mnarayan mnarayan

Introduction

Here is an example of single-subject time-series during R pMFG stimulation.

Break down of global time-series by wavelet scales

Measuring total variance in the signal at each ROI could be very useful to do, particularly across scales 1 to 4.

Additional Algorithm for Two Sample Differences in Populations of Graphical Models

Consider two graphical models case

$$\mathbf{X}^{(1,i)} \sim \mathcal{N}(0,\boldsymbol\Sigma^{(1,i)})$$ $$\mathbf{X}^{(2,i)} \sim \mathcal{N}(0,\boldsymbol\Sigma^{(2,i)})$$

Idea:

Create pooled sample covariance matrix given by $\frac{\widehat{\boldsymbol\Sigma^{1}} + \widehat{\boldsymbol\Sigma^{2}}}{2}$
Obtain multiple estimates of $\Delta^{(1,i)}, i=1,\ldots, n_g$ and similarly for $g = 2$ using the sparse log-likelihood ratio

Here is an improvement over a nice answer from @herbert that took advantage of pstricks-add and xelatex.

The earlier answer however did not create a proper grid for every cell in the matrix.It only displayed the grid structure for values set to 1. This enables a more generic solution beyond [0,1] valued matrices.

What we would like to see however is something like this —

[![Alternative color scheme, highlights grid over all cells][2]][2]

Here is a code snippet to achieve this:

How to backup data from sherlock to google drive

Download and install rclone to your $HOME/bin directory. Setup up rclone to connect to your google drive. Suppose you call your remote google drive drive.
Create a bash script called backup_gdrive.sh with the following information

#!/bin/sh

STUDY_DIR=STUDY
LOCAL_DIR=${SCRATCH}/${STUDY_DIR}

Direct links to free Springer maths books (pdf versions)

duplicates = multiple editions

A Classical Introduction to Modern Number Theory,Kenneth IrelandMichael Rosen

A Course in Arithmetic,Jean-Pierre Serre

Note: The betweenness centrality used here is based on the shortest path implementation in the Brain Connectivity Toolbox.

Take a real known correlation matrix $\Sigma$
Simulate multivariate data i.e. observations x regions matrix from normal distribution with known correlation matrix $\mathcal{N}(0,\Sigma)$
For each random sample from step 2, compute betweenness-centrality for a series of thresholds on the correlation matrix. This constitutes one monte-carlo trial run in the first figure.
One can vary the number of observations t from 100 to 500 and see the error bars on betweenness-centrality go down.

Take-ways: Network metric is unstable in two ways: A small change to the threshold leads to huge change in metric. As a result it is also highly unstable between monte-carlo trials as well. **Theory says that all shortest path based metrics are similarly unstable, with unpredictably large variance. Thus z-scores and t-tests don't even converge to any distribution let alone a normal one. There

	import sys
	import numpy as np

	from skopt.space import Real, Categorical, Integer
	from skopt import BayesSearchCV

	from sklearn.grid_search import GridSearchCV
	from sklearn.datasets import make_sparse_spd_matrix
	from sklearn.model_selection import train_test_split
	from sklearn.metrics import make_scorer

	\documentclass{article}

	\usepackage{booktabs}
	\usepackage{geometry}
	\usepackage{tabularx}
	\geometry{lmargin=72pt,tmargin=72pt,textwidth=350pt,marginparwidth=144pt}
	\usepackage{tufte-sidenotes}

	\begin{document}
	Here is demo of the \verb#tufte-sidenotes# style.

	import numpy as np

	# Author : Alexandre Gramfort
	# license : BSD


	def pav(y):
	"""
	PAV uses the pair adjacent violators method to produce a monotonic
	smoothing of y

	var TreeId = "your_tree_id_here";
	var Filename = "output_filename";

	var http =require('http');
	var fs = require('fs');
	var request = require('request');
	var exec = require('child_process').exec;
	var header = fs.readFileSync('parts/header.tex', 'utf8');
	var footer = fs.readFileSync('parts/footer.tex', 'utf8');
	var replacements = { '\\\\begin\\{center\\}\\\\rule\\{3in\\}\\{0\\.4pt\}\\\\end\\{center\\}': '\\hr', '\\\\section\{([^\}])\}\\\\label\{([^\}])\}\\n\\n([^\.][\\.\\\'\\\'\\?\\!])\\s': '\\finishchapter\n\\section{$1}\\label{$2}\n\\setupchapter\n\\newthought{$3} ' };