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Abstract

Imagine we have n particles in our "universe". These particles have a random initial x, y, and z coordinates to begin with. Defined by Newton's law of universal gravitation, each particle attracts every other particles in this universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. As as result, these particles gain (and lose) velocities and change positions over time. The modelling of this physical mechanics is called a N-body simulation.

There currently exists many N-body simulation algorithms. Some are less advanced and highly computational costly (execution time in the order of O(N^2)) - but simple and easy to understand. Some others are more advanced and significantly more efficient (execution in the order of O(n*log(n)) - but not as simple and easy to understand. This articles focuses on the implementation aspect of the less advanced toy algorithm - for the benefit of ease o

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module AgdaBasics where

apply : (A : Set)(B : A → Set) → ((x : A) → B x) → (a : A) → B a
apply A B f a = f a

_∘_ : {A : Set}{B : A → Set}{C : (x : A) → B x → Set}
      (f : {x : A}(y : B x) → C x y)(g : (x : A) → B x)
      (x : A) → C x (g x)
(f ∘ g) x = f (g x)

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#!/bin/bash

wget -q -O - https://dl-ssl.google.com/linux/linux_signing_key.pub | sudo apt-key add - 
sudo sh -c 'echo "deb http://dl.google.com/linux/chrome/deb/ stable main" >> /etc/apt/sources.list.d/google.list'
sudo apt-get update 
sudo apt-get install -y google-chrome-stable

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from keras.models import Model
from keras.layers import (
    Input,
    Dense,
    Flatten,
    merge,
    Lambda
)
from keras.layers.convolutional import (
    Convolution2D,

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#! /usr/bin/env python
#
# Mixpanel, Inc. -- http://mixpanel.com/
#
# Python API client library to consume mixpanel.com analytics data.

import hashlib
import urllib
import time
try:

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package com.agilogy.spray.cors

import spray.http.{HttpMethods, HttpMethod, HttpResponse, AllOrigins}
import spray.http.HttpHeaders._
import spray.http.HttpMethods._
import spray.routing._

// see also https://developer.mozilla.org/en-US/docs/Web/HTTP/Access_control_CORS
trait CORSSupport {
  this: HttpService =>

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# DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
# Version 2, December 2004
#
# Copyright (C) 2015 Swen Wenzel <[email protected]>
#
# Everyone is permitted to copy and distribute verbatim or modified
# copies of this license document, and changing it is allowed as long
# as the name is changed.
#
# DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE

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/*
This example uses Scala.  Please see the MLlib documentation for a Java example.

Try running this code in the Spark shell.  It may produce different topics each time (since LDA includes some randomization), but it should give topics similar to those listed above.

This example is paired with a blog post on LDA in Spark: http://databricks.com/blog
Spark: http://spark.apache.org/
*/

import scala.collection.mutable

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# DATA FRAME OPERATIONS IN R

# Create data frame
# A dataset is ~ table (list of vectors)
id <- c(1,2,3)
name <- c("John", "Kirk", "AJ")
age <- c(21,27,18)
employees <- data.frame(ID=id, Name=name, Age=age)
employees