
4. Optimal state sequence backtracking:
∗ ∗
qt = ψt+1 (qt+1 ), t = T − 1, T − 2, · · · , 1. (25)
The recursion step is illustrated in figure 5. The main difference with the forward algorithm
in the recursions step is that we are maximising, rather than summing, and storing the state
that was chosen as the maximum for use as a backpointer. The backtracking step is shown in
6. The backtracking allows the best state sequence to be found from the back pointers stored
in the recursion step, but it should be noted that there is no easy way to find the second best
state sequence.
5
6. 4 Learning
Given a set of examples from a process, we would like to be able to estimate the model pa-
rameters λ = (A, B, π) that best describe that process. There are two standard approaches to
this task, dependent on the form of the examples, which will be referred to here as supervised
and unsupervised training. If the training examples contain both the inputs and outputs of a
process, we can perform supervised training by equating inputs to observations, and outputs
to states, but if only the inputs are provided in the training data then we must used unsuper-
vised training to guess a model that may have produced those observations. In this section we
will discuss the supervised approach to training, for a discussion of the Baum-Welch algorithm
for unsupervised training see [5].
The easiest solution for creating a model λ is to have a large corpus of training examples,
each annotated with the correct classification. The classic example for this approach is PoS
tagging. We define two sets:
• t1 · · · tN is the set of tags, which we equate to the HMM state set s1 · · · sN
• w1 · · · wM is the set of words, which we equate to the HMM observation set v1 · · · vM
so with this model we frame part-of-speech tagging as decoding the most probable hidden
state sequence of PoS tags given an observation sequence of words. To determine the model
parameters λ, we can use maximum likelihood estimates(MLE) from a corpus containing
sentences tagged with their correct PoS tags. For the transition matrix we use:
Count(ti , tj )
aij = P (ti |tj ) = (26)
Count(ti )
where Count(ti , tj ) is the number of times tj followed ti in the training data. For the obser-
vation matrix:
Count(wk , tj )
bj (k) = P (wk |tj ) = (27)
Count(tj )
where Count(wk , tj ) is the number of times wk was tagged tj in the training data. And lastly
the initial probability distribution:
Count(q1 = ti )
πi = P (q1 = ti ) = (28)
Count(q1 )
In practice when estimating a HMM from counts it is normally necessary to apply smoothing
in order to avoid zero counts and improve the performance of the model on data not appearing
in the training set.
5 Multi-Dimensional Feature Space
A limitation of the model described is that observations are assumed to be single dimensional
features, but many tasks are most naturally modelled using a multi-dimensional feature space.
One solution to this problem is to use a multinomial model that assumes the features of the
observations are independent [4]:
vk = (f1 , · · · , fN ) (29)
N
P (vk |sj ) = P (fj |sj ) (30)
j=1
This model is easy to implement and computationally simple, but obviously many features
one might want to use are not independent. For many NLP systems it has been found that
flawed Baysian independence assumptions can still be very effective.
6
7. 6 Implementing HMMs
When implementing a HMM, floating-point underflow is a significant problem. It is apparent
that when applying the Viterbi or forward algorithms to long sequences the extremely small
probability values that would result could underflow on most machines. We solve this problem
differently for each algorithm:
Viterbi underflow As the Viterbi algorithms only multiplies probabilities, a simple solution
to underflow is to log all the probability values and then add values instead of multiply.
In fact if all the values in the model matrices (A, B, π) are stored logged, then at runtime
only addition operations are needed.
forward algorithm underflow The forward algorithm sums probability values, so it is
not a viable solution to log the values in order to avoid underflow. The most common
solution to this problem is to use scaling coefficients that keep the probability values in
the dynamic range of the machine, and that are dependent only on t. The coefficient ct
is defined as:
1
ct = N
(31)
i=1
αt (i)
and thus the new scaled value for α becomes:
αt (i)
αt (i) = ct × αt (i) =
ˆ N
(32)
i=1 t
α (i)
ˆ
a similar coefficient can be computed for βt (i).
References
[1] Huang et. al. Spoken Language Processing. Prentice Hall PTR.
[2] L. Baum et. al. A maximization technique occuring in the statistical analysis of probab-
listic functions of markov chains. Annals of Mathematical Statistics, 41:164–171, 1970.
[3] A. Markov. An example of statistical investigation in the text of eugene onyegin, illustrat-
ing coupling of tests in chains. Proceedings of the Academy of Sciences of St. Petersburg,
1913.
[4] A. McCallum and K. Nigram. A comparison of event models for naive bayes classification.
In AAAI-98 Workshop on Learning for Text Categorization, 1998.
[5] L. Rabiner. A tutorial on hidden markov models and selected applications in speech
recognition. Proceedings of IEEE, 1989.
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