•

1 like•712 views

This presentation in the conference medprai'16 ( the 1st Mediterranean Conference on Pattern Recognition and Artificial Intelligence) in Tebessa, Algeria on November 22-23, 2016.

Report

Share

Report

Share

Download to read offline

Hidden Markov Random Fields and Direct Search Methods for Medical Image Segme...

The goal of image segmentation is to simplify the representation of an image to items meaningful and easier to
analyze. Medical image segmentation is one of the fundamental problems in image processing field. It aims to
provide a crucial decision support to physicians. There is no one way to perform the segmentation. There are
several methods based on HMRF. Hidden Markov Random Fields (HMRF) constitute an elegant way to model
the problem of segmentation. This modelling leads to the minimization of an energy function. In this paper
we investigate direct search methods that are Nelder-Mead and Torczon methods to solve this optimization
problem. The quality of segmentation is evaluated on grounds truths images using the Kappa index called also
Dice Coefficient (DC). The results show the supremacy of the methods used compared to others methods.

Finite-difference modeling, accuracy, and boundary conditions- Arthur Weglein...

This short report gives a brief review on the finite difference modeling method used in MOSRP
and its boundary conditions as a preparation for the Green’s theorem RTM. The first
part gives the finite difference formulae we used and the second part describes the implemented
boundary conditions. The last part, using two examples, points out some impacts of the accuracy
of source fields on the results of modeling.

5th Semester Electronic and Communication Engineering (June/July-2015) Questi...

5th Semester Electronic and Communication Engineering (June/July-2015) Questi...BGS Institute of Technology, Adichunchanagiri University (ACU)

This document contains questions related to management and entrepreneurship. It begins with questions about planning functions, strategic and tactical planning, and types of decisions. It then covers questions about organization structure, communication, control systems, and motivation theories. The second part includes questions about entrepreneurs, their characteristics and role in economic development. It also discusses barriers to entrepreneurship, small scale industries, and government support programs. The last section focuses on project contents, feasibility studies, and project appraisal steps.5th Semester Electronic and Communication Engineering (2013-June) Question Pa...

5th Semester Electronic and Communication Engineering (2013-June) Question Pa...BGS Institute of Technology, Adichunchanagiri University (ACU)

This document contains questions for an examination in Information Theory and Coding. It has two parts, with multiple choice and long answer questions. Part A focuses on information theory concepts like entropy, mutual information, and channel capacity. Questions ask students to calculate entropy and capacity for given sources and channels. Part B covers error control coding techniques, including linear block codes, cyclic codes, and convolutional codes. Questions require encoding and decoding binary codes, finding generator polynomials, and describing different coding schemes.ADAPTIVE FUZZY KERNEL CLUSTERING ALGORITHM

Fuzzy clustering algorithm can not obtain good clustering effect when the sample characteristic is not
obvious and need to determine the number of clusters firstly. For thi0s reason, this paper proposes an
adaptive fuzzy kernel clustering algorithm. The algorithm firstly use the adaptive function of clustering
number to calculate the optimal clustering number, then the samples of input space is mapped to highdimensional
feature space using gaussian kernel and clustering in the feature space. The Matlab simulation
results confirmed that the algorithm's performance has greatly improvement than classical clustering algorithm and has faster convergence speed and more accurate clustering results

Tutorial of topological_data_analysis_part_1(basic)

This document provides an overview of topological data analysis (TDA) concepts, including:
- Simplicial complexes which represent topological spaces and holes of different dimensions
- Persistent homology which tracks the appearance and disappearance of holes over different scales
- Applications of TDA concepts like using persistent homology to analyze protein compressibility.

Me paper gate solved 2013

This document contains a 25 question multiple choice quiz on engineering topics like partial differential equations, matrix properties, numerical integration techniques, stress and strain analysis, probability, heat transfer, thermodynamics, fluid mechanics, welding processes, machining, solidification, mechanical properties, turbines, kinematics, and vector calculus. It also provides the solutions and explanations for each question. The document serves as a practice test for the GATE (Graduate Aptitude Test in Engineering) exam administered by one of India's largest GATE exam preparation institutes.

Relative squared distances to a conic

The midpoint method or technique is a “measurement” and as each measurement it has a tolerance, but
worst of all it can be invalid, called Out-of-Control or OoC. The core of all midpoint methods is the accurate
measurement of the difference of the squared distances of two points to the “polar” of their midpoint
with respect to the conic. When this measurement is valid, it also measures the difference of the squared
distances of these points to the conic, although it may be inaccurate, called Out-of-Accuracy or OoA. The
primary condition is the necessary and sufficient condition that a measurement is valid. It is comletely
new and it can be checked ultra fast and before the actual measurement starts. .
Modeling an incremental algorithm, shows that the curve must be subdivided into “piecewise monotonic”
sections, the start point must be optimal, and it explains that the 2D-incremental method can find, locally,
the global Least Square Distance. Locally means that there are at most three candidate points for a given
monotonic direction; therefore the 2D-midpoint method has, locally, at most three measurements.
When all the possible measurements are invalid, the midpoint method cannot be applied, and in that case
the ultra fast “OoC-rule” selects the candidate point. This guarantees, for the first time, a 100% stable,
ultra-fast, berserkless midpoint algorithm, which can be easily transformed to hardware. The new algorithm
is on average (26.5±5)% faster than Mathematica, using the same resolution and tested using 42
different conics. Both programs are completely written in Mathematica and only ContourPlot[] has been
replaced with a module to generate the grid-points, drawn with Mathematica’s
Graphics[Line{gridpoints}] function.

Hidden Markov Random Fields and Direct Search Methods for Medical Image Segme...

The goal of image segmentation is to simplify the representation of an image to items meaningful and easier to
analyze. Medical image segmentation is one of the fundamental problems in image processing field. It aims to
provide a crucial decision support to physicians. There is no one way to perform the segmentation. There are
several methods based on HMRF. Hidden Markov Random Fields (HMRF) constitute an elegant way to model
the problem of segmentation. This modelling leads to the minimization of an energy function. In this paper
we investigate direct search methods that are Nelder-Mead and Torczon methods to solve this optimization
problem. The quality of segmentation is evaluated on grounds truths images using the Kappa index called also
Dice Coefficient (DC). The results show the supremacy of the methods used compared to others methods.

Finite-difference modeling, accuracy, and boundary conditions- Arthur Weglein...

This short report gives a brief review on the finite difference modeling method used in MOSRP
and its boundary conditions as a preparation for the Green’s theorem RTM. The first
part gives the finite difference formulae we used and the second part describes the implemented
boundary conditions. The last part, using two examples, points out some impacts of the accuracy
of source fields on the results of modeling.

5th Semester Electronic and Communication Engineering (June/July-2015) Questi...

5th Semester Electronic and Communication Engineering (June/July-2015) Questi...BGS Institute of Technology, Adichunchanagiri University (ACU)

This document contains questions related to management and entrepreneurship. It begins with questions about planning functions, strategic and tactical planning, and types of decisions. It then covers questions about organization structure, communication, control systems, and motivation theories. The second part includes questions about entrepreneurs, their characteristics and role in economic development. It also discusses barriers to entrepreneurship, small scale industries, and government support programs. The last section focuses on project contents, feasibility studies, and project appraisal steps.5th Semester Electronic and Communication Engineering (2013-June) Question Pa...

5th Semester Electronic and Communication Engineering (2013-June) Question Pa...BGS Institute of Technology, Adichunchanagiri University (ACU)

This document contains questions for an examination in Information Theory and Coding. It has two parts, with multiple choice and long answer questions. Part A focuses on information theory concepts like entropy, mutual information, and channel capacity. Questions ask students to calculate entropy and capacity for given sources and channels. Part B covers error control coding techniques, including linear block codes, cyclic codes, and convolutional codes. Questions require encoding and decoding binary codes, finding generator polynomials, and describing different coding schemes.ADAPTIVE FUZZY KERNEL CLUSTERING ALGORITHM

Fuzzy clustering algorithm can not obtain good clustering effect when the sample characteristic is not
obvious and need to determine the number of clusters firstly. For thi0s reason, this paper proposes an
adaptive fuzzy kernel clustering algorithm. The algorithm firstly use the adaptive function of clustering
number to calculate the optimal clustering number, then the samples of input space is mapped to highdimensional
feature space using gaussian kernel and clustering in the feature space. The Matlab simulation
results confirmed that the algorithm's performance has greatly improvement than classical clustering algorithm and has faster convergence speed and more accurate clustering results

Tutorial of topological_data_analysis_part_1(basic)

This document provides an overview of topological data analysis (TDA) concepts, including:
- Simplicial complexes which represent topological spaces and holes of different dimensions
- Persistent homology which tracks the appearance and disappearance of holes over different scales
- Applications of TDA concepts like using persistent homology to analyze protein compressibility.

Me paper gate solved 2013

This document contains a 25 question multiple choice quiz on engineering topics like partial differential equations, matrix properties, numerical integration techniques, stress and strain analysis, probability, heat transfer, thermodynamics, fluid mechanics, welding processes, machining, solidification, mechanical properties, turbines, kinematics, and vector calculus. It also provides the solutions and explanations for each question. The document serves as a practice test for the GATE (Graduate Aptitude Test in Engineering) exam administered by one of India's largest GATE exam preparation institutes.

Relative squared distances to a conic

The midpoint method or technique is a “measurement” and as each measurement it has a tolerance, but
worst of all it can be invalid, called Out-of-Control or OoC. The core of all midpoint methods is the accurate
measurement of the difference of the squared distances of two points to the “polar” of their midpoint
with respect to the conic. When this measurement is valid, it also measures the difference of the squared
distances of these points to the conic, although it may be inaccurate, called Out-of-Accuracy or OoA. The
primary condition is the necessary and sufficient condition that a measurement is valid. It is comletely
new and it can be checked ultra fast and before the actual measurement starts. .
Modeling an incremental algorithm, shows that the curve must be subdivided into “piecewise monotonic”
sections, the start point must be optimal, and it explains that the 2D-incremental method can find, locally,
the global Least Square Distance. Locally means that there are at most three candidate points for a given
monotonic direction; therefore the 2D-midpoint method has, locally, at most three measurements.
When all the possible measurements are invalid, the midpoint method cannot be applied, and in that case
the ultra fast “OoC-rule” selects the candidate point. This guarantees, for the first time, a 100% stable,
ultra-fast, berserkless midpoint algorithm, which can be easily transformed to hardware. The new algorithm
is on average (26.5±5)% faster than Mathematica, using the same resolution and tested using 42
different conics. Both programs are completely written in Mathematica and only ContourPlot[] has been
replaced with a module to generate the grid-points, drawn with Mathematica’s
Graphics[Line{gridpoints}] function.

Gate 2013 complete solutions of ec electronics and communication engineering

The document is a sample paper for GATE 2013 that contains 25 multiple choice questions related to engineering topics like logic gates, vector fields, impulse response of systems, diodes, IC technology, and more. Each question is followed by a brief explanation of the answer. The questions cover a range of fundamental concepts in areas like signals and systems, electronics, semiconductor devices, and mathematics.

Multicasting in Linear Deterministic Relay Network by Matrix Completion

This document presents a new algorithm for multicasting in linear deterministic relay networks (LDRNs) that is faster than previous algorithms. The algorithm works by first solving the unicast subproblems using an existing algorithm, then determining the linear encoding matrices for each layer simultaneously using mixed matrix completion. This allows the encoding matrices for an entire layer to be determined at once, rather than one node at a time. The new algorithm runs in O(dq(nr)^3 log(nr)) time, which is faster than the previous best algorithm when n = o(r).

Foreground Detection : Combining Background Subspace Learning with Object Smo...

Foreground Detection : Combining Background Subspace Learning with Object Smo...Shanghai Jiao Tong University(上海交通大学)

This document proposes a new method for foreground detection that combines background subspace learning with an object smoothing model. It uses 2D PCA to learn the background subspace and model the foreground as a sparse matrix. An object smoothing model is then applied to refine the foreground by exploiting the spatial clustered property. The method is tested on three public datasets and achieves better F-score performance compared to GMM, KDE and sparse coding methods for foreground detection.ARIC Team Seminar

This document discusses the implementation of digital filters in fixed-point arithmetic on embedded systems. It presents the need for methodology and tools to design fixed-point embedded filter systems. The key steps are: 1) choosing a filter algorithm, 2) rounding coefficients to fixed-point, and 3) implementing the algorithm. Optimal implementations minimize degradation from quantization errors while meeting resource constraints. The document outlines a global flow from filter design to code generation and optimization.

Grds international conference on pure and applied science (5)

The document proposes a new hybrid conjugate gradient method called SW-A that combines the WYL and AMRI conjugate gradient methods. It presents the algorithm for SW-A and evaluates its performance on 18 standard unconstrained optimization test functions compared to WYL and AMRI in terms of number of iterations and CPU time. The results show that SW-A is able to solve all test problems while WYL solves 97% and AMRI solves 95%, demonstrating the effectiveness of the new hybrid method.

FPGA based BCH Decoder

This document presents the design and implementation of an FPGA-based BCH decoder. It discusses BCH codes, which are binary error-correcting codes used in wireless communications. The implemented decoder is for a (15, 5, 3) BCH code, meaning it can correct up to 3 errors in a block of 15 bits. The decoder uses a serial input/output architecture and is implemented using VHDL on a FPGA device. It performs BCH decoding through syndrome calculation, running the Berlekamp-Massey algorithm to solve the key equation, and using Chien search to find error locations. The simulation result verifies correct decoding operation.

Lt2419681970

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

Unit 6.3

This document discusses parametric equations and motion. It defines parametric curves as graphs of ordered pairs (x,y) where x and y are functions of a parameter t. Parametric equations can be used to model the path of objects in motion. Examples are provided of graphing parametric equations, eliminating the parameter to get a standard equation, and finding parametric equations to represent a line. The document also contains sample problems testing understanding of parametric equations and related concepts.

CVGIP_Chia-Pin Tseng

This document presents a novel algorithm that combines signature method and linear filtering techniques to detect convex polygons, specifically finder and alignment patterns, in slanted or distorted QR code images. The algorithm scans the image contour to generate a signature function, then applies linear filtering to extract high frequency components and identify vertices. It can locate multiple anchor patterns in one scan, arrange them to straighten the image. Only requiring a single scan, it is computationally efficient and suitable for real-time applications like QR code decoding.

Matrix part 3.2 (1)

The document contains proofs of trigonometric identities relating inverse trigonometric functions sin-1x, cos-1x, tan-1x, and cot-1x. It proves the fundamental identities sin-1x + cos-1x = π/2 and sin-1x = π/2 - cos-1x for values of x between -1 and 1. It then provides examples of applying these identities to solve equations involving inverse trigonometric functions. The examples range from simple substitutions to more complex algebraic manipulations to solve for values of variables.

Linear Cryptanalysis Lecture 線形解読法

Linear cryptanalysis is a method used to break encryption standards like DES. It involves finding linear approximations between plaintext, ciphertext, and key bits that hold with probability greater than 50%. These approximations are used to determine partial key bits using maximum likelihood algorithms on known or ciphertext-only data. For S-DES, the method finds a linear expression involving S-box inputs/outputs that predicts a key bit with 78% accuracy, allowing recovery of multiple key bits.

Spsp fw

The document discusses different algorithms for solving the single-pair shortest path problem in graph theory. It describes the Dijkstra, Bellman-Ford, and Floyd-Warshall algorithms. The Floyd-Warshall algorithm finds the shortest paths between all pairs of vertices in a graph and can handle graphs with negative edge weights, though it cannot have negative cycles. Pseudocode is provided to illustrate how the algorithm works by iteratively updating a shortest path matrix.

Efficient Solution of Two-Stage Stochastic Linear Programs Using Interior Poi...

The document describes efficient solution methods for two-stage stochastic linear programs (SLPs) using interior point methods. Interior point methods require solving large, dense systems of linear equations at each iteration, which can be computationally difficult for SLPs due to their structure leading to dense matrices. The paper reviews methods for improving computational efficiency, including reformulating the problem, exploiting special structures like transpose products, and explicitly factorizing the matrices to solve smaller independent systems in parallel. Computational results show explicit factorizations generally require the least effort.

Mathketball

The document is a review game for Chapter 11 geometry concepts that includes:
1) Formulas for calculating the area of basic shapes like rectangles, polygons, circles, etc.
2) Practice problems calculating missing measures and areas using the formulas.
3) Finding surface areas and geometric probabilities of various shapes.

Show ant-colony-optimization-for-solving-the-traveling-salesman-problem

The document describes using ant colony optimization to solve the traveling salesman problem. It outlines the traveling salesman problem and introduces ant colony optimization as a metaheuristic for solving optimization problems inspired by ant behavior. The document then provides an example of using ant colony optimization to iteratively find the shortest route between 5 cities, with ants probabilistically choosing paths based on pheromone levels and distance.

Goldberg-Coxeter construction for 3- or 4-valent plane maps

The Goldberg-Coxeter construction takes two integers (k,l) a 3-or 4-valent plane graph and returns a 3- or 4-valent plane graph. This construction is useful in virus study, numerical analysis, architecture, chemistry and of course mathematics.
Here we consider the zigzags and central circuits of 3- or 4-valent plane graph. It turns out that we can define an algebraic construction of (k,l)-product that allows to find the length of the zigzags and central circuits in a compact way. All possible lengths of zigzags are determined by this (k,l)-product and the normal structure of the automorphism group allows to find them for some congruence conditions.

Lecture 2: Stochastic Hydrology

- The document discusses representation of stochastic processes in real and spectral domains and Monte Carlo sampling.
- Stochastic processes can be represented in the real (time or space) domain using autocorrelation and variogram functions, and in the spectral domain using power spectral density functions.
- Monte Carlo sampling uses techniques to generate random numbers from a probability density function for random sampling.

A Fast Hadamard Transform for Signals with Sub-linear Sparsity

The Hadamard transform is a popular orthogonal transform with a low-complexity algorithm with O(N log N) complexity. In this presentation, we describe a new sub-linear complexity algorithm to compute the Hadamard transform of signals whose Hadamard transform coefficients are sparse - that is very few are non-zero.

Data sparse approximation of Karhunen-Loeve Expansion

In this work we discuss how to compute KLE with complexity O(k n log n), how to approximate large covariance matrices (in H-matrix format), how to use the Lanczos method.

Slides

We solve elliptic PDE with uncertain coefficients. We apply Karhunen-Loeve expansion to separate stochastic part from spatial part. The corresponding eigenvalue problem with covariance function is solved via the Hierarchical Matrix technique. We also demonstrate how low-rank tensor method can be applied for high-dimensional problems (e.g., to compute higher order statistical moments) . We provide explicit formulas to compute statistical moments of order k with linear complexity.

Data sparse approximation of the Karhunen-Loeve expansion

There are different techniques to compute Karhunen Loeve Expansion (KLE): FFT, hierarchical matrices, low-rank tensors

Delayed acceptance for Metropolis-Hastings algorithms

The document proposes a delayed acceptance method for accelerating Metropolis-Hastings algorithms. It begins with a motivating example of non-informative inference for mixture models where computing the prior density is costly. It then introduces the delayed acceptance approach which splits the acceptance probability into pieces that are evaluated sequentially, avoiding computing the full acceptance ratio each time. It validates that the delayed acceptance chain is reversible and provides bounds on its spectral gap and asymptotic variance compared to the original chain. Finally, it discusses optimizing the delayed acceptance approach by considering the expected square jump distance and cost per iteration to maximize efficiency.

Gate 2013 complete solutions of ec electronics and communication engineering

The document is a sample paper for GATE 2013 that contains 25 multiple choice questions related to engineering topics like logic gates, vector fields, impulse response of systems, diodes, IC technology, and more. Each question is followed by a brief explanation of the answer. The questions cover a range of fundamental concepts in areas like signals and systems, electronics, semiconductor devices, and mathematics.

Multicasting in Linear Deterministic Relay Network by Matrix Completion

This document presents a new algorithm for multicasting in linear deterministic relay networks (LDRNs) that is faster than previous algorithms. The algorithm works by first solving the unicast subproblems using an existing algorithm, then determining the linear encoding matrices for each layer simultaneously using mixed matrix completion. This allows the encoding matrices for an entire layer to be determined at once, rather than one node at a time. The new algorithm runs in O(dq(nr)^3 log(nr)) time, which is faster than the previous best algorithm when n = o(r).

Foreground Detection : Combining Background Subspace Learning with Object Smo...

Foreground Detection : Combining Background Subspace Learning with Object Smo...Shanghai Jiao Tong University(上海交通大学)

This document proposes a new method for foreground detection that combines background subspace learning with an object smoothing model. It uses 2D PCA to learn the background subspace and model the foreground as a sparse matrix. An object smoothing model is then applied to refine the foreground by exploiting the spatial clustered property. The method is tested on three public datasets and achieves better F-score performance compared to GMM, KDE and sparse coding methods for foreground detection.ARIC Team Seminar

This document discusses the implementation of digital filters in fixed-point arithmetic on embedded systems. It presents the need for methodology and tools to design fixed-point embedded filter systems. The key steps are: 1) choosing a filter algorithm, 2) rounding coefficients to fixed-point, and 3) implementing the algorithm. Optimal implementations minimize degradation from quantization errors while meeting resource constraints. The document outlines a global flow from filter design to code generation and optimization.

Grds international conference on pure and applied science (5)

The document proposes a new hybrid conjugate gradient method called SW-A that combines the WYL and AMRI conjugate gradient methods. It presents the algorithm for SW-A and evaluates its performance on 18 standard unconstrained optimization test functions compared to WYL and AMRI in terms of number of iterations and CPU time. The results show that SW-A is able to solve all test problems while WYL solves 97% and AMRI solves 95%, demonstrating the effectiveness of the new hybrid method.

FPGA based BCH Decoder

This document presents the design and implementation of an FPGA-based BCH decoder. It discusses BCH codes, which are binary error-correcting codes used in wireless communications. The implemented decoder is for a (15, 5, 3) BCH code, meaning it can correct up to 3 errors in a block of 15 bits. The decoder uses a serial input/output architecture and is implemented using VHDL on a FPGA device. It performs BCH decoding through syndrome calculation, running the Berlekamp-Massey algorithm to solve the key equation, and using Chien search to find error locations. The simulation result verifies correct decoding operation.

Lt2419681970

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

Unit 6.3

This document discusses parametric equations and motion. It defines parametric curves as graphs of ordered pairs (x,y) where x and y are functions of a parameter t. Parametric equations can be used to model the path of objects in motion. Examples are provided of graphing parametric equations, eliminating the parameter to get a standard equation, and finding parametric equations to represent a line. The document also contains sample problems testing understanding of parametric equations and related concepts.

CVGIP_Chia-Pin Tseng

This document presents a novel algorithm that combines signature method and linear filtering techniques to detect convex polygons, specifically finder and alignment patterns, in slanted or distorted QR code images. The algorithm scans the image contour to generate a signature function, then applies linear filtering to extract high frequency components and identify vertices. It can locate multiple anchor patterns in one scan, arrange them to straighten the image. Only requiring a single scan, it is computationally efficient and suitable for real-time applications like QR code decoding.

Matrix part 3.2 (1)

The document contains proofs of trigonometric identities relating inverse trigonometric functions sin-1x, cos-1x, tan-1x, and cot-1x. It proves the fundamental identities sin-1x + cos-1x = π/2 and sin-1x = π/2 - cos-1x for values of x between -1 and 1. It then provides examples of applying these identities to solve equations involving inverse trigonometric functions. The examples range from simple substitutions to more complex algebraic manipulations to solve for values of variables.

Linear Cryptanalysis Lecture 線形解読法

Linear cryptanalysis is a method used to break encryption standards like DES. It involves finding linear approximations between plaintext, ciphertext, and key bits that hold with probability greater than 50%. These approximations are used to determine partial key bits using maximum likelihood algorithms on known or ciphertext-only data. For S-DES, the method finds a linear expression involving S-box inputs/outputs that predicts a key bit with 78% accuracy, allowing recovery of multiple key bits.

Spsp fw

The document discusses different algorithms for solving the single-pair shortest path problem in graph theory. It describes the Dijkstra, Bellman-Ford, and Floyd-Warshall algorithms. The Floyd-Warshall algorithm finds the shortest paths between all pairs of vertices in a graph and can handle graphs with negative edge weights, though it cannot have negative cycles. Pseudocode is provided to illustrate how the algorithm works by iteratively updating a shortest path matrix.

Efficient Solution of Two-Stage Stochastic Linear Programs Using Interior Poi...

The document describes efficient solution methods for two-stage stochastic linear programs (SLPs) using interior point methods. Interior point methods require solving large, dense systems of linear equations at each iteration, which can be computationally difficult for SLPs due to their structure leading to dense matrices. The paper reviews methods for improving computational efficiency, including reformulating the problem, exploiting special structures like transpose products, and explicitly factorizing the matrices to solve smaller independent systems in parallel. Computational results show explicit factorizations generally require the least effort.

Mathketball

The document is a review game for Chapter 11 geometry concepts that includes:
1) Formulas for calculating the area of basic shapes like rectangles, polygons, circles, etc.
2) Practice problems calculating missing measures and areas using the formulas.
3) Finding surface areas and geometric probabilities of various shapes.

Show ant-colony-optimization-for-solving-the-traveling-salesman-problem

The document describes using ant colony optimization to solve the traveling salesman problem. It outlines the traveling salesman problem and introduces ant colony optimization as a metaheuristic for solving optimization problems inspired by ant behavior. The document then provides an example of using ant colony optimization to iteratively find the shortest route between 5 cities, with ants probabilistically choosing paths based on pheromone levels and distance.

Goldberg-Coxeter construction for 3- or 4-valent plane maps

The Goldberg-Coxeter construction takes two integers (k,l) a 3-or 4-valent plane graph and returns a 3- or 4-valent plane graph. This construction is useful in virus study, numerical analysis, architecture, chemistry and of course mathematics.
Here we consider the zigzags and central circuits of 3- or 4-valent plane graph. It turns out that we can define an algebraic construction of (k,l)-product that allows to find the length of the zigzags and central circuits in a compact way. All possible lengths of zigzags are determined by this (k,l)-product and the normal structure of the automorphism group allows to find them for some congruence conditions.

Lecture 2: Stochastic Hydrology

- The document discusses representation of stochastic processes in real and spectral domains and Monte Carlo sampling.
- Stochastic processes can be represented in the real (time or space) domain using autocorrelation and variogram functions, and in the spectral domain using power spectral density functions.
- Monte Carlo sampling uses techniques to generate random numbers from a probability density function for random sampling.

Gate 2013 complete solutions of ec electronics and communication engineering

Gate 2013 complete solutions of ec electronics and communication engineering

Multicasting in Linear Deterministic Relay Network by Matrix Completion

Multicasting in Linear Deterministic Relay Network by Matrix Completion

Foreground Detection : Combining Background Subspace Learning with Object Smo...

Foreground Detection : Combining Background Subspace Learning with Object Smo...

ARIC Team Seminar

ARIC Team Seminar

Grds international conference on pure and applied science (5)

Grds international conference on pure and applied science (5)

FPGA based BCH Decoder

FPGA based BCH Decoder

Lt2419681970

Lt2419681970

Unit 6.3

Unit 6.3

CVGIP_Chia-Pin Tseng

CVGIP_Chia-Pin Tseng

Matrix part 3.2 (1)

Matrix part 3.2 (1)

Linear Cryptanalysis Lecture 線形解読法

Linear Cryptanalysis Lecture 線形解読法

Spsp fw

Spsp fw

Efficient Solution of Two-Stage Stochastic Linear Programs Using Interior Poi...

Efficient Solution of Two-Stage Stochastic Linear Programs Using Interior Poi...

Mathketball

Mathketball

Show ant-colony-optimization-for-solving-the-traveling-salesman-problem

Show ant-colony-optimization-for-solving-the-traveling-salesman-problem

Goldberg-Coxeter construction for 3- or 4-valent plane maps

Goldberg-Coxeter construction for 3- or 4-valent plane maps

Lecture 2: Stochastic Hydrology

Lecture 2: Stochastic Hydrology

A Fast Hadamard Transform for Signals with Sub-linear Sparsity

The Hadamard transform is a popular orthogonal transform with a low-complexity algorithm with O(N log N) complexity. In this presentation, we describe a new sub-linear complexity algorithm to compute the Hadamard transform of signals whose Hadamard transform coefficients are sparse - that is very few are non-zero.

Data sparse approximation of Karhunen-Loeve Expansion

In this work we discuss how to compute KLE with complexity O(k n log n), how to approximate large covariance matrices (in H-matrix format), how to use the Lanczos method.

Slides

We solve elliptic PDE with uncertain coefficients. We apply Karhunen-Loeve expansion to separate stochastic part from spatial part. The corresponding eigenvalue problem with covariance function is solved via the Hierarchical Matrix technique. We also demonstrate how low-rank tensor method can be applied for high-dimensional problems (e.g., to compute higher order statistical moments) . We provide explicit formulas to compute statistical moments of order k with linear complexity.

Data sparse approximation of the Karhunen-Loeve expansion

There are different techniques to compute Karhunen Loeve Expansion (KLE): FFT, hierarchical matrices, low-rank tensors

Delayed acceptance for Metropolis-Hastings algorithms

The document proposes a delayed acceptance method for accelerating Metropolis-Hastings algorithms. It begins with a motivating example of non-informative inference for mixture models where computing the prior density is costly. It then introduces the delayed acceptance approach which splits the acceptance probability into pieces that are evaluated sequentially, avoiding computing the full acceptance ratio each time. It validates that the delayed acceptance chain is reversible and provides bounds on its spectral gap and asymptotic variance compared to the original chain. Finally, it discusses optimizing the delayed acceptance approach by considering the expected square jump distance and cost per iteration to maximize efficiency.

計算材料学

This document provides an overview of a computational materials science lecture at Tokyo Tech. The lecture will cover first principles calculations, focusing on numerical analysis of electronic states. First principles calculations determine electronic states without experimental parameters by only using fundamental physical constants and numerical parameters. The lecture notes can be downloaded online and questions are welcome. Example materials that will be discussed include graphene and magnetic materials interfaces. Computational methods like density functional theory and plane wave basis sets will be introduced.

Conjugate Gradient method for Brain Magnetic Resonance Images Segmentation

Image segmentation is the process of partitioning the im-
age into regions of interest in order to provide a meaningful represen-
tation of information. Nowadays, segmentation has become a necessity
in many practical medical imaging methods as locating tumors and dis-
eases. Hidden Markov Random Field model is one of several techniques
used in image segmentation. It provides an elegant way to model the
segmentation process. This modeling leads to the minimization of an ob-
jective function. Conjugate Gradient algorithm (CG) is one of the best
known optimization techniques. This paper proposes the use of the non-
linear Conjugate Gradient algorithm (CG) for image segmentation, in
combination with the Hidden Markov Random Field modelization. Since
derivatives are not available for this expression, finite differences are used
in the CG algorithm to approximate the first derivative. The approach
is evaluated using a number of publicly available images, where ground
truth is known. The Dice Coefficient is used as an objective criterion to
measure the quality of segmentation. The results show that the proposed
CG approach compares favorably with other variants of Hidden Markov
Random Field segmentation algorithms.

k-MLE: A fast algorithm for learning statistical mixture models

This document describes a fast algorithm called k-MLE for learning statistical mixture models. k-MLE is based on the connection between exponential family mixture models and Bregman divergences. It extends Lloyd's k-means clustering algorithm to optimize the complete log-likelihood of an exponential family mixture model using Bregman divergences. The algorithm iterates between assigning data points to clusters based on Bregman divergence, and updating the cluster parameters by taking the Bregman centroid of each cluster's assigned points. This provides a fast method for maximum likelihood estimation of exponential family mixture models.

Strong convergence of an algorithm about strongly quasi nonexpansive mappings

This document presents an algorithm to solve the split common fixed-point problem (SCFPP) in Hilbert space. The algorithm is a modification of an existing algorithm for strongly quasi-nonexpansive operators. The author proves that under certain conditions, including the operators being demiclosed and the solution set being nonempty, the sequence generated by the algorithm converges strongly to a solution of the SCFPP. This extends and improves previous results on algorithms for solving split feasibility problems and common fixed-point problems.

An investigation of inference of the generalized extreme value distribution b...

This document presents an investigation of parameter estimation for the generalized extreme value distribution based on record values. Maximum likelihood estimation is used to estimate the parameters β (scale parameter) and ξ (shape parameter). Likelihood equations are derived and solved numerically. Bootstrap and Markov chain Monte Carlo methods are proposed to construct confidence intervals for the parameters since intervals based on asymptotic normality may not perform well due to small sample sizes of records. Bayesian estimation of the parameters using MCMC is also investigated. An illustrative example involving simulated records is provided.

Recursive Compressed Sensing

A very wide spectrum of optimization problems can be efficiently solved with proximal gradient methods which hinge on the celebrated forward-backward splitting (FBS) schema. But such first-order methods are only effective when low or medium accuracy is required and are known to be rather slow or even impractical for badly conditioned problems. Moreover, the straightforward introduction of second-order (Hessian) information is beset with shortcomings as, typically, at every iteration we need to solve a non-separable optimisation problem. In this talk we will follow a different route to the solution of such optimisation problems. We will recast non-smooth optimisation problems as the minimisation of a real-valued, continuously differentiable function known as the forward-backward envelope. We will then employ a semismooth Newton method to solve the equivalent optimisation problem instead of the original one. We will then apply the proposed semismooth Newton method to L1-regularised least squares (LASSO) problems which is motivated by an an interesting application: recursive compressed sensing. Compressed sensing is a signal processing methodology for the reconstruction of sparsely sampled signals and it offers a new paradigm for sampling signals based on their innovation, that is, the minimum number of coefficients sufficient to accurately represent it in an appropriately selected basis. Compressed sensing leads to a lower sampling rate compared to theories using some fixed basis and has many applications in image processing, medical imaging and MRI, photography, holography, facial recognition, radio astronomy, radar technology and more. The traditional compressed sensing approach is naturally offline, in that it amounts to sparsely sampling and reconstructing a given dataset. Recently, an online algorithm for performing compressed sensing on streaming data was proposed; the scheme uses recursive sampling of the input stream and recursive decompression to accurately estimate stream entries from the acquired noisy measurements. We will see how we can tailor the forward-backward Newton method to solve recursive compressed sensing problems at one tenth of the time required by other algorithms such as ISTA, FISTA, ADMM and interior-point methods (L1LS).

Применение машинного обучения для навигации и управления роботами

The document discusses applications of machine learning for robot navigation and control. It describes how surrogate models can be used for predictive modeling in engineering applications like aircraft design. Dimension reduction techniques are used to reduce high-dimensional design parameters to a lower-dimensional space for faster surrogate model evaluation. For robot navigation, regression models on image manifolds are used for visual localization by mapping images to robot positions. Manifold learning is also applied to find low-dimensional representations of valid human hand poses from images to enable easier robot control.

Tensor Train data format for uncertainty quantification

We start with motivation, few examples of uncertainties. Then we discretize elliptic PDE with uncertain coefficients, apply TT format for permeability, the stochastic operator and for the solution. We compare sparse multi-index set approach with full multi-index+TT.
Tensor Train format allows us to keep the whole multi-index set, without any multi-index set truncation.

Knowledge extraction from support vector machines

Fuzzy Logic Seminar
Knowledge extraction from support vector machines
we introduce you to the SVM and why it is called SVM, then we demonstrate an algorithm that converts an SVM to an Artificial Neural Network, and how to obtain knowledge from it.

Paris Lecture 4: Practical issues in Bayesian modeling

The document discusses Bayesian linear mixed models and practical issues when using them. It covers the following key points:
1) Bayesian LMMs require MCMC sampling to obtain samples from the posterior distribution, as the distribution is only known up to proportionality. Gibbs sampling and other MCMC methods like Metropolis-Hastings sampling are introduced.
2) Evaluating model fit and checking assumptions is important, which can be done using functions from the lme4, Stan, or JAGS packages. Trace plots and Gelman diagnostics help assess if the MCMC sampler has converged.
3) More complex examples of Bayesian LMMs are briefly mentioned, along with discussing the Box-Cox procedure to obtain

Current limitations of sequential inference in general hidden Markov models

The document discusses sequential inference methods for hidden Markov models (HMMs). It outlines current limitations of exact sequential inference in general HMMs. Particle filters provide a plug-and-play sequential Monte Carlo method for approximating filtering distributions in HMMs, but require being able to simulate the hidden process and evaluate the measurement density. The document also introduces sequential Monte Carlo squared (SMC2) as a sequential method for HMMs, but notes it is not online.

Presentation_Tan

This document summarizes a presentation on using statistical models to characterize textures in high resolution transmission electron microscopy (TEM) images. It proposes using the statistical invariances and geometry (SIGMA) modeling approach and auto-regressive fractional Brownian field (ARFBF) models. Specifically, it discusses:
1) Modeling textures using generalized fractional Brownian fields, auto-regressive models, and 2-factor fractional Brownian fields.
2) Methods for estimating Hurst parameters and pole locations from these models.
3) Applying the ARFBF model to characterize TEM images by estimating parameters from the image spectrum and modeling residuals.

Vladimir Milov and Andrey Savchenko - Classification of Dangerous Situations...

Classification of Dangerous Situations for Small Sample Size Problem in Maintenance Decision Support Systems

AOT2 Single Variable Optimization Algorithms.pdf

The document discusses single variable optimization algorithms. It describes direct search methods and gradient-based optimization methods for single variable optimization. It also defines local optimal points, global optimal points, and inflection points. The document then discusses optimality criteria, methods to identify local/global minima and inflection points, and conditions of optimality. It introduces bracketing methods like exhaustive search method and bounding phase method to find the bounds of the minimum of a function. Finally, it discusses region elimination methods like interval halving method.

Bayesian inference on mixtures

This document discusses Bayesian inference on mixtures models. It covers several key topics:
1. Density approximation and consistency results for mixtures as a way to approximate unknown distributions.
2. The "scarcity phenomenon" where the posterior probabilities of most component allocations in mixture models are zero, concentrating on just a few high probability allocations.
3. Challenges with Bayesian inference for mixtures, including identifiability issues, label switching, and complex combinatorial calculations required to integrate over all possible component allocations.

A Fast Hadamard Transform for Signals with Sub-linear Sparsity

A Fast Hadamard Transform for Signals with Sub-linear Sparsity

Data sparse approximation of Karhunen-Loeve Expansion

Data sparse approximation of Karhunen-Loeve Expansion

Slides

Slides

Data sparse approximation of the Karhunen-Loeve expansion

Data sparse approximation of the Karhunen-Loeve expansion

Delayed acceptance for Metropolis-Hastings algorithms

Delayed acceptance for Metropolis-Hastings algorithms

計算材料学

計算材料学

Conjugate Gradient method for Brain Magnetic Resonance Images Segmentation

Conjugate Gradient method for Brain Magnetic Resonance Images Segmentation

k-MLE: A fast algorithm for learning statistical mixture models

k-MLE: A fast algorithm for learning statistical mixture models

Strong convergence of an algorithm about strongly quasi nonexpansive mappings

Strong convergence of an algorithm about strongly quasi nonexpansive mappings

An investigation of inference of the generalized extreme value distribution b...

An investigation of inference of the generalized extreme value distribution b...

Recursive Compressed Sensing

Recursive Compressed Sensing

Применение машинного обучения для навигации и управления роботами

Применение машинного обучения для навигации и управления роботами

Tensor Train data format for uncertainty quantification

Tensor Train data format for uncertainty quantification

Knowledge extraction from support vector machines

Knowledge extraction from support vector machines

Paris Lecture 4: Practical issues in Bayesian modeling

Paris Lecture 4: Practical issues in Bayesian modeling

Current limitations of sequential inference in general hidden Markov models

Current limitations of sequential inference in general hidden Markov models

Presentation_Tan

Presentation_Tan

Vladimir Milov and Andrey Savchenko - Classification of Dangerous Situations...

Vladimir Milov and Andrey Savchenko - Classification of Dangerous Situations...

AOT2 Single Variable Optimization Algorithms.pdf

AOT2 Single Variable Optimization Algorithms.pdf

Bayesian inference on mixtures

Bayesian inference on mixtures

Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf

Sickle cell in children

mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt

Dòng khí hóa Plasma

THEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...

THEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...Abdul Wali Khan University Mardan,kP,Pakistan

hematic appreciation test is a psychological assessment tool used to measure an individual's appreciation and understanding of specific themes or topics. This test helps to evaluate an individual's ability to connect different ideas and concepts within a given theme, as well as their overall comprehension and interpretation skills. The results of the test can provide valuable insights into an individual's cognitive abilities, creativity, and critical thinking skillsbordetella pertussis.................................ppt

Bordettela is a gram negative cocobacilli spread by air born drop let

3D Hybrid PIC simulation of the plasma expansion (ISSS-14)

3D Particle-In-Cell (PIC) algorithm,
Plasma expansion in the dipole magnetic field.

Eukaryotic Transcription Presentation.pptx

ukaryotic Transcription Presentation and RNA Precessing

Bob Reedy - Nitrate in Texas Groundwater.pdf

Presented at June 6-7 Texas Alliance of Groundwater Districts Business Meeting

NuGOweek 2024 Ghent programme overview flyer

NuGOweek 2024 Ghent programme overview flyer

The binding of cosmological structures by massless topological defects

Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.

Orion Air Quality Monitoring Systems - CWS

Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.

20240520 Planning a Circuit Simulator in JavaScript.pptx

Evaporation step counter work. I have done a physical experiment.
(Work in progress.)

Deep Software Variability and Frictionless Reproducibility

Deep Software Variability and Frictionless ReproducibilityUniversity of Rennes, INSA Rennes, Inria/IRISA, CNRS

The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
The debris of the ‘last major merger’ is dynamically young

The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.

Shallowest Oil Discovery of Turkiye.pptx

The Petroleum System of the Çukurova Field - the Shallowest Oil Discovery of Türkiye, Adana

ANAMOLOUS SECONDARY GROWTH IN DICOT ROOTS.pptx

Abnormal or anomalous secondary growth in plants. It defines secondary growth as an increase in plant girth due to vascular cambium or cork cambium. Anomalous secondary growth does not follow the normal pattern of a single vascular cambium producing xylem internally and phloem externally.

Medical Orthopedic PowerPoint Templates.pptx

medical orto

Nucleic Acid-its structural and functional complexity.

This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.

aziz sancar nobel prize winner: from mardin to nobel

aziz sancar nobel prize winner

What is greenhouse gasses and how many gasses are there to affect the Earth.

What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.

DERIVATION OF MODIFIED BERNOULLI EQUATION WITH VISCOUS EFFECTS AND TERMINAL V...

In this book, we use conservation of energy techniques on a fluid element to derive the Modified Bernoulli equation of flow with viscous or friction effects. We derive the general equation of flow/ velocity and then from this we derive the Pouiselle flow equation, the transition flow equation and the turbulent flow equation. In the situations where there are no viscous effects , the equation reduces to the Bernoulli equation. From experimental results, we are able to include other terms in the Bernoulli equation. We also look at cases where pressure gradients exist. We use the Modified Bernoulli equation to derive equations of flow rate for pipes of different cross sectional areas connected together. We also extend our techniques of energy conservation to a sphere falling in a viscous medium under the effect of gravity. We demonstrate Stokes equation of terminal velocity and turbulent flow equation. We look at a way of calculating the time taken for a body to fall in a viscous medium. We also look at the general equation of terminal velocity.

Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf

Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf

mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt

mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt

THEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...

THEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...

bordetella pertussis.................................ppt

bordetella pertussis.................................ppt

3D Hybrid PIC simulation of the plasma expansion (ISSS-14)

3D Hybrid PIC simulation of the plasma expansion (ISSS-14)

Eukaryotic Transcription Presentation.pptx

Eukaryotic Transcription Presentation.pptx

Bob Reedy - Nitrate in Texas Groundwater.pdf

Bob Reedy - Nitrate in Texas Groundwater.pdf

NuGOweek 2024 Ghent programme overview flyer

NuGOweek 2024 Ghent programme overview flyer

The binding of cosmological structures by massless topological defects

The binding of cosmological structures by massless topological defects

Orion Air Quality Monitoring Systems - CWS

Orion Air Quality Monitoring Systems - CWS

20240520 Planning a Circuit Simulator in JavaScript.pptx

20240520 Planning a Circuit Simulator in JavaScript.pptx

Deep Software Variability and Frictionless Reproducibility

Deep Software Variability and Frictionless Reproducibility

The debris of the ‘last major merger’ is dynamically young

The debris of the ‘last major merger’ is dynamically young

Shallowest Oil Discovery of Turkiye.pptx

Shallowest Oil Discovery of Turkiye.pptx

ANAMOLOUS SECONDARY GROWTH IN DICOT ROOTS.pptx

ANAMOLOUS SECONDARY GROWTH IN DICOT ROOTS.pptx

Medical Orthopedic PowerPoint Templates.pptx

Medical Orthopedic PowerPoint Templates.pptx

Nucleic Acid-its structural and functional complexity.

Nucleic Acid-its structural and functional complexity.

aziz sancar nobel prize winner: from mardin to nobel

aziz sancar nobel prize winner: from mardin to nobel

What is greenhouse gasses and how many gasses are there to affect the Earth.

What is greenhouse gasses and how many gasses are there to affect the Earth.

DERIVATION OF MODIFIED BERNOULLI EQUATION WITH VISCOUS EFFECTS AND TERMINAL V...

DERIVATION OF MODIFIED BERNOULLI EQUATION WITH VISCOUS EFFECTS AND TERMINAL V...

- 1. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers 1th Mediterranean Conference on Pattern Recognition and Artiﬁcial Intelligence EL-Hachemi Samy Dominique Ramdane Guerrout Ait-Aoudia Michelucci Mahiou Hidden Markov Random Field model and BFGS algorithm for Brain Image Segmentation LMCS Laboratory, ESI, Algeria & LE2I Laboratory, UB, France 1 / 19
- 2. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers 1 Introduction 2 Hidden Markov Random Field 3 BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm 4 Experimental Results 5 Conclusion & Perspective 2 / 19
- 3. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers Problematic & Solution 1 Nowadays, We face a huge number of medical images 2 Manual analysis and interpretation became a tedious task 3 Automatic image analysis and interpretation is a necessity 4 To simplify the representation of an image into items meaningful and easier to analyze, we need a segmentation method 3 / 19
- 4. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers A segmentation methods Segmentation methods can be classiﬁed in four main categories : 1 Threshold-based methods 2 Region-based methods 3 Model-based methods 4 Classiﬁcation methods 1 HMRF - Hidden Markov Random Field 2 etc We have chosen HMRF as a model to perform segmentation 4 / 19
- 5. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers Hidden Markov Random Field 1 HMRF provides an elegant way to model the segmentation problem 2 HMRF is a generalization of Hidden Markov Model 3 Each pixel is seen as a realization of Markov random variable 4 Each image is seen as a realization of set or family of Markov random variables 5 / 19
- 6. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers Hidden Markov Random Field The image to segment y = {ys}s∈S into K classes is a realization of Y 1 Y = {Ys}s∈S is a family of random variables 2 ys ∈ [0...255] The segmented image into K classes x = {xs}s∈S is realization of X 1 X = {Xs}s∈S is a family of random variables 2 xs ∈ {1,...,K} An example of segmentation into K = 4 classes The goal of HMRF is looking for x∗ x∗ = argx∈Ω max {P[X = x | Y = y]} 6 / 19
- 7. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers Hidden Markov Random Field 1 This elegant model leads to the optimization of an energy function Ψ(x,y) = ∑s∈S ln(σxs )+ (ys−µxs )2 2σ2 xs + β T ∑c2={s,t} (1 −2δ(xs,xt )) 2 Our way to look for the minimization of Ψ(x,y) is to look for the minimization Ψ(µ), µ = (µ1,...,µK ) where µi are means of gray values of class i 3 The main idea is to focus on the means adjustment instead of treating pixels adjustment 7 / 19
- 8. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers Hidden Markov Random Field 1 Now, we seek for u∗ µ∗ = argµ∈[0...255]K min{Ψ(µ)} Ψ(µ) = ∑K j=1 f(µj ) f(µj ) = ∑ s∈Sj [ln(σj )+ (ys−µj )2 2σ2 j ]+ β T ∑ c2={s,t} (1 −2δ(xs,xt )) 2 To apply optimization techniques, we redeﬁne the function Ψ(µ) for µ ∈ RK instead µ ∈ [0...255]K . For that, we distinguish two forms Ψ1 (µ) and Ψ2 (µ). 8 / 19
- 9. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers Hidden Markov Random Field Form 1 Ψ1 (µ) = Ψ(µ) if µ ∈ [0...255]K +∞ otherwise Ψ1 treats all points outside [0...255] in the same way Form 2 Ψ2 (µ) = ∑K j=1 F(µj ) where µj ∈ R F(µj ) = f(0)−uj if µj < 0 f(µj ) if µj ∈ [0...255] f(255)+(uj −255) if µj > 255 9 / 19
- 10. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm 1 BFGS is one of the most powerful methods to solve unconstrained optimization problem 2 BFGS is the most popular quasi-Newton method 3 BFGS is based on the gradient descent to reach the local minimum 4 Main idea of descent gradient is : 1 We start from the initial point µ0 2 At the iteration k +1, the point µk+1 is calculated from the point µk according to the following formula : µk+1 = µk +αk dk - αk is the step size at the iteration k - dk the search direction at the iteration k 10 / 19
- 11. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Summary of BFGS algorithm 1 Initialization : Set k := 0, Choose µ0 close to the solution Set H0 := I, Set α0 = 1 Choose the required accuracy ε ∈ R,ε>0 2 At the iteration k : Compute Hessian matrix approximation Hk Compute the inverse of Hessian matrix Compute the search direction dk Compute the step size αk Compute the point µk+1 3 The stopping criterion : If Ψ (µk ) <ε then ˆµ := µk 4 k := k +1 11 / 19
- 12. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers DC - The Dice Coefﬁcient The Dice coefﬁcient measures how much the segmentation result is close to the ground truth DC = 2|A ∩B| |A ∪B| 1 DC equals 1 in the best case (perfect segmentation) 2 DC equals 0 in the worst case (every pixel is misclassiﬁed) FIGURE – The Dice Coefﬁcient 12 / 19
- 13. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers BFGS in practice 1 We used the Gnu Scientiﬁc Library implementation of the BFGS 2 To apply BFGS, we need at least the ﬁrst derivative 3 In our case, computing the ﬁrst derivative is not obvious 4 We have used the centric form to compute an approximation of the ﬁrst derivative Centric form of the ﬁrst derivative Ψ (µ)) = ( ∂Ψ ∂µ1 ,..., ∂Ψ ∂µn ) ∂Ψ ∂µi = Ψ(µ1,...,µi +ε,...,µn)−Ψ(µ1,...,µi −ε,...,µn) 2ε 5 Good approximation of the ﬁrst derivative relies on the choice of the value of the parameter ε 13 / 19
- 14. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers BFGS in practice - Results 1 Through the numerous tests conducted we have selected ε = 0.01 as the best value for a good approximation of the ﬁrst derivative 2 We have tested two functions Ψ1 and Ψ2 , Ψ1 treats all points outside [0...255] in the same way 3 In practice, Ψ1 and Ψ2 give nearly the same results 14 / 19
- 15. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers HMRF-BFGS VS Classical MRF, MRF-ACO-Gossiping & MRF-ACO Methods Dice coefﬁcient GM WM CSF Mean Classical-MRF 0.763 0.723 0.780 0.756 MRF-ACO 0.770 0.729 0.785 0.762 MRF-ACO-Gossiping 0.770 0.729 0.786 0.762 HMRF-BFGS 0.974 0.991 0.960 0.975 15 / 19
- 16. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers Results with (N-Noise,I-Intensity non-uniformity) (N,I) The initial Dice coefﬁcient Time(s) point GM WM CSF Mean (0 % , 0 %) µ0,1 0.974 0.991 0.960 0.975 27.544 (2 % , 20 %) µ0,2 0.942 0.969 0.939 0.950 15.630 (5 % , 20 %) µ0,3 0.919 0.952 0.920 0.930 84.967 16 / 19
- 17. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers Example of segmentation using HMRF-BFGS (0%,0%) (3%,20%) (5%,20%) 17 / 19
- 18. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers Conclusion & Perspective 1 We have presented a combination method HMRF-BFGS 2 Through the tests conducted, 1 We have ﬁgured out good parameter settings 2 HMRF-BFGS method shows a good results 3 We conclude that HMRF-BFGS method it is very promising 4 Nevertheless, the opinion of specialists must be considered in the evaluation 18 / 19
- 19. Introduction Hidden Markov Random Field BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm Experimental Results Conclusion & Pers Thank you for your attention 19 / 19