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Smoothed Analysis of Discrete Tensor Decomposition and Assemblies of Neurons [article]

Nima Anari, Constantinos Daskalakis, Wolfgang Maass, Christos H. Papadimitriou, Amin Saberi, Santosh Vempala
2018 arXiv   pre-print
Our analysis builds upon [BCMV14] but allows for a wider range of perturbation models, including discrete ones. We give an application to recovering assemblies of neurons.  ...  We analyze linear independence of rank one tensors produced by tensor powers of randomly perturbed vectors. This enables efficient decomposition of sums of high-order tensors.  ...  [3] when the tensors are of high enough order. The main feature of our analysis is that it can handle discrete perturbations.  ... 
arXiv:1810.11896v1 fatcat:m6kpnq25tzgjtinm3cykwgzv2i

Unsupervised Discovery of Demixed, Low-Dimensional Neural Dynamics across Multiple Timescales through Tensor Component Analysis

Alex H. Williams, Tony Hyun Kim, Forea Wang, Saurabh Vyas, Stephen I. Ryu, Krishna V. Shenoy, Mark Schnitzer, Tamara G. Kolda, Surya Ganguli
2018 Neuron  
We demonstrate a simple tensor component analysis (TCA) can meet this challenge by extracting three interconnected, low-dimensional descriptions of neural data: neuron factors, reflecting cell assemblies  ...  , and multielectrode recordings of macaque motor cortex during brain machine interface learning.  ...  ACKNOWLEDGMENTS The authors thank Subhaneil Lahiri (Stanford University), Jeff Seely (Cognes-cent Corporation), and Casey Battaglino (Georgia Tech) for discussions pertaining to this work.  ... 
doi:10.1016/j.neuron.2018.05.015 pmid:29887338 pmcid:PMC6907734 fatcat:7wfwookp2nbttesy4bxnjnhmwa

Unsupervised discovery of demixed, low-dimensional neural dynamics across multiple timescales through tensor components analysis [article]

Alex H Williams, Tony Hyun Kim, Forea Wang, Saurabh Vyas, Stephen I Ryu, Krishna V Shenoy, Mark Schnitzer, Tamara G Kolda, Surya Ganguli
2017 bioRxiv   pre-print
We demonstrate a simple tensor components analysis (TCA) can meet this challenge by extracting three interconnected low dimensional descriptions of neural data: neuron factors, reflecting cell assemblies  ...  , and multielectrode recordings of macaque motor cortex during brain machine interface learning.  ...  Illustration of tensor unfolding for applying matrix decompositions to tensor datasets.  ... 
doi:10.1101/211128 fatcat:sgn637xjczb3xbjwpugxw6lyeq

Nonlinear anisotropic diffusion filtering of three-dimensional image data from two-photon microscopy

Philip. J. Broser, R. Schulte, S. Lang, A. Roth Fritjof, Helmchen, J. Waters, Bert Sakmann, G. Wittum
2004 Journal of Biomedical Optics  
The filter is a valuable general tool for smoothing cellular processes and is well suited for preparing data for subsequent image segmentation and neuron reconstruction. © 2004 Society of Photo-Optical  ...  The key idea is to use structural information in the raw datathe local moments of inertia-to locally control the strength and direction of diffusion filtering.  ...  Reisinger for the help with software development and P. Frolkovic for stimulating discussions on solving partial differential equations.  ... 
doi:10.1117/1.1806832 pmid:15574067 fatcat:dgnr4kivjnecvgndyewvom7jey

1PT191 Time-series analysis for protein dynamics using discrete wavelet transform with kernel canonical correlation analysis(The 50th Annual Meeting of the Biophysical Society of Japan)
1PT191 カーネル正準相関分析と離散ウェーブレット変換を用いたタンパク質立体構造の時系列解析(日本生物物理学会第50回年会(2012年度))

Mayumi Kamada, Miikito Toda, Tatsuya Akutsu
2012 Seibutsu Butsuri  
, Thus we decided te compare them systematically, i, e., our present purpose is to eva]uate the quality of 3D reconstruction and the usability of these software packages, show the pros and cons of them  ...  We acqu{red tilt seT{es of modet structure (phantom data) and axonemes by cryo-TEM, and computed the 3D structure using IMOD, Inspect3D, TEMography ancl Eos from each ofthem, respeetively.  ...  and singular value decomposition(SVD)).  ... 
doi:10.2142/biophys.52.s101_5 fatcat:fqf4gwoqiney5h6f3huvcw5ig4

Smoothed Analysis in Unsupervised Learning via Decoupling [article]

Aditya Bhaskara, Aidao Chen, Aidan Perreault, Aravindan Vijayaraghavan
2019 arXiv   pre-print
While polynomial time smoothed analysis guarantees have been obtained for worst-case intractable problems like tensor decompositions and learning mixtures of Gaussians, such guarantees have been hard to  ...  Smoothed analysis is a powerful paradigm in overcoming worst-case intractability in unsupervised learning and high-dimensional data analysis.  ...  been obtained for other problems like overcomplete ICA [GVX14] , learning mixtures of general Gaussians [GHK15] , fourth-order tensor decompositions [MSS16] , and recovering assemblies of neurons [ADM  ... 
arXiv:1811.12361v2 fatcat:n5wwtk5fwvg7xj4unt2bp3qlry

Parameter estimation and bifurcation analysis of stochastic models of gene regulatory networks: tensor-structured methods [article]

Shuohao Liao, Tomas Vejchodsky, Radek Erban
2015 arXiv   pre-print
In this paper, tensor-structured parametric analysis (TPA) is presented. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors.  ...  This methodology is exemplified to study the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks.  ...  S1.2.2 Decomposition of the parametric part Having the low-parametric discrete tensor-structured representations (S7) of the non-parametric operators A [j] , we write a discrete tensor-structured representation  ... 
arXiv:1406.7825v2 fatcat:glgbtadqmnacbjndum32uuqhlq

Biomechanical functional and sensory modelling of the gastrointestinal tract

D. Liao, D. Lelic, F. Gao, A. M. Drewes, H. Gregersen
2008 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
Such computational modelling combines imaging data, GI physiology, the gut-brain axis, geometrical and biomechanical reconstruction, and computer graphics for mechanical, electronic and pain analysis.  ...  The aim of this review is to describe the biomechanical, functional and sensory modelling work that can be used to integrate the physiological, anatomical and medical knowledge of the gastrointestinal  ...  There were also more discrete changes in the cingulate gyrus where the neuronal source was more posterior in patients.  ... 
doi:10.1098/rsta.2008.0091 pmid:18593660 fatcat:aaz7ue44ybblndrdi4kdog7j4e

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks

Shuohao Liao, Tomáš Vejchodský, Radek Erban
2015 Journal of the Royal Society Interface  
It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors.  ...  In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges.  ...  The (canonical) tensor decomposition [21] , as a discrete counterpart of (2.2), then allows a multi-dimensional array to be approximated as a sum of tensor products of one-dimensional vectors.  ... 
doi:10.1098/rsif.2015.0233 pmid:26063822 pmcid:PMC4528587 fatcat:vteqeioxvrhwjjgz5if5f3us3y

Extending Fuzzy Cognitive Maps With Tensor-Based Distance Metrics

Georgios Drakopoulos, Andreas Kanavos, Phivos Mylonas Mylonas, Panagiotis Pintelas
2020 Mathematics  
The primary contribution of this article is the construction of cognitive map for the sixteen Myers-Briggs personality types with a tensor distance metric.  ...  Currently such maps play a crucial role in cognitive sciences as it is believed this is how clusters of dedicated neurons at hippocampus construct internal representations.  ...  Acknowledgments: The authors gratefully acknowledge the support of NVIDIA corporation with the donation of Titan Xp GPU used in this research.  ... 
doi:10.3390/math8111898 fatcat:auptwe5z2jhmdolvzgplqx7qzm

Comparing Open-Source Toolboxes for Processing and Analysis of Spike and Local Field Potentials Data

Valentina A. Unakafova, Alexander Gail
2019 Frontiers in Neuroinformatics  
Analysis of spike and local field potential (LFP) data is an essential part of neuroscientific research.  ...  We overview major open-source toolboxes for spike and LFP data analysis as well as toolboxes with tools for connectivity analysis, dimensionality reduction and generalized linear modeling.  ...  ACKNOWLEDGMENTS The authors would like to thank Lauren Cassidy for feedback on previous versions of the manuscript.  ... 
doi:10.3389/fninf.2019.00057 pmid:31417389 pmcid:PMC6682703 fatcat:jcxyri24hjgjta3hvhe3ytb72e

A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning

Kun Wang, WaiChing Sun
2018 Computer Methods in Applied Mechanics and Engineering  
When fractures propagate in these multi-porosity materials, these pores may enlarge and coalesce and therefore change the magnitude and the principal directions of the effective permeability tensors.  ...  permeability tensor field is insufficient to characterize the evolving hydraulic properties of these materials at smaller time scale.  ...  Dynamic Materials and Interactions Program from the Air Force Office of Scientific Research under grant contract FA9550-17-1-0169, while analysis on the multi-permeability porous media is supported by  ... 
doi:10.7916/d8c83nsh fatcat:gelwavdshjfshogmf5zou2nqeu

Variational, geometric, and statistical methods for modeling brain anatomy and function

Olivier Faugeras, Geoffray Adde, Guillaume Charpiat, Christophe Chefd'Hotel, Maureen Clerc, Thomas Deneux, Rachid Deriche, Gerardo Hermosillo, Renaud Keriven, Pierre Kornprobst, Jan Kybic, Christophe Lenglet (+8 others)
2004 NeuroImage  
We then go to the statistical modeling of functional magnetic resonance imaging (fMRI) signals from the viewpoint of their decomposition in a pseudo-deterministic and stochastic part that we then use to  ...  Anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but, in the current state of the technology, it must be preceded by a robust estimation and regularization stage  ...  Meunier of the Physiology and Physiopathology of Human Motricity Lab., La Salpétrière Hospital, INSERM, Paris, for permission to use the somatosensory MEG data. They thank L. Garnero, S.  ... 
doi:10.1016/j.neuroimage.2004.07.015 pmid:15501100 fatcat:ecgjc4ltzbhqxitigynxapflpi

Comparing open-source toolboxes for processing and analysis of spike and local field potentials data [article]

Valentina A. Unakafova, Alexander Gail
2019 bioRxiv   pre-print
ABSTRACTAnalysis of spike and local field potential (LFP) data is an essential part of neuroscientific research.  ...  We overview major open-source toolboxes for spike and LFP data analysis as well as toolboxes with tools for connectivity analysis, dimensionality reduction and generalized linear modeling.  ...  support by updates at least once per year. ccpTD -coupled canonical polyadic Tensor Decomposition, comments).  ... 
doi:10.1101/600486 fatcat:nj437wn4kngslhjtaa6a4bwmay

A Physics-Informed Assembly of Feed-Forward Neural Network Engines to Predict Inelasticity in Cross-Linked Polymers

Aref Ghaderi, Vahid Morovati, Roozbeh Dargazany
2020 Polymers  
Using a sequential order-reduction, we have simplified the 3D stress–strain tensor mapping problem into a limited number of super-constrained 1D mapping problems.  ...  By capturing all loading modes through a simplified set of dispersed experimental data, the proposed hybrid assembly of L-agents provides a new generation of machine-learned approaches that simply outperform  ...  matrix representing assembly of all W j .  ... 
doi:10.3390/polym12112628 pmid:33182257 fatcat:h72vzucczjbhnooqa5ddhekqcy
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