Slide set presented for the Wireless Communication module at Jacobs University Bremen, Fall 2015.
Teacher: Dr. Stefano Severi, assistant: Andrei Stoica
The document summarizes the LabPQR color space model proposed by researchers at Rochester Institute of Technology. The model uses a transformation from tristimulus values and a set of basis vectors derived from principal component analysis to represent color spectra in a lower dimensional space. This representation allows spectral data to be compressed while maintaining accuracy for applications like multi-spectral color reproduction. The model builds on prior work using matrix algebra to decompose color stimuli into fundamental and residue components.
This is concerned with designing an exact exponential time algorithm that is better than the well-known 2^n algorithm for the problem Path Contraction. This answers an open question of van't Hof et. al [TCS 2009]. This is based on the article that appeared in ICALP 2019.
Fine Grained Complexity of Rainbow Coloring and its VariantsAkankshaAgrawal55
The document discusses rainbow coloring and its variants in graphs. It presents the following:
- The goal of fine-grained reductions between problems A and B to show if B has a faster algorithm then A does as well.
- Definitions of rainbow paths and rainbow colorings in edge-colored graphs.
- Variants of the rainbow coloring problem including subset rainbow coloring and Steiner rainbow coloring which restrict the pairs of vertices required to have a rainbow path between them.
- Previous works showing various rainbow coloring problems are NP-hard and studying their fine-grained complexity.
- The document proposes improving previous results, showing subset rainbow coloring admits a faster algorithm for k=3 using color coding
Understanding Dynamic Programming through Bellman OperatorsAshwin Rao
Policy Iteration and Value Iteration algorithms are best understood by viewing them from the lens of Bellman Policy Operator and Bellman Optimality Operator
Guarding Terrains though the Lens of Parameterized ComplexityAkankshaAgrawal55
The Terrain Guarding problem is a well-studied visibility problem in Discrete and Computational Geometry. So far, the understanding of the parameterized complexity of Terrain Guarding has been very limited, and, more generally, exact (exponential-time) algorithms for visibility problem are extremely scarce. In this talk we will look at two results regarding Terrain Guarding, from the viewpoint of parameterized complexity. Both of these results will utilize new and known structural properties of terrains. The first result that we will see is a polynomial kernel for Terrain Guarding, when parameterized by the number of reflex vertices. (A reflex vertex is a vertex of the terrain where the angle is at least 180 degrees.) The next result will be regarding a special version of Terrain Guarding, called Orthogonal Terrain Guarding. We will consider the above problem when parameterized by the number of minima in the input terrain, and obtain a dynamic programming based XP algorithm for it.
This presentation is the one that I gave at the Parameterized Complexity Seminar (https://sites.google.com/view/pcseminar).
Practical Spherical Harmonics Based PRT MethodsNaughty Dog
The document summarizes methods for compressing precomputed radiance transfer (PRT) coefficients using spherical harmonics. It presents 4 methods with progressively higher compression ratios: Method 1 uses 9 bytes by removing a factor and scaling, Method 2 uses 6 bytes with a bit field allocation, Method 3 uses 6 bytes with a Lloyd-Max non-uniform quantizer, and Method 4 achieves 4 bytes with a different bit allocation. The methods are evaluated based on storage size, reconstruction quality, and rendering performance.
To make Reinforcement Learning Algorithms work in the real-world, one has to get around (what Sutton calls) the "deadly triad": the combination of bootstrapping, function approximation and off-policy evaluation. The first step here is to understand Value Function Vector Space/Geometry and then make one's way into Gradient TD Algorithms (a big breakthrough to overcome the "deadly triad").
The document summarizes the LabPQR color space model proposed by researchers at Rochester Institute of Technology. The model uses a transformation from tristimulus values and a set of basis vectors derived from principal component analysis to represent color spectra in a lower dimensional space. This representation allows spectral data to be compressed while maintaining accuracy for applications like multi-spectral color reproduction. The model builds on prior work using matrix algebra to decompose color stimuli into fundamental and residue components.
This is concerned with designing an exact exponential time algorithm that is better than the well-known 2^n algorithm for the problem Path Contraction. This answers an open question of van't Hof et. al [TCS 2009]. This is based on the article that appeared in ICALP 2019.
Fine Grained Complexity of Rainbow Coloring and its VariantsAkankshaAgrawal55
The document discusses rainbow coloring and its variants in graphs. It presents the following:
- The goal of fine-grained reductions between problems A and B to show if B has a faster algorithm then A does as well.
- Definitions of rainbow paths and rainbow colorings in edge-colored graphs.
- Variants of the rainbow coloring problem including subset rainbow coloring and Steiner rainbow coloring which restrict the pairs of vertices required to have a rainbow path between them.
- Previous works showing various rainbow coloring problems are NP-hard and studying their fine-grained complexity.
- The document proposes improving previous results, showing subset rainbow coloring admits a faster algorithm for k=3 using color coding
Understanding Dynamic Programming through Bellman OperatorsAshwin Rao
Policy Iteration and Value Iteration algorithms are best understood by viewing them from the lens of Bellman Policy Operator and Bellman Optimality Operator
Guarding Terrains though the Lens of Parameterized ComplexityAkankshaAgrawal55
The Terrain Guarding problem is a well-studied visibility problem in Discrete and Computational Geometry. So far, the understanding of the parameterized complexity of Terrain Guarding has been very limited, and, more generally, exact (exponential-time) algorithms for visibility problem are extremely scarce. In this talk we will look at two results regarding Terrain Guarding, from the viewpoint of parameterized complexity. Both of these results will utilize new and known structural properties of terrains. The first result that we will see is a polynomial kernel for Terrain Guarding, when parameterized by the number of reflex vertices. (A reflex vertex is a vertex of the terrain where the angle is at least 180 degrees.) The next result will be regarding a special version of Terrain Guarding, called Orthogonal Terrain Guarding. We will consider the above problem when parameterized by the number of minima in the input terrain, and obtain a dynamic programming based XP algorithm for it.
This presentation is the one that I gave at the Parameterized Complexity Seminar (https://sites.google.com/view/pcseminar).
Practical Spherical Harmonics Based PRT MethodsNaughty Dog
The document summarizes methods for compressing precomputed radiance transfer (PRT) coefficients using spherical harmonics. It presents 4 methods with progressively higher compression ratios: Method 1 uses 9 bytes by removing a factor and scaling, Method 2 uses 6 bytes with a bit field allocation, Method 3 uses 6 bytes with a Lloyd-Max non-uniform quantizer, and Method 4 achieves 4 bytes with a different bit allocation. The methods are evaluated based on storage size, reconstruction quality, and rendering performance.
To make Reinforcement Learning Algorithms work in the real-world, one has to get around (what Sutton calls) the "deadly triad": the combination of bootstrapping, function approximation and off-policy evaluation. The first step here is to understand Value Function Vector Space/Geometry and then make one's way into Gradient TD Algorithms (a big breakthrough to overcome the "deadly triad").
The document describes optimizing a lighting calculation for the SPU by analyzing memory requirements, partitioning data, and rearranging data for a streaming model. It then provides an example of optimizing a lighting calculation function, including vectorizing the calculation by hand to process 4 vertices simultaneously. The optimizations reduced the calculation time from 231.6 cycles per vertex per light to 208.5 cycles through compiler hints and further to an estimated higher performance by manual vectorization.
Bayesian adaptive optimal estimation using a sieve priorJulyan Arbel
This document presents results on Bayesian optimal adaptive estimation using a sieve prior. It derives posterior concentration rates and risk convergence rates for models that accommodate a sieve prior. For the Gaussian white noise model, it shows the rates are adaptive optimal under global loss but a lower bound on the rate is obtained under pointwise loss, indicating the sieve prior is not optimal. Further work on posterior concentration rates under pointwise loss is suggested.
This document discusses how the Traveling Salesman Problem (TSP) is NP-Complete. It first shows that TSP is in NP by describing a nondeterministic polynomial time algorithm to solve it. It then reduces the known NP-Complete Hamiltonian Cycle problem to TSP by constructing an equivalent instance of TSP from any Hamiltonian Cycle problem instance in polynomial time, showing that Hamiltonian Cycle is polynomial time reducible to TSP. Therefore, since any problem in NP can be reduced to Hamiltonian Cycle and Hamiltonian Cycle can be reduced to TSP, any problem in NP can be reduced to TSP, proving that TSP is NP-Complete.
This document discusses canonical-Laplace transforms and various testing function spaces. It begins by defining the canonical-Laplace transform and establishes some testing function spaces using Gelfand-Shilov technique, including CLa,b,γ, CLab,β, CLγa,b,β, CLa,b,β,n, and CLγa,,m,β,n. It then presents results on countable unions of s-type spaces, proving that various spaces can be expressed as countable unions and discussing topological properties. The document concludes by stating that canonical-Laplace transforms are generalized in a distributional sense and results on countable unions of s-type spaces are discussed, along with the topological structure
The document discusses the Fourier transform, which relates a signal sampled in time or space to the same signal sampled in frequency. It explains the mathematical definition and provides an example of using a Fourier transform to convert time domain data to the frequency domain. Specifically, it uses a cosine wave as input data and calculates the Fourier transform to reveal a strong amplitude at the expected frequency component.
This document provides an introduction to SPU optimizations by summarizing the SPU assembly instructions. It begins by explaining the SPU execution environment and memory model. It then categorizes the instruction set into classes based on arity and latency. The majority of the document details the various instructions in the Single Precision Floating Point (SP), Fixed precision (FX), and other classes; explaining their syntax, latency, and examples of use. The goal is to familiarize programmers with the SPU hardware and instruction set to enable improved performance through optimization techniques.
RSS discussion of Girolami and Calderhead, October 13, 2010Christian Robert
1. The document discusses discretizing Hamiltonians for Markov chain Monte Carlo (MCMC) methods. Specifically, it examines reproducing Hamiltonian equations through discretization, such as via generalized leapfrog.
2. However, the invariance and stability properties of the continuous-time process may not carry over to the discretized version. Approximations can be corrected with a Metropolis-Hastings step, so exactly reproducing the continuous behavior is not necessarily useful.
3. Discretization induces a calibration problem of determining the appropriate step size. Convergence issues for the MCMC algorithm should not be impacted by imperfect renderings of the continuous-time process in discrete time.
What is Fourier Transform
Spatial to Frequency Domain
Fourier Transform
Forward Fourier and Inverse Fourier transforms
Properties of Fourier Transforms
Fourier Transformation in Image processing
Symbolic Execution as DPLL Modulo TheoriesQuoc-Sang Phan
The document discusses symbolic execution, which is a program analysis technique that executes programs with symbolic inputs instead of concrete inputs. It describes symbolic execution as an approach for solving satisfiability modulo theories (SMT) problems, by viewing symbolic execution as an SMT solver. It presents an implementation of symbolic execution based on a Boolean executor that performs a depth-first search, combined with an SMT solver to check satisfiability of path conditions.
This document discusses the design of finite impulse response (FIR) filters. It begins by describing the basic FIR filter model and properties such as filter order and length. It then covers topics such as linear phase response, different filter types (low-pass, high-pass, etc.), deriving the ideal impulse response, and filter specification in terms of passband/stopband edges and ripple levels. The document concludes by outlining the common FIR design method of windowing the ideal impulse response, describing popular window functions, and providing a step-by-step example of designing a low-pass FIR filter using the Hamming window.
This document provides definitions and examples related to Fourier series and Fourier transforms. It defines the Fourier transform and inverse Fourier transform of a function f(x). It gives the Fourier integral representation of a function and provides an example of finding the Fourier integral representation of a rectangle function. It also defines Fourier sine and cosine integrals. Finally, it outlines some properties of Fourier transforms, including the modulation theorem and convolution theorem.
This document discusses Doppler estimation of radar signals using complex wavelet transforms (CWT). It begins by introducing existing Doppler estimation methods like FFT and adaptive estimation techniques that have limitations. CWT provides advantages over real wavelet transforms by generating complex coefficients. The document then describes the dual tree CWT formulation and use of analytic signals for amplitude and frequency analysis. It proposes using CWT with a custom thresholding algorithm to estimate Doppler profiles from radar data. Results on test radar signals show the method can estimate Doppler at higher altitudes where existing techniques fail due to noise.
This document presents distributed algorithms for k-truss decomposition of large graphs. It begins with introducing the problem of k-truss decomposition and definitions. It then describes how k-truss decomposition can be performed using traditional sequential algorithms. It proposes two distributed algorithms: MRTruss, which uses MapReduce but has limitations; and i-MRTruss, an improved version that aims to address the issues with MRTruss. The document outlines the different sections that will evaluate these distributed algorithms and experimentally analyze their performance.
The Fourier transform is a mathematical tool that transforms functions between the time and frequency domains. It breaks down any function or signal into the frequencies that make it up. This allows analysis of signals in the frequency domain, enabling applications like image and signal processing. The Fourier transform represents functions as a combination of sinusoidal functions like sines and cosines. The inverse Fourier transform reconstructs the original function from its frequency representation. Fourier transforms have many uses including solving differential equations, filtering sound and images, and analyzing signals like heartbeats.
This document discusses the Fourier transformation, including:
1) It defines continuous and discrete Fourier transformations and their properties such as separability, translation, periodicity, and convolution.
2) The fast Fourier transformation (FFT) improves the computational complexity of the discrete Fourier transformation from O(N^2) to O(NlogN).
3) FFT works by rewriting the DFT calculation in a way that exploits symmetry and reduces redundant computations.
This document summarizes two algorithms for computing properties of high-dimensional polytopes given access to certain oracle functions:
1. An algorithm for computing the edge-skeleton of a polytope in oracle polynomial-time using an oracle that returns the vertex maximizing a linear function.
2. A randomized algorithm for approximating the volume of a polytope by generating random points within it using a hit-and-run process, and estimating the volume from these points. The algorithm runs in oracle polynomial-time and provides an approximation with high probability.
Experimental results show the volume algorithm can approximate volumes of polytopes up to 100 dimensions within 1% error in under 2 hours, outperforming exact
Discussion of Fearnhead and Prangle, RSS< Dec. 14, 2011Christian Robert
The document discusses approximate Bayesian computation (ABC), a technique used when the likelihood function is intractable. ABC works by simulating data under different parameter values and accepting simulations that are close to the observed data according to a distance measure. The key challenges are choosing a sufficient summary statistic of the data and setting the tolerance level. Later sections discuss using a noisy ABC approach, where the summary statistic is perturbed, and calibrating the method so that the ABC posterior converges to the true parameter as the number of simulations increases. The document examines issues around choosing optimal summary statistics and tolerance levels to minimize errors in the ABC approximation.
This document discusses redesigning the health, safety, and environment (HSE) function in companies. It notes that HSE functions are often being downsized with limited risk consideration. The document provides signs that an HSE function may need to change, such as functional overload or inefficient resource allocation. It also outlines steps to redesign the HSE function, including defining customer needs and mapping the current and desired operating models. The goal is to right-size the HSE function to effectively support operations and demonstrate value to the organization.
The document describes optimizing a lighting calculation for the SPU by analyzing memory requirements, partitioning data, and rearranging data for a streaming model. It then provides an example of optimizing a lighting calculation function, including vectorizing the calculation by hand to process 4 vertices simultaneously. The optimizations reduced the calculation time from 231.6 cycles per vertex per light to 208.5 cycles through compiler hints and further to an estimated higher performance by manual vectorization.
Bayesian adaptive optimal estimation using a sieve priorJulyan Arbel
This document presents results on Bayesian optimal adaptive estimation using a sieve prior. It derives posterior concentration rates and risk convergence rates for models that accommodate a sieve prior. For the Gaussian white noise model, it shows the rates are adaptive optimal under global loss but a lower bound on the rate is obtained under pointwise loss, indicating the sieve prior is not optimal. Further work on posterior concentration rates under pointwise loss is suggested.
This document discusses how the Traveling Salesman Problem (TSP) is NP-Complete. It first shows that TSP is in NP by describing a nondeterministic polynomial time algorithm to solve it. It then reduces the known NP-Complete Hamiltonian Cycle problem to TSP by constructing an equivalent instance of TSP from any Hamiltonian Cycle problem instance in polynomial time, showing that Hamiltonian Cycle is polynomial time reducible to TSP. Therefore, since any problem in NP can be reduced to Hamiltonian Cycle and Hamiltonian Cycle can be reduced to TSP, any problem in NP can be reduced to TSP, proving that TSP is NP-Complete.
This document discusses canonical-Laplace transforms and various testing function spaces. It begins by defining the canonical-Laplace transform and establishes some testing function spaces using Gelfand-Shilov technique, including CLa,b,γ, CLab,β, CLγa,b,β, CLa,b,β,n, and CLγa,,m,β,n. It then presents results on countable unions of s-type spaces, proving that various spaces can be expressed as countable unions and discussing topological properties. The document concludes by stating that canonical-Laplace transforms are generalized in a distributional sense and results on countable unions of s-type spaces are discussed, along with the topological structure
The document discusses the Fourier transform, which relates a signal sampled in time or space to the same signal sampled in frequency. It explains the mathematical definition and provides an example of using a Fourier transform to convert time domain data to the frequency domain. Specifically, it uses a cosine wave as input data and calculates the Fourier transform to reveal a strong amplitude at the expected frequency component.
This document provides an introduction to SPU optimizations by summarizing the SPU assembly instructions. It begins by explaining the SPU execution environment and memory model. It then categorizes the instruction set into classes based on arity and latency. The majority of the document details the various instructions in the Single Precision Floating Point (SP), Fixed precision (FX), and other classes; explaining their syntax, latency, and examples of use. The goal is to familiarize programmers with the SPU hardware and instruction set to enable improved performance through optimization techniques.
RSS discussion of Girolami and Calderhead, October 13, 2010Christian Robert
1. The document discusses discretizing Hamiltonians for Markov chain Monte Carlo (MCMC) methods. Specifically, it examines reproducing Hamiltonian equations through discretization, such as via generalized leapfrog.
2. However, the invariance and stability properties of the continuous-time process may not carry over to the discretized version. Approximations can be corrected with a Metropolis-Hastings step, so exactly reproducing the continuous behavior is not necessarily useful.
3. Discretization induces a calibration problem of determining the appropriate step size. Convergence issues for the MCMC algorithm should not be impacted by imperfect renderings of the continuous-time process in discrete time.
What is Fourier Transform
Spatial to Frequency Domain
Fourier Transform
Forward Fourier and Inverse Fourier transforms
Properties of Fourier Transforms
Fourier Transformation in Image processing
Symbolic Execution as DPLL Modulo TheoriesQuoc-Sang Phan
The document discusses symbolic execution, which is a program analysis technique that executes programs with symbolic inputs instead of concrete inputs. It describes symbolic execution as an approach for solving satisfiability modulo theories (SMT) problems, by viewing symbolic execution as an SMT solver. It presents an implementation of symbolic execution based on a Boolean executor that performs a depth-first search, combined with an SMT solver to check satisfiability of path conditions.
This document discusses the design of finite impulse response (FIR) filters. It begins by describing the basic FIR filter model and properties such as filter order and length. It then covers topics such as linear phase response, different filter types (low-pass, high-pass, etc.), deriving the ideal impulse response, and filter specification in terms of passband/stopband edges and ripple levels. The document concludes by outlining the common FIR design method of windowing the ideal impulse response, describing popular window functions, and providing a step-by-step example of designing a low-pass FIR filter using the Hamming window.
This document provides definitions and examples related to Fourier series and Fourier transforms. It defines the Fourier transform and inverse Fourier transform of a function f(x). It gives the Fourier integral representation of a function and provides an example of finding the Fourier integral representation of a rectangle function. It also defines Fourier sine and cosine integrals. Finally, it outlines some properties of Fourier transforms, including the modulation theorem and convolution theorem.
This document discusses Doppler estimation of radar signals using complex wavelet transforms (CWT). It begins by introducing existing Doppler estimation methods like FFT and adaptive estimation techniques that have limitations. CWT provides advantages over real wavelet transforms by generating complex coefficients. The document then describes the dual tree CWT formulation and use of analytic signals for amplitude and frequency analysis. It proposes using CWT with a custom thresholding algorithm to estimate Doppler profiles from radar data. Results on test radar signals show the method can estimate Doppler at higher altitudes where existing techniques fail due to noise.
This document presents distributed algorithms for k-truss decomposition of large graphs. It begins with introducing the problem of k-truss decomposition and definitions. It then describes how k-truss decomposition can be performed using traditional sequential algorithms. It proposes two distributed algorithms: MRTruss, which uses MapReduce but has limitations; and i-MRTruss, an improved version that aims to address the issues with MRTruss. The document outlines the different sections that will evaluate these distributed algorithms and experimentally analyze their performance.
The Fourier transform is a mathematical tool that transforms functions between the time and frequency domains. It breaks down any function or signal into the frequencies that make it up. This allows analysis of signals in the frequency domain, enabling applications like image and signal processing. The Fourier transform represents functions as a combination of sinusoidal functions like sines and cosines. The inverse Fourier transform reconstructs the original function from its frequency representation. Fourier transforms have many uses including solving differential equations, filtering sound and images, and analyzing signals like heartbeats.
This document discusses the Fourier transformation, including:
1) It defines continuous and discrete Fourier transformations and their properties such as separability, translation, periodicity, and convolution.
2) The fast Fourier transformation (FFT) improves the computational complexity of the discrete Fourier transformation from O(N^2) to O(NlogN).
3) FFT works by rewriting the DFT calculation in a way that exploits symmetry and reduces redundant computations.
This document summarizes two algorithms for computing properties of high-dimensional polytopes given access to certain oracle functions:
1. An algorithm for computing the edge-skeleton of a polytope in oracle polynomial-time using an oracle that returns the vertex maximizing a linear function.
2. A randomized algorithm for approximating the volume of a polytope by generating random points within it using a hit-and-run process, and estimating the volume from these points. The algorithm runs in oracle polynomial-time and provides an approximation with high probability.
Experimental results show the volume algorithm can approximate volumes of polytopes up to 100 dimensions within 1% error in under 2 hours, outperforming exact
Discussion of Fearnhead and Prangle, RSS< Dec. 14, 2011Christian Robert
The document discusses approximate Bayesian computation (ABC), a technique used when the likelihood function is intractable. ABC works by simulating data under different parameter values and accepting simulations that are close to the observed data according to a distance measure. The key challenges are choosing a sufficient summary statistic of the data and setting the tolerance level. Later sections discuss using a noisy ABC approach, where the summary statistic is perturbed, and calibrating the method so that the ABC posterior converges to the true parameter as the number of simulations increases. The document examines issues around choosing optimal summary statistics and tolerance levels to minimize errors in the ABC approximation.
This document discusses redesigning the health, safety, and environment (HSE) function in companies. It notes that HSE functions are often being downsized with limited risk consideration. The document provides signs that an HSE function may need to change, such as functional overload or inefficient resource allocation. It also outlines steps to redesign the HSE function, including defining customer needs and mapping the current and desired operating models. The goal is to right-size the HSE function to effectively support operations and demonstrate value to the organization.
Louis Vuitton was founded in 1854 and is now part of LVMH, the world's largest luxury conglomerate. LV is known for its luxury leather goods, monogram canvas prints, and status as a symbol of wealth and prestige. While it faces competition from other luxury brands, LV differentiates itself through its heritage, craftsmanship in products that can take 60 hours to produce, and policy of not offering discounts on its high-quality, ultra-luxurious goods. Counterfeiting of the brand can have some positive effects of increasing brand awareness, but loyal customers value the precision and quality of authentic LV products.
This document introduces Emocloud, a service that helps music producers get feedback from peers and fans on the emotions their songs elicit in order to improve their music making. Emocloud gathers feedback on the emotions listeners experience during songs to provide more useful information to producers than typical high-level reviews. The service has different pricing tiers for amateurs, composers, and publishers and is developed by a small founding team.
Dokumen tersebut membahas tentang manfaat melakukan dakwah melalui media sosial seperti YouTube, Instagram, dan lainnya. Tujuannya antara lain untuk menarik pemuda, mencegah masalah toleransi dan kebebasan beragama, serta meningkatkan ilmu pengetahuan agama. Dibahas pula strategi yang dapat dilakukan seperti membentuk kelompok kecil dan melakukan secara pribadi, serta hambatan seperti menghadapi koment
This document summarizes a research paper about the effects of adolescent pregnancy on educational attainment. It discusses how adolescent mothers often have lower educational attainment than their non-parenting peers. The author examines previous literature on the topic and policies supporting adolescent mothers. They describe their internship at Hephzibah Children's Home, which provides housing and education support to adolescent mothers in Macon, Georgia. Through this experience and a critical theory framework, the author analyzes how adolescent motherhood impacts educational outcomes.
A construction safety program has several key elements: assigning responsibilities; identifying and controlling hazards; providing training; documenting safety rules and enforcement. The program aims to maintain safe work conditions, set performance goals, reward safety, and review incidents to take corrective actions. Establishing safety objectives and including safety in performance reviews helps measure effectiveness. Benefits include reduced injuries, expenses, absenteeism and increased productivity and morale. Developing project-specific safety activities includes planning, defining roles, and identifying typical safety programs and top violations. Formulating a comprehensive safety plan requires a team effort to identify hazards and controls. Implementing and continually improving the work plan is essential to reducing injuries and maintaining a safe work environment.
This document discusses self-driving cars and their advantages and disadvantages. It outlines some of the warning and safety features autonomous vehicles offer, such as lane departure warnings, blind spot monitoring, and adaptive cruise control. However, it also notes disadvantages like potential hacking risks, high costs, and the ethical dilemmas around assigning blame in accidents or deciding between protecting passengers versus pedestrians. Overall, the document provides an overview of both benefits and challenges regarding the adoption of self-driving automobile technology.
Michael Floyd is a security professional with over 5 years of experience in security roles. He has a Associate of Arts degree from Judson University and relevant certifications in first aid, CPR, active shooter response, and anti-terrorism training. Floyd currently works as a Security Officer for Weber-Stephen Products where he performs duties such as access control, safety compliance, incident reporting, and emergency response. He also volunteers with local organizations, serving on a nonprofit board and providing childcare. Floyd is currently training to become a Guardian Ad Litem to represent children in abuse and neglect cases.
THE CHORD GAP DIVERGENCE AND A GENERALIZATION OF THE BHATTACHARYYA DISTANCEFrank Nielsen
The document introduces the chord gap divergence, a generalization of the Bhattacharyya distance and skew Jensen divergence. The chord gap divergence is defined as the vertical distance between an upper and lower chord in the graph of a convex function, and can be expressed as the difference of two skew Jensen divergences. This provides a geometric interpretation and allows the chord gap divergence to be used as a distance metric for clustering algorithms like k-means++. The divergence is also linked to statistical divergences between distributions in the same exponential family.
This document discusses using the Wasserstein distance for inference in generative models. It begins by introducing ABC methods that use a distance between samples to compare observed and simulated data. It then discusses using the Wasserstein distance as an alternative distance metric that has lower variance than the Euclidean distance. The document covers computational aspects of calculating the Wasserstein distance, asymptotic properties of minimum Wasserstein estimators, and applications to time series data.
Ramin Anushiravani's document outlines techniques for sound source localization using microphone arrays. It discusses beamforming methods like delay-and-sum and MVDR beamforming, as well as subspace-based algorithms like MUSIC. It also covers topics like uniform linear arrays, beampatterns, and spatial aliasing. The document presents results from experiments localizing 1-2 sound sources using arrays with 2-4 microphones.
DPPs everywhere: repulsive point processes for Monte Carlo integration, signa...Advanced-Concepts-Team
Determinantal point processes (DPPs) are specific repulsive point processes, which were introduced in the 1970s by Macchi to model fermion beams in quantum optics. More recently, they have been studied as models and sampling tools by statisticians and machine learners. Important statistical quantities associated to DPPs have geometric and algebraic interpretations, which makes them a fun object to study and a powerful algorithmic building block.
After a quick introduction to determinantal point processes, I will discuss some of our recent statistical applications of DPPs. First, we used DPPs to sample nodes in numerical integration, resulting in Monte Carlo integration with fast convergence with respect to the number of integrand evaluations. Second, we used DPP machinery to characterize the distribution of the zeros of time-frequency transforms of white noise, a recent challenge in signal processing. Third, we turned DPPs into low-error variable selection procedures in linear regression.
k-MLE: A fast algorithm for learning statistical mixture modelsFrank Nielsen
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.
Introduction to Fourier transform and signal analysis宗翰 謝
The document discusses Fourier analysis techniques. It introduces continuous and discrete Fourier transforms, and covers properties like orthogonality, completeness of basis functions (e.g. cosines and sines), and Fourier series representations of periodic functions like step functions. It also defines the Fourier transform and its properties like linearity, translation, modulation, scaling, and conjugation. Concepts like Dirac delta functions and convolution theory are explained in relation to Fourier analysis.
The document discusses Fourier analysis techniques. It introduces continuous and discrete Fourier transforms, and covers properties like orthogonality, completeness of basis functions (e.g. cosines and sines), Fourier series expansion of periodic functions, and Fourier transform properties such as linearity, translation and modulation. It also defines the Dirac delta function and discusses convolution theory and the Parseval relation.
This document discusses the Hofstadter butterfly model for the honeycomb lattice structure of graphene. It shows that the Hall conductivity σH in an energy gap must satisfy a Diophantine equation relating σH, the magnetic flux per unit cell p/q, and an integer s. For the honeycomb lattice, the conjecture is that σH lies in the window (-q,q) rather than the typical (-q/2,q/2). The bulk-edge correspondence relates σH to the number of edge state crossings in the Brillouin zone. Numerical results for σH calculated from the edge state spectrum agree with the Diophantine equation in 99.8% of cases.
This document discusses using the Wasserstein distance for inference in generative models. It begins with an overview of approximate Bayesian computation (ABC) and how distances between samples are used. It then introduces the Wasserstein distance as an alternative distance that can have lower variance than the Euclidean distance. Computational aspects and asymptotics of using the Wasserstein distance are discussed. The document also covers how transport distances can handle time series data.
Building Compatible Bases on Graphs, Images, and ManifoldsDavide Eynard
Spectral methods are used in computer graphics, machine learning, and computer vision, where many important problems boil down to constructing a Laplacian operator and finding its eigenvalues and eigenfunctions. We show how to generalize spectral geometry to multiple data spaces. Our construction is based on the idea of simultaneous diagonalization of Laplacian operators. We describe this problem and discuss numerical methods for its solution. We provide several synthetic and real examples of manifold learning, object classification, and clustering, showing that the joint spectral geometry better captures the inherent structure of multi-modal data.
Talk at SIAM-IS 2014 (http://www.math.hkbu.edu.hk/SIAM-IS14/). A big thanks to Michael Bronstein for providing a great set of slides this presentation is a mere extension of.
On Spaces of Entire Functions Having Slow Growth Represented By Dirichlet SeriesIOSR Journals
In this paper spaces of entire function represented by Dirichlet Series have been considered. A
norm has been introduced and a metric has been defined. Properties of this space and a characterization of
continuous linear functionals have been established.
Slides: A glance at information-geometric signal processingFrank Nielsen
This document discusses information geometry and its applications in statistical signal processing. It introduces several key concepts:
1) Statistical signal processing models data with probability distributions like Gaussians and histograms. Information geometry provides a geometric framework for intuitive reasoning about these statistical models.
2) Exponential family mixture models generalize Gaussian and Rayleigh mixtures and are algorithmically useful in dually flat spaces.
3) Distances between statistical models, like Kullback-Leibler divergence and Bregman divergences, can be interpreted geometrically in terms of convex conjugates and Legendre transformations.
This document summarizes a research paper that proposes using complex wavelet transform (CWT) with a custom thresholding algorithm to estimate Doppler profiles from MST radar signals. CWT has advantages over real wavelet transforms by generating complex coefficients. The custom thresholding function is continuous around the threshold and can be adapted to signal characteristics. The algorithm applies CWT thresholding to the radar signal spectrum before Doppler estimation. Results on test radar data show the method can estimate Doppler at higher altitudes where noise dominates, unlike existing techniques.
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11TH INTERNATIONAL CONFERENCE ON ELECTRICAL, ELECTRONIC AND COMPUTING ENGINEERING
3-6 June 2024, Niš, Serbia
1. Wireless Localization: Ranging
Stefano Severi and Giuseppe Abreu
s.severi@jacobs-university.de
School of Engineering & Science - Jacobs University Bremen
October 7, 2015
2. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Phase-Difference Ranging
Basic Principle
x(t) = A0 cos (2πf1t + ϕA).
y(t) = B0 cos (2πf1t + ϕB).
ϕ1 = ϕB − ϕA.
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 2/18
3. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Phase-Difference Ranging
Frequency shifting
f1 = c/λ1,
ϕ1 = 2π
2d
λ1
− N1 = 2π
2f1d
c
− N1 ,
f2 = f1 + ∆f ,
ϕ2 = 2π
2d
λ2
− N2 = 2π
2f2d
c
− N2 ,
ϕ2 − ϕ1 = ∆ϕ =
4πd∆f
c
,
d =
c
4π
∆ϕ
∆f
.
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 3/18
4. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Ranging for Indoor Localization
Smart Ranging
Current localization solutions:
GNSS and cellular based,
otherwise fragile and underdeployed,
still suffering multipath and NLOS conditions.
Furthermore, mainly based on triangulation/trilateration:
requires point-to-point measurements,
pairwise communication,
overhead and redundancy.
They are far from being optimal!
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 4/18
5. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Ranging for Indoor Localization
Increasing the Efficiency
Superresolution Multipoint Ranging with Optimized Sampling
via Orthogonally Designed Golomb Rulers [1].
Exploit the differential nature of measurements,
avoid broadcast → measurement toward anchor nodes,
orthogonal Golumb Ruler design,
optimized genetic algorithm for Golumb Ruler generation,
already implemented on 802.15.4-based commercial
solution (ToA and PDoA)!
[1], Oshiga O., Severi S., Abreug G.T.F, "Superresolution Multipoint Ranging with Optimized Sampling via
Orthogonally Designed Golomb Rulers", to appear on IEEE Transactions on Wireless Communications.
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 5/18
6. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Superresolution Ranging
Uniform Set of adjacent Frequencies
Let us consider a uniform set of adjacent frequencies:
F {f1, · · · , fn}, with fn = (n − 1)∆f + f1, (1)
The corresponding phase estimates at the respective frequencies are
ϕ = {ϕ1, · · · , ϕn}. (2)
and, in turn, the phase differences
ϕi+1 − ϕ1, with i = 1, · · · , n − 1 (3)
can be put in the vector
∆Φ = {∆ϕ1, · · · , ∆ϕn−1}. (4)
Matlab Tip
To obtain the phase differences, use the command:
phi = unwrap(phi);
dphi = phi(2:end,:)-repmat(phi(1,:),length(freq)-1,1);
Use every four columns to obtain the phase difference dphi.
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 6/18
7. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Superresolution Ranging
The Steering Vector
Taking the vector ∆Φ as the argument of the element-wise complex
exponential function g(x) = exp(jx), we obtain
g(∆Φ) = [ej∆ϕ1
, · · · , ej∆ϕn−1
]T
= [e
j4πd∆f
c , · · · , e
j4πd(n−1)∆f
c ]T
.
(5)
One can immediately recognize from the above, the similarity between the
vector g(∆Φ) and the steering vector of a linear antenna array
[TUNCER09].
Steering Vector
A steering vector represents the set of phase delays a plane wave
experiences, evaluated at a set of array elements (antennas). The phases
are specified with respect to an arbitrary origin.
[TUNCER09 ] T. Tuncer and B. Friedlander, “Classical and Modern Direction-of-Arrival Estimation”. Elsevier
Science, 2009.
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 7/18
8. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Superresolution Ranging
The Sample Array Covariance Matrix
The Sample Array Covariance Matrix Fundamental Property
The space spanned by its eigenvectors are partitioned into two orthogonal
subspaces, namely the signal plus noise subspace and the noise only
subspace; the steering vectors corresponding to the direction of the signal
are orthogonal to the noise subspace assuming they are uncorrelated.
ˆRx =
1
K
K
k=1
g(∆ ˆΦ(k))g(∆ ˆΦ(k))H
(6)
where K is the number of snapshots and MH
stands for the transpose of
the matrix M.
Matlab Tip
To obtain the sample covariance matrix R, use the command:
x = exp(1j*dphi.’);
Rx = x’*x;
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 8/18
9. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Superresolution Ranging
Signal- and Noise-Subspace
Define M = n − 1 and make the following assumptions:
rank g(∆ ˆΦ(k)) = 1,
uniformity of the set of adjacent frequencies F.
The eigendecomposition of the sample covariance matrix ˆRx gives:
ˆRx = ˆess
ˆΛssˆeH
ss
signal-subspace
+ ˆEns
ˆΛns
ˆEH
ns
noise-subspace
(7)
where the sample eigenvalues are sorted in descending order and the
matrices ˆess [ˆe1][M×1] and ˆEns [ˆe2, · · · , ˆeM ][M×M−1] contain in
their columns the signal- and noise-subspace eigenvectors of ˆRx
respectively.
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 9/18
10. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Superresolution Ranging
Signal- and Noise-Subspace
The basis of noise-subspace ˆEns formed by the (M − 1) eigenvectors
associated with the (M − 1) smallest eigenvalues are orthogonal to the
complex exponential steering vector.
Therefore we can write this in mathematical terms:
g(∆Φ(k)) ⊥ Ens, (8)
or equivalently:
g(∆Φ(k))H
EnsEH
nsg(∆Φ(k)) = 0. (9)
Super-Resolution Goal
From g(∆ˆΦ(k)) we can construct ˆRx and, in turn, obtain Ens: the goal is
now to get a good estimate of the true steering vector g(∆Φ(k)).
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 10/18
11. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Golomb Ruler
A Nice but Challenging Tool
It’s a ruler without 2 pairs of marks at the same distance.
Example of perfect
Golomb ruler.
No perfect ruler exists beyond 4
marks,
optimal → no shorter of the same
order exists,
to find optimal high-order GR is a
NP-problem,
to find orthogonal high-order GRs
→ unsolved.
new genetic algorithm → proposed
approach.
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 11/18
13. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Spectral Music
Multiple Signal Classification (MUSIC)
Recalling the full formulation of the measured steering vector
g(∆ˆΦ) = [e
j4π ˆd∆f
c , · · · , e
j4π ˆdM∆f
c ]T
,
the spectral MUSIC estimates the distance ˆd between the source s and
target t from the minimum of the function
f( ˆd) = g(∆ ˆΦ(k))H ˆEns
ˆEH
nsg(∆ ˆΦ(k)) (10)
by searching over ˆd using a fine grid as it exploits the orthogonality in eq.
(9).
Matlab Tip
To define the fine grid, use the command:
RangeD = 0:01:50;
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 13/18
14. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Root Music
Polynomial expansion of MUSIC
Root MUSIC replaces the search of the minimum of f( ˆd) by polynomial
rooting, and its only solution is the distance estimate ˆd between the source
s and target t.
The M × 1 complex exponential vector can be written as:
g(∆ ˆΦ(k)) = [e
j4π ˆd∆f
c , · · · , e
j4π ˆdM∆f
c ]T
(11)
= [z1
, · · · , zM
]T
,
where zi
ej4π ˆdi∆f/c
, and ∆f is the common uniform inter-frequency
spacing.
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 14/18
15. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Root Music
Polynomial expansion of MUSIC
The function f( ˆd) is instead rewritten as:
f( ˆd) = g(z−1
)T ˆEns
ˆEH
nsg(z) f(z)
= [z−1
, · · · , z−M
]
e11 · · · e1M
... · · ·
...
eM1 · · · eMM
z1
...
zM
,
f(z) =
(M−1)
l=−(M−1)
alzl
, (12)
where al is the sum of the lth diagonal entries of ˆEns
ˆEH
ns.
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 15/18
16. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Root Music
Polynomial expansion of MUSIC
The polynomial f(z) has (2M − 1) unitary modulus roots which form
conjugate reciprocal pairs
z = ej4π ˆd∆f/c
and ¯z = e−j4π ˆd∆f/c
. (13)
Due to the presence of noise, the root locations are distorted and the root
corresponding to the true distance d does not lie on the unit circle.
Therefore, the Root-Music computes all roots of f(z) and estimates the
distance ˆd by selecting the largest-magnitude root from those lying inside
the circle.
Matlab Tip
To obtain the distances for Music and Root-Music and the function in Eq.
(10), use the command:
[EstDistMusic f] = MusicSpectrum(Rx,1,1,RangeD);
EstDistRMusic = RootMUSIC(Rx,1);
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 16/18
17. Accurate
Ranging
Recap
Steering Vector
Golomb Ruler
Spectral Music
Root Music
Report 2/3
Ranging
Complete the lab experience writing a report with:
1 plot 4 different phase measurements ϕ (dphi(:,[a:b])) of all
frequencies for both cable and wireless measurements.
2 compute the distance estimates using Music and Root-Music algorithms
using every four phase measurements (400/4 = 100 distance estimates).
3 plot the f from the Music algorithm for one distance estimate.
Please print and deliver the report within the aforementioned deadline to
s.severi@jacobs-university.de,
r.stoica@jacobs-university.de.
Specialization Lab - Fall 2015 Wireless Localization: Ranging October 7, 2015 17/18