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Spectral Methods For Numerical Differentiation And Integration
 
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Here we explain something about how spectral methods (Fourier methods in particular) can be used for numerical differentiation, and integration. With a bit of background we arrive at the type series used by the fast fourier transform that is used in many numerical applications of spectral methods. We then establish results about how these ideas can be used to perform spectral differentiation, and how spectral methods can be used to evaluate convolution integrals. We also prove the validity of these methods. Thanks to Gustav Delius at the University of York for explaining these ideas to me, although I am sure any errors in this video come from my own misinterpretations.
Views: 2186 Richard Southwell
GG413: Introduction to Spectral Analysis
 
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University of Hawaii, Dept. of Geology & Geophysics, Garrett Apuzen-Ito, GG413: Geological Data Analysis www.soest.hawaii.edu/GG/FACULTY/ITO/GG413
Views: 15998 Garrett Apuzen-Ito
Lec 21 | MIT 18.085 Computational Science and Engineering I
 
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Spectral method: dynamic equations A more recent version of this course is available at: http://ocw.mit.edu/18-085f08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 9325 MIT OpenCourseWare
Introduction to Spectral data analysis
 
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This webinar shows how to use The Unscrambler® for analysing spectra. It addresses people dealing with or having preliminary knowledge of spectral data. It uses a case study that can help understanding these methods. During this webinar, you will see how to: 1) Perform pre-treatments of the spectra 2) Analyse spectral data using first an exploratory data analysis method (PCA) and then a classification method (SIMCA)
Views: 18921 Camo Analytics
Time Series Analysis (Georgia Tech) - 5.1.2 - Spectral Analysis - Introduction
 
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Time Series Analysis PLAYLIST: https://tinyurl.com/TimeSeriesAnalysis-GeorgiaTech Unit 5: Other Time Series Methods Part 1: Univariate Time Series Modelling Lesson: 2 - Spectral Analysis - Introduction Notes, Code, Data: https://tinyurl.com/Time-Series-Analysis-NotesData
Views: 99 Bob Trenwith
Broad overview of EEG data analysis analysis
 
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This lecture is a very broad introduction to the most commonly used data analyses in cognitive electrophysiology. There is no math, no Matlab, and no data to download. For more information about MATLAB programming: https://www.udemy.com/matlab-programming-mxc/?couponCode=MXC-MATLAB10 For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 13030 Mike X Cohen
Lecture - 34 Introduction to Spectral Analysis
 
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Lecture Series on Probability and Random Variables by Prof. M.Chakraborty, Dept. of Electronics and Electrical Engineering,I.I.T.,Kharagpur.For more Courses visit http://nptel.iitm.ac.in
Views: 23746 nptelhrd
Spectral learning techniques Part 1
 
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Spectral Learning Techniques for Weighted Automata, Transducers, and Grammars Borja Balle, Ariadna Quattoni and Xavier Carreras October 25, 2014 - Morning Tutorial notes Dedicated page Abstract: In recent years we have seen the development of efficient and provably correct algorithms for learning weighted automata and closely related function classes such as weighted transducers and weighted context-free grammars. The common denominator of all these algorithms is the so-called spectral method, which gives an efficient and robust way to estimate recursively defined functions from empirical estimations of observable statistics. These algorithms are appealing because of the of existence of theoretical guarantees (e.g. they are not susceptible to local minima) and because of their efficiency. However, despite their simplicity and wide applicability to real problems, their impact in NLP applications is still moderate. One of the goals of this tutorial is to remedy this situation. The contents that will be presented in this tutorial will offer a complementary perspective with respect to previous tutorials on spectral methods presented at ICML-2012, ICML-2013 and NAACL-2013. Rather than using the language of graphical models and signal processing, we tell the story from the perspective of formal languages and automata theory (without assuming a background in formal algebraic methods). Our presentation highlights the common intuitions lying behind different spectral algorithms by presenting them in a unified framework based on the concepts of low-rank factorizations and completions of Hankel matrices. In addition, we provide an interpretation of the method in terms of forward and backward recursions for automata and grammars. This provides extra intuitions about the method and stresses the importance of matrix factorization for learning automata and grammars. We believe that this complementary perspective might be appealing for an NLP audience and serve to put spectral learning in a wider and, perhaps for some, more familiar context. Our hope is that this will broaden the understanding of these methods by the NLP community and empower many researchers to apply these techniques to novel problems. The content of the tutorial will be divided into four blocks of 45 minutes each, as follows. The first block will introduce the basic definitions of weighted automata and Hankel matrices, and present a key connection between the fundamental theorem of weighted automata and learning. In the second block we will discuss the case of probabilistic automata in detail, touching upon all aspects from the underlying theory to the tricks required to achieve accurate and scalable learning algorithms. The third block will present extensions to related models, including sequence tagging models, finite-state transducers and weighted context-free grammars. The last block will describe a general framework for using spectral techniques in more general situations where a matrix completion pre-processing step is required; several applications of this approach will be described. Instructors: Borja Balle, postdoctoral fellow, McGill University Borja Balle is currently a postdoctoral fellow at McGill University, and prior to that he obtained his PhD from Universitat Politecnica de Catalunya (UPC) in July 2013. His research interests lie on the intersection between automata theory and machine learning, in particular on applications of spectral learning techniques to natural language processing, grammatical inference, and reinforcement learning. He is area chair for NIPS 2014, program committee member for ICGI 2014, and has recently organized three workshops (at ICML 2013, NIPS 2013 and ICML 2014) on methods of moments and spectral learning. Ariadna Quattoni, Researcher, Xerox Research Centre Europe (XRCE) Ariadna Quattoni is currently a researcher at Xerox Research Centre Europe (XRCE), prior to that she was a researcher at the Universitat Politecnica de Catalunya (UPC). She obtained her PhD from MIT in 2009. Her main research focuses on latent variable models for structured prediction with applications to natural language processing and computer vision. On the last years her work has centered on spectral learning techninques for structured prediction problems with applications to sequence tagging, learning general transductions, and parsing. Xavier Carreras, senior researcher, Xerox Research Centre Europe Xavier Carreras research is in natural language processing and machine learning. He is interested in grammatical induction and parsing methods for syntactic-semantic analysis and translation of natural languages. In 2005 he completed his PhD at the Universitat Politecnica de Catalunya (UPC). From 2006 to 2009 he was a postdoctoral researcher at MIT/CSAIL. From 2009 to 2014 he was a researcher at UPC and since June 2014 he is senior researcher at Xerox Research Centre Europe.
Views: 1851 emnlp acl
Application of Spectral Methods to Pianos, Part 1 of 7
 
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An introduction to the line spectrum, cumulative line spectrum, spectral centroid and autocorrelation for three simple waves. check out https://sites.google.com/site/analysisofsoundsandvibrations/ for more videos on sounds and vibrations. This site also contains information on collecting and analyzing piano data.
Views: 371 Dave Koenig
UV Vis spectroscopy explained lecture
 
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UV Visible spectroscopy explained lecture - This lecture explains about the UV visible spectroscopy technique.This explains how colorimetric analysis of samples are done using the transmittance and absorbance of the sample molecule using beer Lambert law. UV vis spectroscopy is used to identify the concentration of the test sample. Here I also explained the beer lambert law and how beer lambert law is derived. For more information, log on to- http://www.shomusbiology.com/ Get Shomu's Biology DVD set here- http://www.shomusbiology.com/dvd-store/ Download the study materials here- http://shomusbiology.com/bio-materials.html Remember Shomu’s Biology is created to spread the knowledge of life science and biology by sharing all this free biology lectures video and animation presented by Suman Bhattacharjee in YouTube. All these tutorials are brought to you for free. Please subscribe to our channel so that we can grow together. You can check for any of the following services from Shomu’s Biology- Buy Shomu’s Biology lecture DVD set- www.shomusbiology.com/dvd-store Shomu’s Biology assignment services – www.shomusbiology.com/assignment -help Join Online coaching for CSIR NET exam – www.shomusbiology.com/net-coaching We are social. Find us on different sites here- Our Website – www.shomusbiology.com Facebook page- https://www.facebook.com/ShomusBiology/ Twitter - https://twitter.com/shomusbiology SlideShare- www.slideshare.net/shomusbiology Google plus- https://plus.google.com/113648584982732129198 LinkedIn - https://www.linkedin.com/in/suman-bhattacharjee-2a051661 Youtube- https://www.youtube.com/user/TheFunsuman Thank you for watching the video lecture on UV Vis spectroscopy.
Views: 311263 Shomu's Biology
Application of Spectral Methods to Pianos, Part 4 of 7
 
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The line spectrum is used to demonstrate the inharmonicity or octave stretching for a C1 piano note. check out https://sites.google.com/site/analysisofsoundsandvibrations/ for more videos on sounds and vibrations. This site also contains information on collecting and analyzing piano data.
Views: 194 Dave Koenig
Time Series Analysis (Georgia Tech) - 5.1.3 - Spectral Analysis - Spectral Density and Covariance Fn
 
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Time Series Analysis PLAYLIST: https://tinyurl.com/TimeSeriesAnalysis-GeorgiaTech Unit 5: Other Time Series Methods Part 1: Univariate Time Series Modelling Lesson: 3 - Spectral Analysis - Spectral Density and Covariance Functions Notes, Code, Data: https://tinyurl.com/Time-Series-Analysis-NotesData
Views: 24 Bob Trenwith
Mod-01 Lec-16 Orthogonal Collocations Method for Solving ODE - BVPs and PDEs
 
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Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
Views: 12676 nptelhrd
Spectral Flow Cytometry and Data Analysis Techniques
 
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View the webinar recording to learn more about the technology and methodology behind Spectral Flow Cytometry via the Sony SA3800 and SP6800 instruments. Spectral Analyzers from Sony now also include FCS Express 6 which provides native support for spectral data files with linking to the raw spectral data as well as standard flow cytometry files, plots, and methods.  The seamless integration allows you to move from acquisition to results quickly and easily while retaining access to spectral information and advanced batch processing, custom calculation, plate based, and dimensionality reduction transformation tools.
Views: 1785 DeNovoSoftware
Example of Spectral Theorem (3x3 Symmetric Matrix)
 
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Linear Algebra: We verify the Spectral Theorem for the 3x3 real symmetric matrix A = [ 0 1 1 / 1 0 1 / 1 1 0 ]. That is, we show that the eigenvalues of A are real and that there exists an orthonormal basis of eigenvectors. In other words, we can put A in real diagonal form using an orthogonal matrix P. (Eigenvalues and eigenvectors for this A are found in the video "Eigenvalues and Eigenvectors.")
Views: 27281 MathDoctorBob
Polynomial Time and Sample Complexity for Non-Gaussian Component Analysis: Spectral Methods
 
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Yan Shuo Tan and Roman Vershynin Polynomial Time and Sample Complexity for Non-Gaussian Component Analysis: Spectral Methods ABSTRACT. The problem of Non-Gaussian Component Analysis (NGCA) is about finding a maximal low-dimensional subspace $E$ in $\R^n$ so that data points projected onto $E$ follow a non-Gaussian distribution. Vempala and Xiao (2011) proposed a local search algorithm, and showed that it was able to estimate $E$ accurately with polynomial time and sample complexity, if the dimension of $E$ is treated as a constant and with the assumption that all one-dimensional marginals of the non-Gaussian distribution over $E$ have non-Gaussian moments. In this paper, we propose a simple spectral algorithm called \textsc{Reweighted PCA}, and prove that it possesses the same guarantee. The principle that underlies this approach is a new characterization of multivariate Gaussian distributions.
Views: 61 COLT
Application of Spectral Methods to Pianos, Part 5 of 7
 
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The cumulative line spectrum map is used to study several pianos. check out https://sites.google.com/site/analysisofsoundsandvibrations/ for more videos on sounds and vibrations. This site also contains information on collecting and analyzing piano data.
Views: 220 Dave Koenig
Spectral analysis of 2x2 matrix -- efficient tricks
 
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I show that in the case of 2x2 matrices, the analysis via characteristic polynomial (http://youtu.be/rNiUgJhqR2o) can be shortened, and often eigenvalues be guessed, with the help of the concept trace and determinant of matrix. I present an example which demonstrates the method. This video is part Mathematics 1251 http://web.maths.unsw.edu.au/~potapov/1251_2014/
Views: 7775 Denis Potapov
Mod-04 Lec-03 Fatigue loading and fatigue analysis
 
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Advanced Marine Structures by Prof. Dr. Srinivasan Chandrasekaran, Department of Ocean Engineering, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
Views: 55043 nptelhrd
Lecture 24 (CEM) -- Introduction to Variational Methods
 
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This lecture introduces to the student to variational methods including finite element method, method of moments, boundary element method, and spectral domain method. It describes the Galerkin method for transforming a linear equation into matrix form as well as populating the global matrix from element matrices. Also described are topics such as node vs edge elements, volume vs surfaces meshes, and more.
Views: 30683 CEM Lectures
Frequency Domain Bootstrap Methods for Spectral Analysis
 
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Dr. Abdelhak M Zoubir May 13, 2010
Views: 1130 NC State ECE
Multiple endmember spectral unmixing within a multi-task framework
 
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A novel spectral unmixing technique is presented which addresses the problem of spectral variability within each endmember class and determines endmember types present in each pixel. The proposed unmixing method is a multi-task framework, based on Multi-task Gaussian Process (MTGP). The Unmixing within a MTGP framework (UMTGP) is different to conventional unmixing approaches in that it assumes that spectral variation exists within each endmember class. Using synthetic and real data, the fractional abundances estimated by the UMTGP are compared with conventional methods such as Fully Constrained Least Squares (FCLS) and Multiple Endmember Spectral Mixture Analysis (MESMA). Hyperspectral data acquired from field-based platforms are used for evaluation because intra-class spectral variability is commonly large in these datasets. The results show that the UMTGP outperforms FCLS in terms of estimating fractional abundance and provides better estimates than MESMA, especially when a small number of endmember spectra for each class are available.
Views: 1195 MIT Education
Mod-01 Lec-36 Spectral Theorem
 
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Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
Views: 1758 nptelhrd
PDE solver: Diffusion equation in spectral method (Lec 19 B)
 
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Subject: Physics Course Name: Computational Science and Engineering Using Python Keyword: Swayamprabha
Power Spectrum Estimation Examples: Welch's Method
 
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http://AllSignalProcessing.com for more great signal-processing content: ad-free videos, concept/screenshot files, quizzes, MATLAB and data files. Examples of applying Welch's method to estimate power spectrum highlighting the tradeoffs between bias and variance that are associated with segment length, segment overlap, and window choice.
Views: 22434 Barry Van Veen
The Application of Spectral Methods to Pianos, Part 3 of 7
 
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A flexible string is plucked at two points. The response is presented. A hammer is applied to both a flexible string and a stiff string. The response is presented. The force of the stiff string at the bridge is analyzed in the time and frequency domains. Harmonic stretching is observed. check out https://sites.google.com/site/analysisofsoundsandvibrations/ for more videos on sounds and vibrations. This site also contains information on collecting and analyzing piano data.
Views: 184 Dave Koenig
Liza Levina: Overlapping community detection by spectral methods
 
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Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area Community detection is a fundamental problem in network analysis which is made more challenging by overlaps between communities which often occur in practice. Here we propose a general, flexible, and interpretable generative model for overlapping communities, which can be thought of as a generalization of the degree-corrected stochastic block model. We develop an efficient spectral algorithm for estimating the community memberships, which deals with the overlaps by employing the K-medians algorithm rather than the usual K-means for clustering in the spectral domain. We show that the algorithm is asymptotically consistent when networks are not too sparse and the overlaps between communities not too large. Numerical experiments on both simulated networks and many real social networks demonstrate that our method performs very well compared to a number of benchmark methods for overlapping community detection. This is joint work with Yuan Zhang and Ji Zhu. Recording during the "Meeting in mathematical statistics: new procedures for new data" the December 16, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
PHO121 - Speech Analysis
 
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This E-Lecture first discusses the central methods of sound analysis and then shows how spectrograms are produced and analyzed. This includes a discussion of the formant frequencies of vowels, the acoustic characteristics of consonants and the construction of an acoustic vowel chart.
VSC6000/HS Document Examination Techniques: Hyper Spectral Imaging
 
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The Foster + Freeman VSC 6000/HS remains the premier workstation for questioned document examination. The new hyperspectral imaging module has been designed to complement the systems existing analysis methods by producing superior ink discrimination. Hyperspectral imaging is a relatively new technique in the field of questioned document examination and had previously been considered to be an incredibly high cost method of analysis. Now integrated in the VSC6000/HS system, HSI sensors collect and processes information from across the electromagnetic spectrum combining the results into a 3 dimensional, multi-layered image cube. The images that make up the cube can then be scanned through manually in real time for further processing and examination.
Views: 10219 FosterFreeman
Topic Modeling: A Provable Spectral Method
 
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Ravi Kannan, Microsoft Research India Spectral Algorithms: From Theory to Practice http://simons.berkeley.edu/talks/ravi-kannan-2014-10-27
Views: 916 Simons Institute
Spectral algorithms for graph mining and analysis Yiannis Koutis
 
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Spectral algorithms have long been recognized as a signifi-cant tool in the analysis and mining of large graphs. How-ever, their adoption remains relatively limited because they are perceived as computationally demanding or non-robust. The talk addresses these two issues. We review recent algo-rithmic progress that enables the very fast computation of graph eigenvectors in time nearly linear to the size of the graph, making them very appealing from a computational point of view. We also review theoretical results that pro-vide strong arguments in favor of spectral algorithms from a robustness point of view, showing that Cheeger inequal-ities are rather pessimistic for significant classes of graphs that include real-world networks. We further argue that we have only scratched the surface in understanding the power of spectral methods for graph analysis. We support this claim by discussing non-standard “generalized” graph eigen-vectors, and showing that minor modifications of the default spectral partitioning methods have the potential to enhance their efficacy.
Views: 778 MMDS Foundation
Fundamentals of Electrical Engineering 7 - 4 - Spectral Analysis (www.porbona.com)
 
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This Video is made by Rice University.We are proud to share it with you.......
Views: 4376 Porbona group
MASW (Multichannel Analysis of Surface Waves) Data Acquisition
 
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This video is about MASW (Multichannel Analysis of Surface Waves) data acquisition. [email protected]
Views: 8070 Applied Geophysics
Data Science - Part XVI - Fourier Analysis
 
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For downloadable versions of these lectures, please go to the following link: http://www.slideshare.net/DerekKane/presentations https://github.com/DerekKane/YouTube-Tutorials This lecture provides an overview of the Fourier Analysis and the Fourier Transform as applied in Machine Learning. We will go through some methods of calibration and diagnostics and then apply the technique on a time series prediction of Manufacturing Order Volumes utilizing Fourier Analysis and Neural Networks.
Views: 11490 Derek Kane
InSpectr: Multi-Modal Exploration, Visualization, and Analysis of Spectral Data
 
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This paper addresses the increasing demand in industry for methods to analyze and visualize multimodal data involving a spectral modality. Two data modalities are used: high-resolution X-ray computed tomography (XCT) for structural characterization and low-resolution X-ray fluorescence (XRF) spectral data for elemental decomposition. We present InSpectr, an integrated tool for the interactive exploration and visual analysis of multimodal, multiscalar data. The tool has been designed around a set of tasks identified by domain experts in the fields of XCT and XRF. It supports registered single scalar and spectral datasets optionally coupled with element maps and reference spectra. InSpectr is instantiating various linked views for the integration of spatial and non-spatial information to provide insight into an industrial component's structural and material composition: views with volume renderings of composite and individual 3D element maps visualize global material composition; transfer functions defined directly on the spectral data and overlaid pie-chart glyphs show elemental composition in 2D slice-views; a representative aggregated spectrum and spectra density histograms are introduced to provide a global overview in the spectral view. Spectral magic lenses, spectrum probing and elemental composition probing of points using a pie-chart view and a periodic table view aid the local material composition analysis. Two datasets are investigated to outline the usefulness of the presented techniques: a 3D virtually created phantom with a brass metal alloy and a real-world 2D water phantom with insertions of gold, barium, and gadolinium. Additionally a detailed user evaluation of the results is provided.
Views: 166 CTVis Group Wels
Using Local Spectral Methods to Robustify Graph-Based Learning Algorithms
 
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Authors: David F. Gleich, Michael W. Mahoney Abstract: Graph-based learning methods have a variety of names including semi-supervised and transductive learning. They typically use a diffusion to propagate labels from a small set of nodes with known class labels to the remaining nodes of the graph. While popular, these algorithms, when implemented in a straightforward fashion, are extremely sensitive to the details of the graph construction. Here, we provide four procedures to help make them more robust: recognizing implicit regularization in the diffusion, using a scalable push method to evaluate the diffusion, using rank-based rounding, and densifying the graph through a matrix polynomial. We study robustness with respect to the details of graph constructions, errors in node labeling, degree variability, and a variety of other real-world heterogeneities, studying these methods through a precise relationship with mincut problems. For instance, the densification strategy explicitly adds new weighted edges to a sparse graph. We find that this simple densification creates a graph where multiple diffusion methods are robust to several types of errors. This is demonstrated by a study with predicting product categories from an Amazon co-purchasing network. ACM DL: http://dl.acm.org/citation.cfm?id=2783376 DOI: http://dx.doi.org/10.1145/2783258.2783376
Toeplitz methods in completeness and spectral problems – Alexei Poltoratski – ICM2018
 
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Analysis and Operator Algebras Invited Lecture 8.18 Toeplitz methods in completeness and spectral problems Alexei Poltoratski Abstract: We survey recent progress in the gap and type problems of Fourier analysis obtained via the use of Toeplitz operators in spaces of holomorphic functions. We discuss applications of such methods to spectral problems for differential operators. © International Congress of Mathematicians – ICM www.icm2018.org
Views: 53 Rio ICM2018
A Tutorial Review of Functional Connectivity Analysis Methods and Their Interpretational Pitfalls
 
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Andre M. Bastos - MIT Description: Oscillatory neuronal synchronization has been hypothesized to provide a mechanism for dynamic network coordination. Rhythmic neuronal interactions can be quantified using multiple metrics, each with their own advantages and disadvantages. This tutorial will review and summarize current analysis methods used in the field of invasive and non-invasive electrophysiology to study the dynamic connections between neuronal populations. First, I will review metrics for functional connectivity, including coherence, phase synchronization, phase-slope index, and Granger causality, with the specific aim to provide an intuition for how these metrics work, as well as their quantitative definition. Next, I will highlight a number of interpretational caveats and common pitfalls that can arise when performing functional connectivity analysis, including the common reference problem, the signal to noise ratio problem, the volume conduction problem, the common input problem, and the sample size bias problem. These pitfalls will be illustrated by presenting a series of MATLAB-scripts, which can be executed by the tutorial participants to simulate each of these potential problems. I will discuss how some of these issues can be addressed using current methods.