Vu Pham worked on developing an algorithm for moment-matching scenario generation without optimization. The algorithm generates scenarios and probability weights that match moments like mean, variance, skewness and kurtosis. Vu Pham implemented the algorithm in R and generated scenarios following a given covariance matrix, mean vector, skewness and kurtosis. Vu Pham also researched other papers on scenario generation during an internship with Professor Mikhail Semenov at Tomsk Polytechnic University in Russia.
This document discusses two triangular factorization techniques - LU factorization and Cholesky-Coleman matrix inversion - that can be used to solve simultaneous linear equations in matrix form. LU factorization involves factorizing a matrix A into lower and upper triangular matrices L and U. Cholesky-Coleman matrix inversion allows in-situ inversion of a nonsingular square matrix. Optimal ordering techniques are also introduced, which aim to minimize "fill-ins" or new nonzeros generated during factorization or inversion to maintain sparsity. Examples are provided to demonstrate applying LU factorization and Cholesky-Coleman inversion to solve systems of equations.
The document discusses image stitching, which involves combining overlapping images into a single larger image. It describes detecting feature points in images, finding corresponding point pairs, using the pairs to align images with a homography matrix, and blending the combined images. It outlines an image stitching algorithm that detects keypoints, matches features, estimates homography with RANSAC to handle outliers, and blends images with pyramid blending to minimize seams and ghosting.
This document summarizes a study on evaluating the rate of convergence of the Newton-Raphson method. A computer program was coded in Java to calculate cube roots from 1 to 25 using Newton-Raphson. The lowest rate of convergence was for the cube root of 16, and the highest was for 3. The average rate of convergence was found to be 0.217920. Formulas for estimating the rate of convergence from successive approximations are also presented.
The document discusses algorithms for finding shortest paths in graphs. It describes Dijkstra's algorithm and Bellman-Ford algorithm for solving the single-source shortest path problem. Dijkstra's algorithm runs in O(ElogV) time and works for graphs with non-negative edge weights, while Bellman-Ford algorithm runs in O(EV) time and can handle graphs with negative edge weights as long as there are no negative cycles. The document also discusses Floyd-Warshall algorithm for solving the all-pairs shortest path problem.
The document describes using a genetic algorithm to solve resource-constrained project scheduling problems. It introduces genetic algorithms and describes how they can be applied to optimization problems. It then formulates a sample resource-constrained project scheduling problem as a linear programming problem to find basic feasible solutions and extreme points. The conclusion states that future work will use genetic algorithm operators like selection, reproduction and evaluation on the feasible solutions to find an optimal schedule.
This document summarizes a lecture on randomized algorithms for approximating the median. It introduces a simple randomized algorithm called Rand-Approx-Median that takes an array as input and returns an element whose rank is approximately the median in O(log n log log n) time. The algorithm works by randomly sampling elements, sorting the samples, and returning the median of the sorted samples. The document analyzes the error probability of this algorithm using elementary probability theory and shows it has low error probability. It also emphasizes that designing and analyzing randomized algorithms requires insight into elementary probability concepts.
The document discusses order statistics such as the minimum, maximum, and median of a data set. It describes the selection problem of finding the ith smallest element. A naive solution is to sort the data, but a more efficient approach is presented to find the minimum and maximum in fewer than 2n-2 comparisons by processing elements in pairs. The randomized selection algorithm is then described to find the ith smallest element in expected linear time by partitioning the data around a randomly chosen pivot.
This document discusses asymptotic notations which are mathematical tools used to analyze the time and space complexity of algorithms. It introduces Big O, Big Omega, and Big Theta notations. Big O notation represents the upper bound and worst case time complexity. Big Omega notation represents the lower bound and best case time complexity. Big Theta notation defines the average time complexity of an algorithm. Examples are provided for how to determine the asymptotic notation of polynomial functions.
This document discusses two triangular factorization techniques - LU factorization and Cholesky-Coleman matrix inversion - that can be used to solve simultaneous linear equations in matrix form. LU factorization involves factorizing a matrix A into lower and upper triangular matrices L and U. Cholesky-Coleman matrix inversion allows in-situ inversion of a nonsingular square matrix. Optimal ordering techniques are also introduced, which aim to minimize "fill-ins" or new nonzeros generated during factorization or inversion to maintain sparsity. Examples are provided to demonstrate applying LU factorization and Cholesky-Coleman inversion to solve systems of equations.
The document discusses image stitching, which involves combining overlapping images into a single larger image. It describes detecting feature points in images, finding corresponding point pairs, using the pairs to align images with a homography matrix, and blending the combined images. It outlines an image stitching algorithm that detects keypoints, matches features, estimates homography with RANSAC to handle outliers, and blends images with pyramid blending to minimize seams and ghosting.
This document summarizes a study on evaluating the rate of convergence of the Newton-Raphson method. A computer program was coded in Java to calculate cube roots from 1 to 25 using Newton-Raphson. The lowest rate of convergence was for the cube root of 16, and the highest was for 3. The average rate of convergence was found to be 0.217920. Formulas for estimating the rate of convergence from successive approximations are also presented.
The document discusses algorithms for finding shortest paths in graphs. It describes Dijkstra's algorithm and Bellman-Ford algorithm for solving the single-source shortest path problem. Dijkstra's algorithm runs in O(ElogV) time and works for graphs with non-negative edge weights, while Bellman-Ford algorithm runs in O(EV) time and can handle graphs with negative edge weights as long as there are no negative cycles. The document also discusses Floyd-Warshall algorithm for solving the all-pairs shortest path problem.
The document describes using a genetic algorithm to solve resource-constrained project scheduling problems. It introduces genetic algorithms and describes how they can be applied to optimization problems. It then formulates a sample resource-constrained project scheduling problem as a linear programming problem to find basic feasible solutions and extreme points. The conclusion states that future work will use genetic algorithm operators like selection, reproduction and evaluation on the feasible solutions to find an optimal schedule.
This document summarizes a lecture on randomized algorithms for approximating the median. It introduces a simple randomized algorithm called Rand-Approx-Median that takes an array as input and returns an element whose rank is approximately the median in O(log n log log n) time. The algorithm works by randomly sampling elements, sorting the samples, and returning the median of the sorted samples. The document analyzes the error probability of this algorithm using elementary probability theory and shows it has low error probability. It also emphasizes that designing and analyzing randomized algorithms requires insight into elementary probability concepts.
The document discusses order statistics such as the minimum, maximum, and median of a data set. It describes the selection problem of finding the ith smallest element. A naive solution is to sort the data, but a more efficient approach is presented to find the minimum and maximum in fewer than 2n-2 comparisons by processing elements in pairs. The randomized selection algorithm is then described to find the ith smallest element in expected linear time by partitioning the data around a randomly chosen pivot.
This document discusses asymptotic notations which are mathematical tools used to analyze the time and space complexity of algorithms. It introduces Big O, Big Omega, and Big Theta notations. Big O notation represents the upper bound and worst case time complexity. Big Omega notation represents the lower bound and best case time complexity. Big Theta notation defines the average time complexity of an algorithm. Examples are provided for how to determine the asymptotic notation of polynomial functions.
This document presents an algorithm for calculating conditional probability on random graphs using Markov chains. It defines key terms like Markov chains, probability matrices, and stationary probability vectors. The algorithm computes the steady state probability distribution for random graphs by creating a probability matrix and taking its powers to calculate successive stationary vectors until convergence. Several examples are provided to demonstrate calculating the steady state for unweighted and weighted random graphs, as well as bipartite graphs by changing the starting set of vertices.
The document discusses algorithms for finding order statistics like the median in a list of numbers. It presents a randomized selection algorithm that finds the ith smallest element in expected linear time O(n) by using a randomized partition like in quicksort. It also describes a deterministic selection algorithm that finds the ith element in worst-case linear time O(n) by partitioning the list around the median of medians. Finding the median can then be used to sort in linear time by recursively finding order statistics.
This article examines the differentiation of exponential function. The differentiation yields the rate of the equation. The method of differentiation can be applied to determine the unknown constants of an exponential equation.
This document provides an overview of time series forecasting techniques. It discusses the components of time series data including trends, cycles, seasonality and irregular fluctuations. It also covers stationary and non-stationary time series. Forecasting techniques covered include naive methods, smoothing techniques like moving averages and exponential smoothing, and decomposition methods. Regression models for trend analysis and measuring forecast accuracy are also discussed.
This document contains a student assignment submission for a course on Perspective in Informatics. It includes the student's responses to 3 questions:
1) Analyzing different functions to determine if they satisfy the properties of a distance measure, including max(x,y), diff(x,y), and sum(x,y).
2) Computing sketches of vectors using different random vectors and analyzing the estimated vs. true angles between the vectors.
3) Calculating the expected Jaccard similarity of two randomly selected subsets R and S of a universe U with n elements and size m.
The document discusses brute force algorithms. It provides examples of problems that can be solved using brute force, including sorting algorithms like selection sort and bubble sort. It then summarizes two geometric problems - the closest pair problem and the convex hull problem - and provides pseudocode for brute force algorithms to solve each problem. The time complexity of these brute force algorithms is O(n^3).
- Linear regression is a predictive modeling technique used to establish a relationship between two variables, known as the predictor and response variables.
- The residuals are the errors between predicted and actual values, and the optimal regression line is the one that minimizes the sum of squared residuals.
- Linear regression can be used to predict variables like salary based on experience, or housing prices based on features like crime rates or school quality. Co-relation analysis examines the relationships between predictor variables.
The document summarizes a paper that presents techniques for using dynamic analysis to discover polynomial and array invariants from program traces. It extends previous work by supporting nonlinear polynomial relations and more complex array invariants. The techniques formulate invariant discovery as a satisfiability problem and use mathematical solvers. An evaluation on test programs found most documented invariants, showing the approach can infer invariants for numeric algorithms. However, it may not scale to large programs and is limited by the traces collected.
This document discusses extrapolation, which is constructing new data points outside a range of known data points based on trends. It summarizes extrapolation techniques, assumptions, advantages, and disadvantages. Common extrapolation methods include least squares curve fitting, smooth curve fitting, and nonlinear curve fitting using the Levenberg-Marquardt algorithm. Examples of extrapolation applications given are weather and hurricane forecasting, geophysical modeling, and estimating properties at temperature and depth extremes.
This document contains the answers to an assignment on data stream processing techniques. It discusses using sampling to estimate metrics like average grade and fraction of high-performing students from a student grades data stream. It also covers the Bloom filter and estimating the number of distinct elements in a stream using the Flajolet-Martin algorithm and Count-Sketch. The assignment calculates false positive rates for Bloom filters, applies different hash functions to estimate distinct elements, and shows how Count-Sketch can estimate the join size between two streams.
This presentation gives a brief idea about Interpolation. Methods of interpolating with equally/unequally spaced intervals. Please note that not all the methods are being covered in this presentation. Topics like extrapolation and inverse interpolation have also been kept aside for another ppt.
Gauss Elimination Method With Partial PivotingSM. Aurnob
Gauss Elimination Method with Partial Pivoting:
Goal and purposes:
Gauss Elimination involves combining equations to eliminate unknowns. Although it is one of the earliest methods for solving simultaneous equations, it remains among the most important algorithms in use now a days and is the basis for linear equation solving on many popular software packages.
Description:
In the method of Gauss Elimination the fundamental idea is to add multiples of one equation to the others in order to eliminate a variable and to continue this process until only one variable is left. Once this final variable is determined, its value is substituted back into the other equations in order to evaluate the remaining unknowns. This method, characterized by step‐by‐step elimination of the variables.
Gauss Seidel Method:
Goal and purposes:
The main goal and purpose of the program is to solve a system of n linear simultaneous equation using Gauss Seidel method.
This Slides includes:
Goal and purpose, Description, Algorithm, C-code, Screenshot etc.
The document discusses several iterative methods for solving systems of equations, including Jacobi iteration, Gauss-Seidel method, and relaxation methods. The Gauss-Seidel method is commonly used and improves guesses for unknowns using values from the current iteration. Convergence is determined by calculating the relative percent change between iterations. Relaxation methods can enhance convergence by taking a weighted average of old and new values at each iteration.
Discovery is a media company that owns some of the most popular TV channels – Discovery, TLC, Animal Planet, Opera Winfrey Network (OWN), ID (crime channel), Eurosport among others.
This document provides an overview of global economic news and reports in the first quarter of 2009. It discusses the economic slowdown affecting most regions of the world due to the global financial crisis. While developing countries are expected to continue growing, their growth rates will decline substantially. The document also summarizes economic conditions in various Asian countries and regions, finding that Asia is generally faring better than other parts of the world due to healthy foreign reserves and banking systems.
Bases de la terapeutica quirurgica cancer de endometriogsa14solano
El documento presenta información sobre las bases de la terapéutica quirúrgica para el cáncer de endometrio. En 3 oraciones o menos:
El documento discute los criterios de estadificación FIGO y AJCC para el cáncer de endometrio, así como los procedimientos quirúrgicos recomendados para la estadificación dependiendo del riesgo y tipo histológico. También presenta factores pronósticos como la invasión miometrial, grado histológico y afectación ganglionar, y analiza la
MicroGuide app, pop up uni, 1pm, 3 september 2015NHS England
Expo is the most significant annual health and social care event in the calendar, uniting more NHS and care leaders, commissioners, clinicians, voluntary sector partners, innovators and media than any other health and care event.
Expo 15 returned to Manchester and was hosted once again by NHS England. Around 5000 people a day from health and care, the voluntary sector, local government, and industry joined together at Manchester Central Convention Centre for two packed days of speakers, workshops, exhibitions and professional development.
This year, Expo was more relevant and engaging than ever before, happening within the first 100 days of the new Government, and almost 12 months after the publication of the NHS Five Year Forward View. It was also a great opportunity to check on and learn from the progress of Greater Manchester as the area prepares to take over a £6 billion devolved health and social care budget, pledging to integrate hospital, community, primary and social care and vastly improve health and well-being.
More information is available online: www.expo.nhs.uk
The Art of the Possible – Enabling Care Homes with Technology to Reduce Admis...HIMSS UK
This document discusses enhanced healthcare services provided in homes through digital technologies. Telehealth services like telemonitoring, telecoaching and teleconsultation can provide care at home for patients, support end of life patients, and reduce costs compared to hospital care. A replicable model has been implemented across 361 nursing homes supporting over 14,000 residents through a 24/7 clinical telehealth hub. Initial results found a 5-14% reduction in acute admissions and A&E attendances after deployment of telemedicine. The document also describes a "gold line" telehealth service for patients in their last year of life and their caregivers.
1. El documento examina los factores de riesgo, diagnóstico, evaluación de metástasis y tratamiento del cáncer de endometrio. El cáncer de endometrio es la neoplasia ginecológica más común en los EE.UU. Se diagnostica principalmente en etapas tempranas y la tasa de supervivencia es del 75%.
2. Los síntomas más comunes son sangrado uterino anormal y flujo vaginal. Los factores de riesgo incluyen terapia de reemplazo hormonal sin oposición, ob
This document presents an algorithm for calculating conditional probability on random graphs using Markov chains. It defines key terms like Markov chains, probability matrices, and stationary probability vectors. The algorithm computes the steady state probability distribution for random graphs by creating a probability matrix and taking its powers to calculate successive stationary vectors until convergence. Several examples are provided to demonstrate calculating the steady state for unweighted and weighted random graphs, as well as bipartite graphs by changing the starting set of vertices.
The document discusses algorithms for finding order statistics like the median in a list of numbers. It presents a randomized selection algorithm that finds the ith smallest element in expected linear time O(n) by using a randomized partition like in quicksort. It also describes a deterministic selection algorithm that finds the ith element in worst-case linear time O(n) by partitioning the list around the median of medians. Finding the median can then be used to sort in linear time by recursively finding order statistics.
This article examines the differentiation of exponential function. The differentiation yields the rate of the equation. The method of differentiation can be applied to determine the unknown constants of an exponential equation.
This document provides an overview of time series forecasting techniques. It discusses the components of time series data including trends, cycles, seasonality and irregular fluctuations. It also covers stationary and non-stationary time series. Forecasting techniques covered include naive methods, smoothing techniques like moving averages and exponential smoothing, and decomposition methods. Regression models for trend analysis and measuring forecast accuracy are also discussed.
This document contains a student assignment submission for a course on Perspective in Informatics. It includes the student's responses to 3 questions:
1) Analyzing different functions to determine if they satisfy the properties of a distance measure, including max(x,y), diff(x,y), and sum(x,y).
2) Computing sketches of vectors using different random vectors and analyzing the estimated vs. true angles between the vectors.
3) Calculating the expected Jaccard similarity of two randomly selected subsets R and S of a universe U with n elements and size m.
The document discusses brute force algorithms. It provides examples of problems that can be solved using brute force, including sorting algorithms like selection sort and bubble sort. It then summarizes two geometric problems - the closest pair problem and the convex hull problem - and provides pseudocode for brute force algorithms to solve each problem. The time complexity of these brute force algorithms is O(n^3).
- Linear regression is a predictive modeling technique used to establish a relationship between two variables, known as the predictor and response variables.
- The residuals are the errors between predicted and actual values, and the optimal regression line is the one that minimizes the sum of squared residuals.
- Linear regression can be used to predict variables like salary based on experience, or housing prices based on features like crime rates or school quality. Co-relation analysis examines the relationships between predictor variables.
The document summarizes a paper that presents techniques for using dynamic analysis to discover polynomial and array invariants from program traces. It extends previous work by supporting nonlinear polynomial relations and more complex array invariants. The techniques formulate invariant discovery as a satisfiability problem and use mathematical solvers. An evaluation on test programs found most documented invariants, showing the approach can infer invariants for numeric algorithms. However, it may not scale to large programs and is limited by the traces collected.
This document discusses extrapolation, which is constructing new data points outside a range of known data points based on trends. It summarizes extrapolation techniques, assumptions, advantages, and disadvantages. Common extrapolation methods include least squares curve fitting, smooth curve fitting, and nonlinear curve fitting using the Levenberg-Marquardt algorithm. Examples of extrapolation applications given are weather and hurricane forecasting, geophysical modeling, and estimating properties at temperature and depth extremes.
This document contains the answers to an assignment on data stream processing techniques. It discusses using sampling to estimate metrics like average grade and fraction of high-performing students from a student grades data stream. It also covers the Bloom filter and estimating the number of distinct elements in a stream using the Flajolet-Martin algorithm and Count-Sketch. The assignment calculates false positive rates for Bloom filters, applies different hash functions to estimate distinct elements, and shows how Count-Sketch can estimate the join size between two streams.
This presentation gives a brief idea about Interpolation. Methods of interpolating with equally/unequally spaced intervals. Please note that not all the methods are being covered in this presentation. Topics like extrapolation and inverse interpolation have also been kept aside for another ppt.
Gauss Elimination Method With Partial PivotingSM. Aurnob
Gauss Elimination Method with Partial Pivoting:
Goal and purposes:
Gauss Elimination involves combining equations to eliminate unknowns. Although it is one of the earliest methods for solving simultaneous equations, it remains among the most important algorithms in use now a days and is the basis for linear equation solving on many popular software packages.
Description:
In the method of Gauss Elimination the fundamental idea is to add multiples of one equation to the others in order to eliminate a variable and to continue this process until only one variable is left. Once this final variable is determined, its value is substituted back into the other equations in order to evaluate the remaining unknowns. This method, characterized by step‐by‐step elimination of the variables.
Gauss Seidel Method:
Goal and purposes:
The main goal and purpose of the program is to solve a system of n linear simultaneous equation using Gauss Seidel method.
This Slides includes:
Goal and purpose, Description, Algorithm, C-code, Screenshot etc.
The document discusses several iterative methods for solving systems of equations, including Jacobi iteration, Gauss-Seidel method, and relaxation methods. The Gauss-Seidel method is commonly used and improves guesses for unknowns using values from the current iteration. Convergence is determined by calculating the relative percent change between iterations. Relaxation methods can enhance convergence by taking a weighted average of old and new values at each iteration.
Discovery is a media company that owns some of the most popular TV channels – Discovery, TLC, Animal Planet, Opera Winfrey Network (OWN), ID (crime channel), Eurosport among others.
This document provides an overview of global economic news and reports in the first quarter of 2009. It discusses the economic slowdown affecting most regions of the world due to the global financial crisis. While developing countries are expected to continue growing, their growth rates will decline substantially. The document also summarizes economic conditions in various Asian countries and regions, finding that Asia is generally faring better than other parts of the world due to healthy foreign reserves and banking systems.
Bases de la terapeutica quirurgica cancer de endometriogsa14solano
El documento presenta información sobre las bases de la terapéutica quirúrgica para el cáncer de endometrio. En 3 oraciones o menos:
El documento discute los criterios de estadificación FIGO y AJCC para el cáncer de endometrio, así como los procedimientos quirúrgicos recomendados para la estadificación dependiendo del riesgo y tipo histológico. También presenta factores pronósticos como la invasión miometrial, grado histológico y afectación ganglionar, y analiza la
MicroGuide app, pop up uni, 1pm, 3 september 2015NHS England
Expo is the most significant annual health and social care event in the calendar, uniting more NHS and care leaders, commissioners, clinicians, voluntary sector partners, innovators and media than any other health and care event.
Expo 15 returned to Manchester and was hosted once again by NHS England. Around 5000 people a day from health and care, the voluntary sector, local government, and industry joined together at Manchester Central Convention Centre for two packed days of speakers, workshops, exhibitions and professional development.
This year, Expo was more relevant and engaging than ever before, happening within the first 100 days of the new Government, and almost 12 months after the publication of the NHS Five Year Forward View. It was also a great opportunity to check on and learn from the progress of Greater Manchester as the area prepares to take over a £6 billion devolved health and social care budget, pledging to integrate hospital, community, primary and social care and vastly improve health and well-being.
More information is available online: www.expo.nhs.uk
The Art of the Possible – Enabling Care Homes with Technology to Reduce Admis...HIMSS UK
This document discusses enhanced healthcare services provided in homes through digital technologies. Telehealth services like telemonitoring, telecoaching and teleconsultation can provide care at home for patients, support end of life patients, and reduce costs compared to hospital care. A replicable model has been implemented across 361 nursing homes supporting over 14,000 residents through a 24/7 clinical telehealth hub. Initial results found a 5-14% reduction in acute admissions and A&E attendances after deployment of telemedicine. The document also describes a "gold line" telehealth service for patients in their last year of life and their caregivers.
1. El documento examina los factores de riesgo, diagnóstico, evaluación de metástasis y tratamiento del cáncer de endometrio. El cáncer de endometrio es la neoplasia ginecológica más común en los EE.UU. Se diagnostica principalmente en etapas tempranas y la tasa de supervivencia es del 75%.
2. Los síntomas más comunes son sangrado uterino anormal y flujo vaginal. Los factores de riesgo incluyen terapia de reemplazo hormonal sin oposición, ob
El documento resume la biología molecular del cáncer cérvico uterino (CaCu). El virus del papiloma humano (VPH) es un factor causal clave, detectable en casi el 100% de los casos. Las proteínas E6 y E7 del VPH interfieren con las proteínas supresoras de tumores p53 y Rb, respectivamente, lo que causa una proliferación celular descontrolada y puede conducir al desarrollo del cáncer. La persistencia de la infección por VPH de alto riesgo (genotipos 16 y 18 en particular) es un factor
O documento fornece um resumo sobre astronomia, descrevendo o que é astronomia, os primeiros astrônomos, o catálogo de Messier, o sistema solar e seus planetas, as luas do sistema solar, eclipses, constelações, a Via Láctea e galáxias, telescópios e nebulosas.
The document provides brand guidelines for Bambuild, a company that promotes the use of bamboo. It outlines Bambuild's mission and values, describes the proper uses of their logo, colors, fonts, photography style, illustrations, and includes examples of how the brand identity can be applied across different marketing materials like websites and apps. The goal is to present a consistent visual story that communicates what Bambuild is and why bamboo is a sustainable alternative material.
El documento discute las técnicas de inyección de medio de contraste intravenoso en tomografía computarizada (TC), destacando cuatro factores críticos para obtener imágenes de alta calidad: 1) el tamaño del paciente y gasto cardíaco, 2) la sincronización entre la inyección y la adquisición, 3) el volumen de inyección y adquisición, y 4) la dosis de radiación. También analiza diferentes protocolos, técnicas y parámetros de inyección, y menciona avances recientes en
O documento descreve os principais métodos de biópsia no câncer de mama, incluindo punção aspirativa por agulha fina, biópsia percutânea de fragmentos com pistola automática e biópsia percutânea assistida a vácuo. Detalha os procedimentos, vantagens e limitações de cada método, além de abordar a biópsia cirúrgica e técnicas de localização pré-cirúrgica.
Rastreamento e diagnóstico precoce do câncer de mama 19 set2012Graciela Luongo
O documento discute o rastreamento e diagnóstico precoce do câncer de mama, abordando a incidência da doença no Brasil e no mundo, fatores de risco, métodos de detecção como mamografia e ultrassonografia, além de classificações para achados mamográficos.
Este documento describe la tomografía computarizada (TC), incluyendo su historia, principios y proceso de reconstrucción de imágenes. La TC permite generar imágenes transversales del cuerpo mediante la medición de la atenuación de rayos X desde múltiples ángulos. Esto proporciona una visualización clara de las estructuras internas sin superposición. El documento explica cómo las mediciones de atenuación se utilizan para reconstruir la imagen píxel a píxel a través de técnicas iterativas. También
1. El documento describe diferentes patrones radiológicos de enfermedades pulmonares, incluyendo disminución o aumento de densidad pulmonar. 2. Se detallan patrones como el alveolar, intersticial, masas y nódulos, y se describen condiciones como neumonía, tuberculosis, edema pulmonar y enfisema. 3. También cubre hallazgos de derrame pleural, neumotórax, fracturas de costillas y patología mediastínica.
Intro to Quant Trading Strategies (Lecture 2 of 10)Adrian Aley
This document provides an introduction to hidden Markov models for algorithmic trading strategies. It discusses key concepts like Bayes' theorem, Markov chains, and the Markov property. It then covers the three main problems in hidden Markov models: likelihood, decoding, and learning. It presents solutions to these problems, including the forward-backward, Viterbi, and Baum-Welch algorithms. It also discusses extensions to non-discrete distributions and trading ideas using hidden Markov models.
Riemannian gossip algorithms for decentralized matrix completionBamdev Mishra
The document proposes a Riemannian gossip algorithm for decentralized matrix completion. Each agent has its own data matrix and aims to complete the matrix while reaching consensus on the common factor matrix U with other agents. The optimization problem is formulated on a Grassmann manifold by minimizing a weighted combination of completion and consensus terms. A parallel variant of the gossip algorithm is also developed, which converges at the same rate as the original algorithm. Numerical tests on synthetic and Netflix data show the algorithm achieves good performance compared to benchmark methods.
A New Deterministic RSA-Factoring AlgorithmJim Jimenez
This document proposes a new deterministic algorithm for factoring RSA numbers (n = p * q) and describes how it works. The algorithm uses schoolboy multiplication and counting/probability concepts to sequentially produce possible values for the prime factors p and q in a way that their product equals the original RSA number n. It has two main procedures: 1) A Producer procedure that sequentially generates values for the digits of p and q to match the first half of the digits in n. 2) An Eliminator procedure that eliminates combinations of p and q that do not match the second half of digits in n, leaving the correct factors. Pseudocode is provided to demonstrate how it works on a sample number. The document concludes by analyzing the running
Universal Approximation Property via Quantum Feature Maps
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The quantum Hilbert space can be used as a quantum-enhanced feature space in machine learning (ML) via the quantum feature map to encode classical data into quantum states. We prove the ability to approximate any continuous function with optimal approximation rate via quantum ML models in typical quantum feature maps.
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Contributed talk at Quantum Techniques in Machine Learning 2021, Tokyo, November 8-12 2021.
By Quoc Hoan Tran, Takahiro Goto and Kohei Nakajima
This document provides an overview of point estimation methods, including maximum likelihood estimation and the method of moments. It begins with an introduction to statistical inference and the theory of estimation. Point estimation is defined as using sample data to calculate a single value as the best estimate of an unknown population parameter. Maximum likelihood estimation maximizes the likelihood function to find the parameter values that make the observed sample data most probable. The method of moments equates sample moments to theoretical moments to derive parameter estimates. Examples are provided to illustrate how to apply each method to obtain point estimators.
Dmitrii Tihonkih - The Iterative Closest Points Algorithm and Affine Transfo...AIST
This document describes modifications made to the iterative closest point (ICP) algorithm. The authors propose a new matching procedure that uses the angles between line segments connecting points to find initial correspondences. They also formulate the ICP variational problem for an arbitrary affine transformation. A computer simulation applies the standard ICP approach and the authors' algorithm to two point sets related by a known transformation, finding the latter estimates the transformation more accurately.
A Computationally Efficient Algorithm to Solve Generalized Method of Moments ...Waqas Tariq
Generalized method of moment estimating function enables one to estimate regression parameters consistently and efficiently. However, it involves one major computational problem: in complex data settings, solving generalized method of moments estimating function via Newton-Raphson technique gives rise often to non-invertible Jacobian matrices. Thus, parameter estimation becomes unreliable and computationally inefficient. To overcome this problem, we propose to use secant method based on vector divisions instead of the usual Newton-Raphson technique to estimate the regression parameters. This new method of estimation demonstrates a decrease in the number of non-convergence iterations as compared to the Newton-Raphson technique and provides reliable estimates.
STLtalk about statistical analysis and its applicationJulieDash5
The document provides an introduction to statistical learning theory. It describes the supervised learning setting, where the goal is to select a predictor from a set of candidates that minimizes the expected loss on new data, given training data, candidates, and a loss function. It discusses how empirical risk minimization (ERM), such as by minimizing error on the training set, can approximate this goal. One sufficient condition for ERM consistency is uniform convergence of the empirical risk to the true risk as more data is observed.
Chi-squared Goodness of Fit Test Project Overview and.docxmccormicknadine86
Chi-squared Goodness of Fit Test Project
Overview and Rationale
This assignment is designed to provide you with hands-on experience in generating
random values and performing statistical analysis on those values.
Course Outcomes
This assignment is directly linked to the following key learning outcomes from the course
syllabus:
• Use descriptive, Heuristic and prescriptive analysis to drive business strategies and
actions
Assignment Summary
Follow the instructions in this project document to generate a number of different random
values using random number generation algorithm in Excel, the Inverse Transform. Then
apply the Chi-squared Goodness of Fit test to verify whether their generated values belong
to a particular probability distribution. Finally, complete a report summarizing the results
in your Excel workbook. Submit both the report and the Excel workbook.
The Excel workbook contains all statistical work. The report should explain the
experiments and their respective conclusions, and additional information as indicated in
each problem. Be sure to include all your findings along with important statistical issues.
Format & Guidelines
The report should follow the following format:
(i) Introduction
(ii) Analysis
(iii) Conclusion
And be 1000 - 1200 words in length and presented in the APA format
Project Instructions:
The project consists of 4 problems and a summary set of questions. For each problem, tom
hints and theoretical background is provided.
Complete each section in a separate worksheet of the same workbook (Excel file). Name
your Excel workbook as follows:
ALY6050-Module 1 Project – Your Last Name – First Initial.xlsx
In the following set of problems, r is the standard uniform random value (a continuous
random value between 0 and 1).
Problem 1
Generate 1000 random values r. For each r generated, calculate the random value 𝑿𝑿 by:
𝒙𝒙 = −𝑳𝑳𝑳𝑳(𝒓𝒓),
where “Ln“ is the natural logarithm function.
Investigate the probability distribution of X by doing the following:
1. Create a relative frequency histogram of X.
2. Select a probability distribution that, in your judgement, is the best fit for X.
3. Support your assertion above by creating a probability plot for X.
4. Support your assertion above by performing a Chi-squared test of best fit with a 0.05
level of significance.
5. In the word document, describe your methodologies and conclusions.
6. In the word document, explain what you have learned from this experiment.
Hints and Theoretical Background
A popular method for generating random values according to a certain probability
distribution is to use the inverse transform method. In this method, the cumulative
function of the distribution (F(x)) is used for such a random number generation. More
specifically, a standard uniform random value r is generated first. Most software
environments are capable of generating such a value. In E
Богдан Павлишенко (Bohdan Pavlyshenko) - "Linear, Machine Learning and Probab...Lviv Startup Club
Lviv Data Science Club 25.01.2018
Богдан Павлишенко (Bohdan Pavlyshenko) - "Linear, Machine Learning and Probabilistic Approaches for Predictive Analytics"
Chi-squared Goodness of Fit Test Project Overview and.docxbissacr
Chi-squared Goodness of Fit Test Project
Overview and Rationale
This assignment is designed to provide you with hands-on experience in generating
random values and performing statistical analysis on those values.
Course Outcomes
This assignment is directly linked to the following key learning outcomes from the course
syllabus:
• Use descriptive, Heuristic and prescriptive analysis to drive business strategies and
actions
Assignment Summary
Follow the instructions in this project document to generate a number of different random
values using random number generation algorithm in Excel, the Inverse Transform. Then
apply the Chi-squared Goodness of Fit test to verify whether their generated values belong
to a particular probability distribution. Finally, complete a report summarizing the results
in your Excel workbook. Submit both the report and the Excel workbook.
The Excel workbook contains all statistical work. The report should explain the
experiments and their respective conclusions, and additional information as indicated in
each problem. Be sure to include all your findings along with important statistical issues.
Format & Guidelines
The report should follow the following format:
(i) Introduction
(ii) Analysis
(iii) Conclusion
And be 1000 - 1200 words in length and presented in the APA format
Project Instructions:
The project consists of 4 problems and a summary set of questions. For each problem, tom
hints and theoretical background is provided.
Complete each section in a separate worksheet of the same workbook (Excel file). Name
your Excel workbook as follows:
ALY6050-Module 1 Project – Your Last Name – First Initial.xlsx
In the following set of problems, r is the standard uniform random value (a continuous
random value between 0 and 1).
Problem 1
Generate 1000 random values r. For each r generated, calculate the random value 𝑿𝑿 by:
𝒙𝒙 = −𝑳𝑳𝑳𝑳(𝒓𝒓),
where “Ln“ is the natural logarithm function.
Investigate the probability distribution of X by doing the following:
1. Create a relative frequency histogram of X.
2. Select a probability distribution that, in your judgement, is the best fit for X.
3. Support your assertion above by creating a probability plot for X.
4. Support your assertion above by performing a Chi-squared test of best fit with a 0.05
level of significance.
5. In the word document, describe your methodologies and conclusions.
6. In the word document, explain what you have learned from this experiment.
Hints and Theoretical Background
A popular method for generating random values according to a certain probability
distribution is to use the inverse transform method. In this method, the cumulative
function of the distribution (F(x)) is used for such a random number generation. More
specifically, a standard uniform random value r is generated first. Most software
environments are capable of generating such a value. In E
1) The paper introduces the influence function for interpreting black-box machine learning models. The influence function traces a model's predictions back to the training data by examining how the model's parameters would change if a particular training point was removed or perturbed.
2) The influence function approximates this change in parameters by assuming a quadratic approximation to the empirical risk function around the learned parameters and taking a single Newton step. It shows the parameter change due to removing a point is approximated by the influence function.
3) The paper demonstrates how the influence function can be used to understand model behavior, find adversarial examples, debug issues, and correct errors, among other applications. It also proposes practical methods to compute the influence function for
A new Evolutionary Reinforcement Scheme for Stochastic Learning Automatainfopapers
F. Stoica, E. M. Popa, A new Evolutionary Reinforcement Scheme for Stochastic Learning Automata, Proceedings of the 12th WSEAS International Conference on COMPUTERS, Heraklion, Greece, July 23-25, ISBN: 978-960-6766-85-5, ISSN: 1790-5109, pp. 268-273, 2008
The document discusses the history and development of hidden Markov models (HMMs). It describes key concepts such as HMMs consisting of hidden states that produce observable outputs, and how they can be used to model sequential data. The document also provides examples of applying HMMs to problems such as gene finding, multiple sequence alignment, and protein secondary structure prediction. It summarizes algorithms like forward-backward, Viterbi, and Baum-Welch that are used to train and make predictions from HMMs. Finally, it mentions some popular HMM software tools like HMMER and SAM.
This summary provides the key details from the document in 3 sentences:
The document discusses a finite difference method for solving a nonlocal singularly perturbed problem. It presents properties of the exact solution and establishes a uniformly convergent finite difference scheme on a Bakhvalov mesh. The scheme is proven to be first-order convergent in the discrete maximum norm and a numerical example is used to validate the theoretical convergence results.
This document summarizes key topics from a lecture on linear regression analysis, including: initial data analysis, defining the linear model, testing hypotheses about parameters, and methods for obtaining confidence intervals and regions with or without assuming normality, such as permutation tests and bootstrapping. Key analysis steps like checking assumptions, fitting models, and comparing models are demonstrated in R code.
This document provides an introduction to a course on business statistics. It discusses topics that will be covered, including average values, variability, distributions, confidence intervals, and parametric tests. The course aims to equip students with knowledge of statistical techniques for analyzing business problems and interpreting quantitative data. It will include lectures, computer labs, and a final exam assessment.
The document discusses topics in discrete mathematics including methods of proof, algorithms, and number theory. It provides overviews and examples of different types of proofs like direct proof, proof by contradiction, and proof by equivalence. It also discusses algorithms like searching algorithms, sorting algorithms, analyzing their properties, and providing pseudocode examples. Specific algorithms discussed include linear search, binary search, bubble sort, and insertion sort.
Similar to Scenario Generation Algortihm using R (20)
1. Vu Pham
Scenario Generation Algorithm using R
(without optimization)
26.12.2016 Scenario Generation Algorithm using R 1Ашу Пракаш | Семенов Михаил Евгеньевич
Ashu Prakash
Indian Institute of Technology Kanpur, India
ashupk@iitk.ac.in
Dr Mikhail Semenov
Tomsk Polytechnic University, Russia
sme@tpu.ru
2. Vu Pham
I’m a third-year undergraduate student majoring in 4 year bachelorship
programme of Mathematics and Scientific Computing in the Department of
Mathematics and Statistics at the Indian Institute of Technology Kanpur,
India
My research area includes parts of Applied Mathematics, Finance,
Microeconomics and Business Analytics. I’m also interested in Computer
Programming and Multivariable Calculus.
I worked as an intern under Prof Mikhail Semenov, Tomsk Polytechnic
University, Russia. My project was to generate scenarios for stock markets
using different techniques (mainly without using optimisation)
A little about myself
26.12.2016 Scenario Generation Algorithm using R 2Ашу Пракаш | Семенов Михаил Евгеньевич
3. Vu Pham
I worked on an algorithm for moment-matching scenario generation. I tried
to produce scenarios and probability weights that match different moments.
In this approach, the statistical properties of the joint distribution are
specified in terms of moments, basically including the covariance matrix.
Optimisation is not employed in this scenario generation process and thus
this method is computationally more advantageous than previous
approaches. The algorithm is used for generating scenarios in a mean-CVaR
portfolio optimisation model.
This method is proposed in the paper "An algorithm for moment-matching
scenario generation with application to financial portfolio optimisation" by
Ponomareva, Roman, Date, (Published 2015)
Scenario Generation
26.12.2016 Scenario Generation Algorithm using R 3Ашу Пракаш | Семенов Михаил Евгеньевич
4. Vu Pham
I also worked on the paper “Generating Scenario Trees for Multistage
Decision Problems” by Høyland and Wallace, (Published 2001)
This paper deals with Tree Scenario Generation for multistage decision
problems with approximating the uncertainties by a limited number of
discrete outcomes.
The motivation for developing the method presented in this paper is the
implementation of a stochastic multistage asset allocation model.
There is a different paper which is actually a comment on this paper, by
Klaassen. "Comment on Generating Scenario Trees for Multistage Decision
Problems" by Pieter Klaassen, (Published 2002). This deals with removal of
arbitrage opportunities.
Scenario Generation
26.12.2016 Scenario Generation Algorithm using R 4Ашу Пракаш | Семенов Михаил Евгеньевич
5. Vu Pham
I have used the programming language R for all the statistical coding for the
generation of proposed algorithms.
My code followed the paper "An algorithm for moment-matching scenario
generation with application to financial portfolio optimisation" by
Ponomareva, Roman, Date, (Published 2015).
I tried to generate probabilities associated with the moment-matching
scenario generation. Mean, Variance, Skewness, Kurtosis are matched in the
proposed algorithm.
The input of the algorithm follows a covariance matrix, mean vector,
skewness and kurtosis. The aim was to generate a vector of positive
probabilities.
Scenario Generation Algorithm
26.12.2016 Scenario Generation Algorithm using R 5Ашу Пракаш | Семенов Михаил Евгеньевич
6. Vu Pham
Let us assume we have an N – variate random vector r = (r1, r2, r3, … , rN)T
We know the distribution of this random vector in terms of following:
µ : target mean vector
∑ : target covariance matrix (positive definite)
kj : marginal third central moment (skewness) of rj, j = 1, 2, 3, … , N
ƺj : marginal fourth central moment (kurtosis) of rj, j = 1, 2, 3, … , N
We denote the average marginal moments as
Mean skewness : k’ =
1
𝑁
σ 𝑗=1
𝑁
kj
Mean kurtosis : ƺ’ =
1
𝑁
σ 𝑗=1
𝑁
ƺj
An even number of scenarios, 2Ns, proportional to the vector’s dimension,
are generated such that they match the first and second moments. These
scenarios are symmetrically distributed around the expected value such that
the variance–covariance matrix is matched
Scenario Generation Algorithm
26.12.2016 Scenario Generation Algorithm using R 6Ашу Пракаш | Семенов Михаил Евгеньевич
7. Vu Pham
Three additional scenarios are generated in order to match the average
marginal skewness and the average marginal kurtosis of each individual
component of the random vector r.
Parameters for Scenario Generation
We have the inputs µ, ∑, kj , ƺj . Our programme must choose an arbitrary
positive integer s, an arbitrary nonzero deterministic vector Z, such that
∑ - ZZT > 0, and a scalar ρ ϵ 0,1
We randomly generate a ρ using a normal distribution.
Also, Z is generated using this ρ . We take Zj = ρ σjj (ρ = 0.45, in my case)
Here ∑jj = vector corresponding to the diagonal elements of ∑
Scenario Generation Algorithm
26.12.2016 Scenario Generation Algorithm using R 7Ашу Пракаш | Семенов Михаил Евгеньевич
8. Vu Pham
The next part is to find L. In the paper, L is defined as a positive definite
matrix such that LLT = ∑ - ZZT . We may use Cholesky decomposition method
on ∑ - ZZT to find L.
Now we generate a random natural number ‘s’ after which we can find the
probability weights. Let pi’s be real scalars such that pi ∈ 0,1 . There are
many ways for generating pi’s.
Note that number of scenarios are independent on the dimension of the
random vector r as ‘s’ is a randomly generated positive integer.
pi’s can be generated by sampling from a uniform distribution or gamma
distribution method. The detailed explanation is provided in the next slide.
Scenario Generation Algorithm
26.12.2016 Scenario Generation Algorithm using R 8Ашу Пракаш | Семенов Михаил Евгеньевич
9. Vu Pham
One method to generate pi is such that it satisfies
pi =
𝑠
𝑁𝛾
+ (
1
2𝑁𝑠
−
𝑠
𝑁𝛾
) U , where U ∈ 0,1 is a uniformly generated random
variable where 𝛾 is defined as
𝛾 = 2𝑠2
𝑁ƺ’ − 3
4
σ 𝑗=1
𝑁
𝑍4
𝑗
𝑁k'
σ 𝑗=1
𝑁
𝑍3
𝑗
2
σ𝑙 σ 𝑘 𝐿4
𝑙𝑘
Another method of generating pi is from gamma distribution. We generate U
in between (
1
𝑒
, 1 ) by gamma distribution, and taking pi = loge(U). In this
method, we must normalise the weights.
p𝑖′ =
𝑝𝑖
𝑁𝑠(2 σ 𝑝𝑖 + max(𝑝𝑖))
Scenario Generation Algorithm
26.12.2016 Scenario Generation Algorithm using R 9Ашу Пракаш | Семенов Михаил Евгеньевич
10. Vu Pham
Now, after finding pi’s we must check that the following two conditions are
satisfied.
1.) σ𝑖=1
𝑠
𝑝𝑖 <
1
2𝑁
2.) σ𝑖=1
𝑠 1
𝑝𝑖
< 𝛾 if 𝛾 𝑖𝑠 𝑢𝑠𝑒𝑑
We define a new element in the vector p, ps+1 = 1 – 2N σ𝑖=1
𝑠
𝑝𝑖
Now we will define 𝜑1 𝑎𝑛𝑑 𝜑2 which will be used to find probabilities.
𝜑1 =
𝑁𝑘′ ps
+
1
σ 𝑗=1
𝑁
𝑍3
𝑗
and 𝜑2 = ps+1
𝑁ƺ’ −
1
2𝑠
2 σ 𝑙 σ 𝑘 𝐿4
𝑙𝑘
(σ𝑖=1
𝑠 1
𝑝𝑖
)
σ 𝑗=1
𝑁
𝑍4
𝑗
After determining the above values, we’ll find 𝛼 and 𝛽.
Scenario Generation Algorithm
26.12.2016 Scenario Generation Algorithm using R 10Ашу Пракаш | Семенов Михаил Евгеньевич
11. Vu Pham
We define 𝛼 and 𝛽 as follows :
𝛼 = +
1
2
𝜑1 +
1
2
4𝜑2 − 3𝜑1
2
𝛽 = −
1
2
𝜑1 +
1
2
4𝜑2 − 3𝜑1
2
In our algorithm, we must have 4𝜑2 − 3𝜑1
2 ≥ 0
We define w1, w2 and w0 .
w1 =
1
𝛼(𝛼+𝛽)
, w2 =
1
𝛽(𝛼+𝛽)
and w0 = 1 -
1
𝛼𝛽
Observe that w1 + w2 + w0 = 1
Scenario Generation Algorithm
26.12.2016 Scenario Generation Algorithm using R 11Ашу Пракаш | Семенов Михаил Евгеньевич
12. Vu Pham
After finding these values, our aim is to find the probability weights P.
We define, S = 2Ns + 3. Given p1, p2, … , ps+1 and w0 , w1, w2 from previous
steps. Vector P is formed as follows :
𝑃 = 𝑝1, 𝑝2, … , 𝑝 𝑠, 𝑝1, 𝑝2, … , 𝑝 𝑠, … , 𝑝 𝑠 + 1 𝑤0, 𝑝 𝑠 + 1 𝑤1, 𝑝 𝑠 + 1 𝑤2
All the elements of P must be non-negative. Also, σ 𝑃 = 1
Note that there is no optimisation involved in this whole algorithm.
Since there is no algorithm involved in this method, it’s the fastest way for
the moment-matching scenario generation.
My code in R is described in coming slides.
Scenario Generation Algorithm
26.12.2016 Scenario Generation Algorithm using R 12Ашу Пракаш | Семенов Михаил Евгеньевич
13. Vu Pham
My code in R
Initialising inputs for the algorithm.
Implementation of Algorithm in R
26.12.2016 Scenario Generation Algorithm using R 13Ашу Пракаш | Семенов Михаил Евгеньевич
14. Vu Pham
My code in R
We randomly generate ‘s’ (an integer ranging between 1 and 10000)
L is generated using Cholesky decomposition method.
Note: L must be positive definite
Implementation of Algorithm in R
26.12.2016 Scenario Generation Algorithm using R 14Ашу Пракаш | Семенов Михаил Евгеньевич
15. Vu Pham
My code in R (Loop is used to find the vector P with only positive elements)
Implementation of Algorithm in R
26.12.2016 Scenario Generation Algorithm using R 15Ашу Пракаш | Семенов Михаил Евгеньевич
16. Vu Pham
My code in R
Implementation of Algorithm in R
26.12.2016 Scenario Generation Algorithm using R 16Ашу Пракаш | Семенов Михаил Евгеньевич
𝛼, 𝛽, 𝑤1, 𝑤2 𝑎𝑛𝑑 𝑤0 𝑎𝑟𝑒 𝑑𝑒𝑓𝑖𝑛𝑒𝑑
Vector P with S = 2Ns + 3
elements is formed
For loop is created so that only
elements with positive values are in the
output result.
This code also checks
4𝜑2 − 3𝜑1
2 ≥ 0
17. Vu Pham
My code in R (Finalising the code)
The main loop is closed.
In the output vector P, sum of all the elements must be 1.
sum(P) = 1 ??? Yes
Finally we can get the value of ‘s’ at which the loop terminated.
Implementation of Algorithm in R
26.12.2016 Scenario Generation Algorithm using R 17Ашу Пракаш | Семенов Михаил Евгеньевич
18. Vu Pham
I also did some works with Prof Semenov. I tried to understand one of his
research paper on Options Portfolio.
I’m still working with an algorithm in that paper and like to work further in
the future.
I read some more research papers on Stock Market Scenario Generation.
I thank Prof Mikhail Semenov for mentoring me in this one month project. I
learned a lot during this time period.
I also thank National Research Tomsk Polytechnic University, Russia for
giving this research internship opportunity.
Internship at TPU
26.12.2016 Scenario Generation Algorithm using R 18Ашу Пракаш | Семенов Михаил Евгеньевич
19. Vu Pham
IIT Kanpur and TPU has an agreement on academic research collaboration
which was signed on 06.07.2015
IITK and TPU have many areas of common interest in education and
research.
This collaborative agreement has programmes like
a) Faculty/Scientist/Staff exchanges
b) Student exchanges (at both UG and PG level)
TPU is the only university in Russia with which IITK has a collaboration.
Our agreement is valid up to 06.07.2020
IITK & TPU Collaboration
26.12.2016 Scenario Generation Algorithm using R 19Ашу Пракаш | Семенов Михаил Евгеньевич
20. Vu Pham
Ponomareva, Roman, Date, “An algorithm for moment-matching scenario
generation with application to financial portfolio optimisation”. (European
Journal of Operational Research, 2015)
Høyland and Wallace, “Generating Scenario Trees for Multistage Decision
Problems”. (Norwegian University of Science and Technology, 2001)
Pieter Klaassen, Comment on “Generating Scenario Trees for Multistage
Decision Problems”. (The Netherlands, Vrije Universiteit, 2002)
Hoffman, “Combinatorial optimization: Current successes and directions for
the future”. (Journal of Computational and Applied Mathematics 124 (2000)
341-360)
Mico Loretan, “Generating market risk scenarios using principal components
analysis: methodological and practical considerations”. (Federal Reserve
Board, March 1997)
Wurtz, Chalabi, Chen, Ellis, “Portfolio Optimization with R/Rmetrics”.
(Zurich, Rmetrics Association & Finance Online, May 2009)
References
26.12.2016 Scenario Generation Algorithm using R 20Ашу Пракаш | Семенов Михаил Евгеньевич
21. Vu Pham
СПАСИБО
Thank You !
26.12.2016 Scenario Generation Algorithm using R 21Ашу Пракаш | Семенов Михаил Евгеньевич