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# How to Solve a Linear Programming model with OpenSolver

OpenSolver is a great Excel Add-in that solves optimization models. The following article will describe how to solve a Linear Programming model using this tool (first you must Download and install OpenSolver in Excel). For educational purposes we will consider a linear programming model with two decision variables and four constraints, nevertheless you can easily extend its application to larger problems.

Maximize $30X+20Y$

Subject to:

• $5X+2Y\leq 140$
• $3X+2Y\leq 120$
• $X,Y\geq 0$

We will then need to prepare an Excel spreadsheet that includes the model’s parameters and variables (this step is similar to loading a problem in Frontline’s Solver). You can see that cells B2 and C2 (yellow color) have been assigned as the decision variables and cell E2 corresponds to the objective function (blue cell), which is a formula that links the decision variables to their respective parameters. Finally cells D5 and D6 are formulas that represent the “left-hand side (LHS)” of the problem’s constraints (for example, cell D5 corresponds to B2*B5+C2*C5 or equivalently SUMPRODUCT(B2:C2;B5:C5)).

Once the previous step has been completed you must run OpenSolver, whose menu can be accessed from the “Data” tab in Excel. Then select “Model…” as shown below:

The interface for implementing the model is quite similar to the traditional Solver (Frontline) version. The objective cell is defined (E2) in maximization; next you must select the range of decision variables (as shown in the following image) and the constraints. If you try to replicate the structure of the example we are going over in this article, then it should look like this:

Then we select “Save Model” (the structure of the template will change and become different colors, one of the characteristics OpenSolver has that makes this Add-in such a intuitive tool for the user).

Finally we select “Solve”:

The program is run and gives us the optimal solution ($X=0$ and $Y=60$) and the optimal value $V(P)=1,200$ for the optimization problem:

The results achieved are consistent with those obtained in the graphical solution of the problem that we went over in the article “What does a Shadow Price of Zero mean in Linear Programming” as shown in the following image:

Below you can download the file that contains OpenSolver’s solution to this problem so that you can familiarize yourself with this Excel Add-in: OpenSolver Excel.

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# Depressed Numbers [duplicate]

$12 = 0$
$1234 = 1$
$123456 = 2$
$12345678 = 4$

$369 = 2$
$248 = 3$

$2 = 0$
$3 = 0$
$5 = 0$
$7 = 0$
$11 = 0$
$13 = 0$

What does:
$123456789 = ?$
Why?

Hopefully isn't too hard, please ask if you need any test cases.

## marked as duplicate by mmking, Bailey M, JLee, Engineer Toast, pacoverflowJul 16 '15 at 16:09

• Wow this was way too easy. Really should amp up the difficulty level – qwertylpc Jul 16 '15 at 16:05

format: plain


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Question

# A block of mass $$2\ kg$$ starts moving with initial speed of $$10\ m/s$$ and accelerates at $$-2 m/s^2$$. How far does the object travel before coming to rest?

A
10m
B
25m
C
50m
D
75m
E
100m

Solution

## The correct option is B $$25 m$$Given that: $$m=2 \ kg; u=10\ m/s; a=-2\ m/s^2$$Using third equation of motion:$$\Rightarrow v^2=u^2+2aS$$$$\Rightarrow 0=10^2+2(-2)S$$$$\Rightarrow S=\dfrac{100}{4}=25 \ m$$Physics

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## Integral bases for the universal enveloping algebra of g tensor A

10/26/2010 - 12:15pm
10/26/2010 - 1:10pm
Speaker:
Sam Chamberlin (UC Riverside)
Abstract:

Given a finite-dimensional, simple Lie algebra g over C and A, a commutative, associative algebra with unity over C, we exhibit a Z-form for the universal enveloping algebra of g tensor A and an explicit Z-basis for this Z-form. We also produce explicit commutation formulas in the universal enveloping algebra of sl_2 tensor A that allow us to write certain elements in PBW basis order.

Where:
Millikan 208 (Pomona College)


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# Keras Sum Layer

keras is an R based interface to the Keras: the Python Deep Learning library. An Embedding layer should be fed sequences of integers, i. What are Embedding Layers in Keras (11. The first layer, which contains 8 hidden notes, on the other hand, has an input_shape of 4. Is it possible to implement mutiple softmaxes in the last layer in Keras? So the sum of Nodes 1-4 = 1; 5-8 = 1; etc. The hidden state must have shape [units], where units must correspond to the number of units this layer uses. function and AutoGraph Distributed training with TensorFlow Eager execution Effective TensorFlow 2 Estimators Keras Keras custom callbacks Keras overview Masking and padding with Keras Migrate your TensorFlow 1 code to TensorFlow 2 Random number generation Recurrent Neural Networks with Keras Save and serialize models with. trainable_weights中。其他的属性还包括self. 2 With tuple. It ranges from 1 to 0 (no error), and returns results similar to binary crossentropy # define custom loss and metric functions. The first layer will have 128-3 x 3 filters followed by a upsampling layer,. It accepts either channels_last or channels_first as value. Flatten ()) # takes our 28x28 and makes it 1x784 model. Lambda keras. Graph() The quantity being optimized by a Graph model is the sum of all loss functions over the different outputs. So in total we’ll have an input layer and the output layer. I visualize the VGG-Face architure to be understood clear. Interface to Keras , a high-level neural networks API. Keras has been structured based on austerity and simplicity, and it provides a programming model without ornaments that maximizes readability. import torch import torchvision from torch import nn from torchvision import models. Keras rolls these two into one, called “Dense. The basis of our model will be the Kaggle Credit Card Fraud Detection dataset, which was collected during a research collaboration of Worldline and the Machine Learning Group of ULB (Université Libre de Bruxelles) on big data mining. when a function is a vector valued function, the partial derivative is a matrix called jacobian. Keras provides a language for building neural networks as connections between general purpose layers. Keras provides both the 16-layer and 19-layer version via the VGG16 and VGG19 classes. I could load up a model and do this: "example. class Add: Layer that adds a list of inputs. Keras library provides a dropout layer, a concept introduced in Dropout: A Simple Way to Prevent Neural Networks from Overfitting(JMLR 2014). class AdditiveAttention. In the next example, we are stacking three dense layers, and keras builds an implicit input layer with your data, using the input_shape parameter. We can clearly see that the sentences are of different length. Matrix layer rotation leetcode. TimeDistributed(layer) This wrapper allows to apply a layer to every temporal slice of an input. The Keras Python library makes creating deep learning models fast and easy. The one word with the highest probability will be the predicted word – in other words, the Keras LSTM network will predict one word out of 10,000 possible categories. sum will simply sum the outputs of the models (therefore all models should have an output with the same shape). Fifth layer, Flatten is used to flatten all its input into single dimension. A Sequential model is appropriate for a plain stack of layers where each layer has exactly one input tensor and one output tensor. Use the cross-entropy loss function. y_pred /= y_pred. class AdditiveAttention. share 0],layers_dim[layer_name][1],layers_dim[layer_name][2]) return np. From Keras, import the Sequential model as well as the Dense, Dropout and the Activation layers. GoogLeNet or MobileNet belongs to this network group. Model or layer object. You can get started with Keras in this Sentiment Analysis with Keras Tutorial. Matrix layer rotation leetcode. non_trainabe_weights（列表）和self. topology import Layer class ZeroMaskedEntries(Layer): """ This layer is called after an Embedding layer. get_weights()：返回层的权重（numpy array） layer. Masking(mask_value=0. A "neuron" computes a weighted sum of all of its inputs, adds a value called "bias" and feeds the result through a so called "activation function". Compiling the Model. Creates a layer that performs an python arbitrary function over the layer’s input data: print_out(Lambda(lambda x: x*x), [1, 2, 3]) # [ 1. Dropout(p) Applies Dropout to the input. # the sample of index i in batch k is. dilation_rate: It can be an integer or tuple/ list of 2 integers that relates to the dilation rate to be used for dilated convolution. summary() to see the names of all layers in the model. Fire and smoke detection with Keras and Deep Learning Figure 1: Wildfires can quickly become out of control and endanger lives in many parts of the world. The basic workflow is to define a model object of class keras. We will also demonstrate how to train Keras models in the cloud using CloudML. backend import constant from keras import optimizers from keras. We can clearly see that the sentences are of different length. The reason for this is that the output layer of our Keras LSTM network will be a standard softmax layer, which will assign a probability to each of the 10,000 possible words. Dropout(p) Applies Dropout to the input. 2 With tuple. Recently we also started looking at Deep Learning, using Keras, a popular Python Library. You can get started with Keras in this Sentiment Analysis with Keras Tutorial. Keras provides a powerful abstraction for recurrent layers such as RNN, GRU and LSTM for Natural Language Processing. From Keras, import the Sequential model as well as the Dense, Dropout and the Activation layers. layers import LSTM, Dense import numpy as np data_dim = 16 timesteps = 8 num_classes = 10 batch_size = 32 # Expected input batch shape: (batch_size, timesteps, data_dim) # Note that we have to provide the full batch_input_shape since the network is stateful. 5 as its value. My study uses the VGG16 model. We will use the LSTM network to classify the MNIST data of handwritten digits. Dropout layer. updates（需要更新的形如（tensor, new_tensor）的tuple的列表）。. Things to try: I assume you have a test program that uses your customer layer. Function fit trains a Keras model. It zeros out all of the masked-out embeddings. Keras forked into tf. Only output layer is different than the imagenet version – you might compare. You will learn how to build a keras model to perform clustering analysis with unlabeled datasets. In just a few lines of code, you can define and train a. Under the new API changes, how do you do element-wise multiplication of layers in Keras? Under the old API, I would try something like this: merge([dense_all, dense_att], output_shape=10, mode='mu. advanced_activations. pyplot as plt from scipy. " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "0Tese2RQ3ouf" }, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 2. When using InputLayer with Keras Sequential model, it can be skipped by moving the input_shape parameter to the first layer after the InputLayer. keras/keras. Fortunately, by showing the wish to add code to (and potentially increase Keras’ maintenance cost, :D) the core source file embedding. A layer's dtype can be queried via the Layer. Keras Visualization Toolkit. Switching to theano fixed the problem. The first layer passed to a Sequential model should have a defined input shape. 2020-06-03 Update: This blog post is now TensorFlow 2+ compatible! In the first part of this tutorial, we are going to discuss the parameters to the Keras Conv2D class. The sequential API allows you to create models layer-by-layer for most problems. model" was a (path to) the model …. Function fit trains a Keras model. In this article, we will learn to conduct fire and smoke detection with Keras and deep learning. The network largely consists of convolutional layers, and just before the final output layer, global average pooling is applied on the convolutional feature maps, and use those as features for a fully-connected layer that produces the desired output (categorial or. sum(x, axis=1, keepdims=False)) However, do I need to explicitly include the mask in the calcuations in order to ignore the padding? If so, does anyone have an example on how to achieve this?. This class can create placeholders for tf. io Find an R package R language docs Run R in your browser R Notebooks. This is not a layer provided by Keras so we have to write it on our own layer with the support provided by the Keras backend. The number of layers is usually limited to two or three, but theoretically, there is no limit! The layers act very much like the biological neurons that you have read about above: the outputs of one layer serve as the inputs for the next layer. optimizers import Adam. Using Keras; Guide to Keras Basics Whether the layer weights will be updated during training. The initial building block of Keras is a model, and the simplest model is called sequential. core import Layer from keras import initializations, regularizers, constraints from keras import backend as K Also, the code gives a IndexError: pop index out of range on using tensorflow backend. if it came from a Keras layer with masking support. 5 What is the purpose of untrainable weights in Keras 2017-12-15T01:08:13. text import one_hot from tensorflow. is_available else "cpu" ) # Assuming that we are on a CUDA machine, this should print a CUDA device: print ( device ). It zeros out all of the masked-out embeddings. Today we’ll train an image classifier to tell us whether an image contains a dog or a cat, using TensorFlow’s eager API. Let’s take a look at those. Size Upsampling factor. Pre-trained autoencoder in the dimensional reduction and parameter initialization, custom built clustering layer trained against a target distribution to refine the accuracy further. input_layer. Regularizers allow you to apply penalties on layer parameters or layer activity during optimization. layers API to keras. Graph() The quantity being optimized by a Graph model is the sum of all loss functions over the different outputs. Keras was developed with a focus on enabling fast experimentation, supports both convolution based networks and recurrent networks (as well as combinations of the two), and runs seamlessly on both CPU and GPU devices. It is limited in that it does not allow you to create models that share layers or have multiple inputs or outputs. Digit Capsule Layer: Logic and algorithm used for this layer is explained in the previous blog. a 2D input of shape (samples, indices). Flatten ()) # takes our 28x28 and makes it 1x784 model. word vectors after embedding) in each. A convolution is the simple application of a filter to an input that results in an activation. The number of layers is usually limited to two or three, but theoretically, there is no limit! The layers act very much like the biological neurons that you have read about above: the outputs of one layer serve as the inputs for the next layer. Fifth layer, Flatten is used to flatten all its input into single dimension. 47% on CIFAR-10. callbacks import EarlyStopping, ModelCheckpoint, TensorBoard, Redu ceLROnPlateau from keras. Notable examples include: Regular dense, MLP type Recurrent layers, LSTM, GRU, etc. Subtract keras. If the layer's call method takes a mask argument (as some Keras layers do), its default value will be set to the mask generated for inputs by the previous layer (if input did come from a layer that generated a corresponding mask, i. set_image_data_format ('channels. import numpy as np import matplotlib. In my Keras code I use GlobalMaxPooling1D after the last 1D convolutional layer: result = GlobalMaxPooling1D()(previous_result). Google Data Center Security: 6 Layers Deep - Duration: 6:10. models import model_from_json, Model def build_tower ( input_layer , features_nr , shape , tower_nr ,. Note how the output layer creates 3 output values, one for each Iris class (versicolor, virginica or setosa). I would hack it together like this: use a lambda layer to acquire a single '1' vector, learn a scaling factor via a dense layer which takes a single input and outputs a single number repmat that scaling factor to the correct size multiply the scaling factor with whatever we are scaling. Let's see how. So in total we’ll have an input layer and the output layer. Some of the first images seem to have duplicated infomation (same colour). " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "0Tese2RQ3ouf" }, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 2. convolutional. The first layer (which actually comes after an input layer) is called the hidden layer, and the second one is called the output layer. Importing And Preprocessing MNIST Data. # the sample of index i in batch k is. You can get started with Keras in this Sentiment Analysis with Keras Tutorial. In Keras, we usually pass arrays of the same length. Pre-trained models and datasets built by Google and the community. Notice how we had to specify the input dimension ( input_dim ) and how we only have 1 unit in the output layer because we’re dealing with a binary classification problem. If you pass tuple, it should be the shape of ONE DATA SAMPLE. py, I got comments from F. This is achieved by Flatten layer. Visualization of VGG-Face. Introduction to Variational Autoencoders. The data is MNIST and the network architecture is two convolutional layers and one global average pooling layer. Sequential model. Assuming you read the answer by Sebastian Raschka and Cristina Scheau and understand why regularization is important. Simple computational layers can be implemented using Lambda wrapper in Keras. Our extensive experiments validate the effectiveness of our algorithm which outperforms state-of-the-art methods by a significant margin on four widely used few-shot classification benchmarks, namely, miniImageNet, tieredImageNet. Keras Backend. 正常DL都是一个forward, backword, update 三个流程,而在 keras 中对于单层 Layer 来说,通过将可训练的权应该在这里被加入列表`self. class Activation: Applies an activation function to an output. Dense layers, also called fully connected layer, since, each node in the input is connected to every node in the output, Activation layer which includes activation functions like ReLU, tanh, sigmoid among others, Dropout layer – used for regularization during training, Flatten, Reshape, etc. The function returns the layers defined in the HDF5 (. We can clearly see that the sentences are of different length. This is not a layer provided by Keras so we have to write it on our own layer with the support provided by the Keras backend. mode: String or lambda/function. R/layers-merge. Digit Capsule Layer: Logic and algorithm used for this layer is explained in the previous blog. jsでWEBアプリケーションに組み込むというのも、なんとなくいけそうな気がします。. However, you will also add a pooling layer. Question 1: I use axis=1 because I assumer the lambda layer gets applied to a whole batch of inputs at a time, meaning axis 0 is the sample index, while axis 1 indexes the words (i. keras and "keras community edition" Latests commits of Keras teasing like tf. Chollet, Keras’ author. datasets import mnist from keras. ∙ 0 ∙ share Implementing artificial neural networks is commonly achieved via high-level programming languages like Python and easy-to-use deep learning libraries like Keras. Keras was chosen in large part due to it being the dominant library for deep learning at the time of this writing [12, 13, 14]. In this vignette we illustrate the basic usage of the R interface to Keras. Repeated application of the same filter to an input results in a map of activations called a feature map, indicating the locations and strength of a […]. Five digits reversed: One layer LSTM (128 HN), 550k training examples = 99% train/test accuracy in 30 epochs. function and AutoGraph Distributed training with TensorFlow Eager execution Effective TensorFlow 2 Estimators Keras Keras custom callbacks Keras overview Masking and padding with Keras Migrate your TensorFlow 1 code to TensorFlow 2 Random number generation Recurrent Neural Networks with Keras Save and serialize models with. Keras documentation. LSTMCell 在整个时间序列输入中处理一个步骤，而 tf. The visualizations of layers of this model are available paper “Supplementary Material for the Paper: Deep Neural Networks with Inexact Matching for Person Re-Identification. models import Sequential from keras. We will also demonstrate how to train Keras models in the cloud using CloudML. Based on the implicit function theorem, the EMD can be inserted as a layer into the network for end-to-end training. datasets import mnist from keras. Keras provides a lambda layer; it can wrap a function of your choosing. Setup import tensorflow as tf from tensorflow import keras from tensorflow. The output layer is a linear activated set of two nodes, corresponding to the two Q values assigned to each state to represent the two possible actions. (In this case I copied the last layers from the previous post. It will take 1152*8 as its input and produces output of size 10*16, where 10 capsules each represents an output class with 16 dimensional vector. Dropout consists in randomly setting a fraction p of input units to 0 at each update during training time, which helps prevent overfitting. The dtype is specified with the dtype constructor. Note that the default input image size for this model is 299x299. Should I go for a different network design?. A "neuron" computes a weighted sum of all of its inputs, adds a value called "bias" and feeds the result through a so called "activation function". Typically you will use metrics=['accuracy']. We need to create two directories namely “train” and “validation” so that we can use the Keras functions for loading images in batches. A layer consists of a tensor-in tensor-out computation function (the layer's call method) and some state, held in TensorFlow variables (the layer's weights). Consider a batch of 32 samples, where each sample is a sequence of 10 vectors of 16 dimensions. subtract(r1, r2) square_diff = keras. The example below illustrates the skeleton of a Keras custom layer. Cropping2D层 keras. This is the class from which all layers inherit. import numpy as np import matplotlib. A Fortran-Keras Deep Learning Bridge for Scientific Computing. The Keras documentation has a good description for writing custom layers. shape[1] #add model layers model. MaxPooling1D(pool_size=2, strides=None, padding='valid') 对时域1D信号进行最大值池化. 2020-06-12 Update: This blog post is now TensorFlow 2+ compatible! Figure 1: Using Keras we can perform multi-output classification where multiple sets of fully-connected heads make it possible to learn disjoint label combinations. Keras provides a lambda layer; it can wrap a function of your choosing. 0) 使用给定的值对输入的序列信号进行“屏蔽”，用以定位需要跳过的时间步 对于输入张量的时间步，即输入张量的第1维度（维度从0开始算，见例子），如果输入张量在该时间步上都等于 mask_value ，则该时间步将在模型接下来的. With great advances in technology and algorithms in recent years, deep learning has opened the door to a new era of AI applications. If your model does not have target values, then you need to hack around. stats import norm from keras import backend as K from keras. In Keras, we usually pass arrays of the same length. Flatten ()) # takes our 28x28 and makes it 1x784 model. " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "0Tese2RQ3ouf" }, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 2. What actually happens internally is that. kerasはシンプルに記述できるので、わかりやすいです。 これができたら、Neural Network Consoleで設計検討したものを、kerasのモデルに置き換えて、学習させて、Tensorflow. It will have the correct. In Pytorch I’m trying to use MaxPool1d. It also swallows the mask without passing it on. The Sequential module is required to initialize the ANN, and the Dense module is required to build the layers of our ANN. About the layer's dtype attribute: Each layer has a dtype, which is typically the dtype of the layer's computations and variables. VGG16 is trained over ImageNet , and the images in ImageNet are classified into animals, geological formation, natural objects, and many other different categories. Although our architecture is about as simple as it gets, it is included in the figure below as an example of what the diagrams look like. The example below illustrates the skeleton of a Keras custom layer. After training the model for 200 epochs, we achieved 100% accuracy on our model. models import model_from_json, Model def build_tower ( input_layer , features_nr , shape , tower_nr ,. layers import Input, Dense, Lambda, Layer, Add, Multiply from keras. The following are 30 code examples for showing how to use keras. Hello, I have built a model using an Embedding layer with Word2Vec. Simple computational layers can be implemented using Lambda wrapper in Keras. In this case, a hidden layer of 10 nodes with sigmoid activation will be used. convolutional import Conv2D, MaxPooling2D from keras. 2020-06-12 Update: This blog post is now TensorFlow 2+ compatible! Figure 1: Using Keras we can perform multi-output classification where multiple sets of fully-connected heads make it possible to learn disjoint label combinations. library (keras) library (stringi). Choice is matter of taste and particular task; We’ll be using Keras to predict handwritten digits with the. With great advances in technology and algorithms in recent years, deep learning has opened the door to a new era of AI applications. These are the following imports that you need to do for the layer to work; from keras. VGG16(weights='imagenet', include_top=False, input_shape=(224, 224, 3)). datasets import mnist from keras. Image data preprocessing, fit_generator for training Keras a model using Python data generators; ImageDataGenerator for real-time data augmentation; layer freezing and Then calling image_dataset_from_directory(main_directory, labels='inferred') will return a tf. Some models may have only one input layer as the root of the two branches. One of them was Keras, which happens to build on top of TensorFlow. Use the cross-entropy loss function. Fortunately, by showing the wish to add code to (and potentially increase Keras’ maintenance cost, :D) the core source file embedding. If your model does not have target values, then you need to hack around. The layer build logic is what makes it structured and easy to comprehend, and each of these layers will comprise the weight of the layer that follows it. Python keras. Hashes for keras-multi-head-0. applications. Notable examples include: Regular dense, MLP type Recurrent layers, LSTM, GRU, etc. Keras forked into tf. Seventh layer, Dropout has 0. These are the following imports that you need to do for the layer to work; from keras. Things to try: I assume you have a test program that uses your customer layer. Lambda keras. convolutional import Conv2D, MaxPooling2D from keras. Switching to theano fixed the problem. gz; Algorithm Hash digest; SHA256: d9bfd6b0a4f953d29b02943581a8579e2c34ba83e6528bde59a3d270700fcce8: Copy MD5. We have our training data ready, now we will build a deep neural network that has 3 layers. Let's see how. Fifth layer, Flatten is used to flatten all its input into single dimension. import numpy as np import matplotlib. merge_mode: Mode by which outputs of the forward and backward RNNs will be combined. # scale preds so that the class probas of each sample sum to 1. import torch import torchvision from torch import nn from torchvision import models. Although our architecture is about as simple as it gets, it is included in the figure below as an example of what the diagrams look like. If your model does not have target values, then you need to hack around. Let’s calculate the jacobian of the hidden layer of our autoencoder then. convolutional. layers: Can be a list of Keras tensors or a list of layer instances. Don’t forget to sum the biases. 关于Keras的“层. A Keras model as a layer. I could load up a model and do this: "example. models import Model. Tensorflow is a powerful and flexible tool, but coding large neural architectures with it is tedious. Let’s calculate the jacobian of the hidden layer of our autoencoder then. Among the layers, you can distinguish an input layer, hidden layers, and an output layer. Basically; I'm implementing this facial point paper for work; and it uses spatial softargmax (just a layer that takes in a stack of images a lot like this - and it returns the most "intense part" of the image (so just the x,y coordinates of the white blob). 256 units are chosen since 128, 512 and 1,024 units have lower performance metrics. In many of these applications, deep learning algorithms performed equal to human experts and sometimes surpassed them. Creates a layer that performs an python arbitrary function over the layer’s input data: print_out(Lambda(lambda x: x*x), [1, 2, 3]) # [ 1. preprocessing. We’ll be building a POS tagger using Keras and a Bidirectional LSTM Layer. This is because your training data iris. Seventh layer, Dropout has 0. Layers and Layers (like an Ogre) Keras has a number of pre-built layers. Let’s say:. Sequential refers to the way you build models in Keras using the sequential api (from keras. Validation of Convolutional Neural Network Model In the training section, we trained our CNN model on the MNIST dataset (Endless dataset), and it seemed to reach a reasonable loss and accuracy. datasets import mnist original_dim = 784 intermediate_dim = 256 latent_dim = 2 batch_size = 100 epochs = 50. Function fit trains a Keras model. Previously, we iterated over the original VGG16 model and added all layers to the new model. is_available else "cpu" ) # Assuming that we are on a CUDA machine, this should print a CUDA device: print ( device ). get_weights()的形状相同. name + str("_") But when I change the names of the layers, the model accuracy become low. In Keras, this can be done by adding an activity_regularizer to our Dense layer: from keras import regularizers encoding_dim = 32 input_img = Input ( shape = ( 784 ,)) # add a Dense layer with a L1 activity regularizer encoded = Dense ( encoding_dim , activation = 'relu' , activity_regularizer = regularizers. for layer in vgg_model. optimizers, and tf. How may I extract the output from a hidden layer? I found an example in python, but it is just I have no idea how to do that in R. Keras is a popular and easy-to-use library for building deep learning models. parameters() if p. For custom weight layers you have to write your own Keras layer class. Note that, for SL and ML tasks the loss function is calculated as: -log p (y t = y t ̂ | x). optimizers import Adam. In Pytorch I’m trying to use MaxPool1d. l1 ( 10e-5 ))( input_img ) decoded. Recently we also started looking at Deep Learning, using Keras, a popular Python Library. callbacks import EarlyStopping, ModelCheckpoint, TensorBoard, Redu ceLROnPlateau from keras. Load the pre-trained model from tensorflow. Hello, I have built a model using an Embedding layer with Word2Vec. $\sum_{\textrm{kernel}}$ The sum goes over 94 windows, running over the picture for conv1. Convolution can be thought of as a weighted sum between two signals ( in terms of signal processing jargon ) or functions ( in terms of mathematics ). Pre-trained models and datasets built by Google and the community. Tensors, tf. Validation of Convolutional Neural Network Model In the training section, we trained our CNN model on the MNIST dataset (Endless dataset), and it seemed to reach a reasonable loss and accuracy. sequence import pad_sequences from tensorflow. class ActivityRegularization: Layer that applies an update to the cost function based input activity. Just your regular densely-connected NN layer. Subtract keras. We need to write a custom layer in keras. if it came from a Keras layer with masking support. Let’s take a look at those. Use the cross-entropy loss function. Sum the parameters from each layer to get the total number of learnable parameters. There are plenty of deep learning toolkits that work on top of it like Slim, TFLearn, Sonnet, Keras. Attention Like many sequence-to-sequence models, Transformer also consist of encoder and decoder. Question 1: I use axis=1 because I assumer the lambda layer gets applied to a whole batch of inputs at a time, meaning axis 0 is the sample index, while axis 1 indexes the words (i. layers import. It zeros out all of the masked-out embeddings. word vectors after embedding) in each. These input sequences should be padded so that they all have the same length in a batch of input data (although an Embedding layer is capable of processing sequence of heterogenous length, if you don't pass an explicit input_length argument to the layer). Keras:基于Python的深度学习库; 致谢; Keras后端; Scikit-Learn接口包装器; utils 工具; For beginners. 04 box and a few hours of Stackoverflow reading I finally got it working with the following python code. Next we need to import a few modules from Keras. keras/keras. The first layer, which contains 8 hidden notes, on the other hand, has an input_shape of 4. updates（需要更新的形如（tensor, new_tensor）的tuple的列表）。. The layer build logic is what makes it structured and easy to comprehend, and each of these layers will comprise the weight of the layer that follows it. TimeDistributed(layer) This wrapper allows to apply a layer to every temporal slice of an input. One of 'sum', 'mul', 'concat', 'ave', NULL. The first thing we need to do is import Keras. The exact API will depend on the layer, but many layers (e. The function returns the layers defined in the HDF5 (. Company running summary() on your layer and a standard layer. So in total we'll have an input layer and the output layer. The prefix is complemented by an index suffix to obtain a unique layer name. Each "neuron" in a neural network does a weighted sum of all of its inputs, so all you have to do is add a tf. 評価を下げる理由を選択してください. class ActivityRegularization: Layer that applies an update to the cost function based input activity. How may I extract the output from a hidden layer? I found an example in python, but it is just I have no idea how to do that in R. import keras from keras. The layer has three modes, it works just like PositionEmbedding in expand mode: import keras from keras_pos_embd import TrigPosEmbedding model = keras. subtract function. Then there is again a maximum pooling layer with filter size 3×3 and a stride of 2. A LSTM layer, will return the last vector by default rather than the entire sequence. VGG16 is trained over ImageNet , and the images in ImageNet are classified into animals, geological formation, natural objects, and many other different categories. Keras is a popular and easy-to-use library for building deep learning models. layer wasn't named; There was no Layer with weights that was actually taking two inputs (I have others layers in my personal repository other then the BiLinearLayer) such as the Similarity that takes two vectors and computes the follows (xWz) and the NeuralTensor Layer used by the Stanford group, but i'm waiting for the join mode to be added. models import Model, Sequential from keras. optimizers import Adam. " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "0Tese2RQ3ouf" }, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 2. backend as K. The neurons in this layer look for specific features. If they find the features they are looking for, they produce a high activation. The first thing we need to do is import Keras. metrics : List of metrics to be evaluated by the model during training and testing. applications. Note that if this port is connected, you also have to connect the second hidden state port. We’ll be building a POS tagger using Keras and a Bidirectional LSTM Layer. A convolution is the simple application of a filter to an input that results in an activation. Python keras. You will learn how to build a keras model to perform clustering analysis with unlabeled datasets. If you pass tuple, it should be the shape of ONE DATA SAMPLE. Although our architecture is about as simple as it gets, it is included in the figure below as an example of what the diagrams look like. Image data preprocessing, fit_generator for training Keras a model using Python data generators; ImageDataGenerator for real-time data augmentation; layer freezing and Then calling image_dataset_from_directory(main_directory, labels='inferred') will return a tf. However, you will also add a pooling layer. backend as K 这里就简单展示两个最近使用到的操作，更多可以参考Keras中文文档。 K. R/layers-merge. preprocessing. 关于Keras的“层”（Layer） 所有的Keras层对象都有如下方法： layer. The sequential API allows you to create models layer-by-layer for most problems. summary() to see the names of all layers in the model. Keras models don't support outputting a different number of samples from the input samples. 0) 使用给定的值对输入的序列信号进行“屏蔽”，用以定位需要跳过的时间步 对于输入张量的时间步，即输入张量的第1维度（维度从0开始算，见例子），如果输入张量在该时间步上都等于 mask_value ，则该时间步将在模型接下来的. Layers and Layers (like an Ogre) Keras has a number of pre-built layers. A convolution is the simple application of a filter to an input that results in an activation. It does not handle itself low-level operations such as tensor products, convolutions and so on. summary() to see the names of all layers in the model. Then we create model we user 3 layers with activation function ReLU and in the last layer add a “softmax” layer. Sequential refers to the way you build models in Keras using the sequential api (from keras. Keras Visualization Toolkit. when a function is a vector valued function, the partial derivative is a matrix called jacobian. # Create model - 3 layers. Is it possible to implement mutiple softmaxes in the last layer in Keras? So the sum of Nodes 1-4 = 1; 5-8 = 1; etc. Some models may have only one input layer as the root of the two branches. In lieu of that I've been trying to figure out how to multiply one of my inputs by a constant -1 tensor and then adding, but I can't figure out how to create that -1 tensor. Masking(mask_value=0. keras and "keras community edition" Latests commits of Keras teasing like tf. See full list on r-bloggers. class Activation: Applies an activation function to an output. layers import LSTM, Dense import numpy as np data_dim = 16 timesteps = 8 num_classes = 10 batch_size = 32 # Expected input batch shape: (batch_size, timesteps, data_dim) # Note that we have to provide the full batch_input_shape since the network is stateful. You can get started with Keras in this Sentiment Analysis with Keras Tutorial. VGG16(weights='imagenet', include_top=False, input_shape=(224, 224, 3)). Strategy Custom training with tf. the LMUCell implementation in the NengoDL example you mention (which is a Nengo network, not a Keras layer). The basis of our model will be the Kaggle Credit Card Fraud Detection dataset, which was collected during a research collaboration of Worldline and the Machine Learning Group of ULB (Université Libre de Bruxelles) on big data mining. A Sequential model is appropriate for a plain stack of layers where each layer has exactly one input tensor and one output tensor. Flatten(data_format = None) data_format is an optional argument and it is used to preserve weight ordering when switching from one data format to another data format. The final layers of our CNN, the densely connected layers, require that the data is in the form of a vector to be processed. from keras. 我们从Python开源项目中，提取了以下7个代码示例，用于说明如何使用keras. In my Keras code I use GlobalMaxPooling1D after the last 1D convolutional layer: result = GlobalMaxPooling1D()(previous_result). Keras example — using the lambda layer. VGG16 is trained over ImageNet , and the images in ImageNet are classified into animals, geological formation, natural objects, and many other different categories. I would hack it together like this: use a lambda layer to acquire a single '1' vector, learn a scaling factor via a dense layer which takes a single input and outputs a single number repmat that scaling factor to the correct size multiply the scaling factor with whatever we are scaling. Keras Visualization Toolkit. topology import Layer class ZeroMaskedEntries(Layer): """ This layer is called after an Embedding layer. Then, we would pop off the output layer and add our own output layer. プログラミングに関係のない質問 やってほしいことだけを記載した丸投げの質問 問題・課題が含まれていない質問 意図的に内容が抹消された質問 過去に投稿した質問と同じ内容の質問 広告と受け取られるような投稿. Basic classification: Classify images of clothing Basic regression: Predict fuel efficiency Classify structured data with feature columns Classify structured data with feature columns Convolutional Neural Network Convolutional Neural Network Custom training with tf. 256 units are chosen since 128, 512 and 1,024 units have lower performance metrics. We will generalize some steps to. After training the model for 200 epochs, we achieved 100% accuracy on our model. parameters() if p. Add model layers: the first two layers are Conv2D—2-dimensional convolutional layers These are convolution layers that deal with the input images, which are seen as 2-dimensional matrices. layers import CuDNNLSTM, Dense, Dropout, LSTM from keras. layers import LSTM, Dense import numpy as np data_dim = 16 timesteps = 8 num_classes = 10 batch_size = 32 # Expected input batch shape: (batch_size, timesteps, data_dim) # Note that we have to provide the full batch_input_shape since the network is stateful. I visualize the VGG-Face architure to be understood clear. layers import. kerasはシンプルに記述できるので、わかりやすいです。 これができたら、Neural Network Consoleで設計検討したものを、kerasのモデルに置き換えて、学習させて、Tensorflow. The output layer is a linear activated set of two nodes, corresponding to the two Q values assigned to each state to represent the two possible actions. The input should be at least 3D, and the dimension of index one will be considered to be the temporal dimension. Reference to paper: Focal Loss for Dense Object Detection Code: mutil-class focal loss implemented in keras In addition to solving the extremely unbalanced positive-negative sample problem, focal loss can also solve the problem of easy example dominant. An Embedding layer should be fed sequences of integers, i. recurrent 模块， SimpleRNN() 实例源码. backend as K from keras. Copy the the test program and switch the copy to not use your custom layer and make sure that works. TensorFlow, CNTK, Theano, etc. add a x -> x^2 layer model. The elements of the output vector are in range (0, 1) and sum to 1. You can read this paper which two loss functions are used for graph embedding or this article for multiple label classification. For custom weight layers you have to write your own Keras layer class. backend as K 这里就简单展示两个最近使用到的操作，更多可以参考Keras中文文档。 K. I would hack it together like this: use a lambda layer to acquire a single '1' vector, learn a scaling factor via a dense layer which takes a single input and outputs a single number repmat that scaling factor to the correct size multiply the scaling factor with whatever we are scaling. When I first started learning about them from the documentation, I couldn’t clearly understand how to prepare input data shape, how various attributes of the layers affect the outputs and how to compose these layers with the. TensorFlow provides several high-level modules and classes such as tf. In the graph, A and B layers share weights. scikit_learn import KerasClassifier import keras. A consequence of adding a dropout layer is that training time is increased, and if the dropout is high, underfitting. Let's see how. The first layer, which contains 8 hidden notes, on the other hand, has an input_shape of 4. 2020-06-12 Update: This blog post is now TensorFlow 2+ compatible! Figure 1: Using Keras we can perform multi-output classification where multiple sets of fully-connected heads make it possible to learn disjoint label combinations. topology import Layer class ZeroMaskedEntries(Layer): """ This layer is called after an Embedding layer. Keras is a Python library that provides a simple and clean way to create a range of deep learning models. Pre-trained models and datasets built by Google and the community. ↳ 1 cell hidden model_builder = keras. Here are some code snippets to illustrate how intuitive and useful Keras for R is: To load 🖼 from a folder:. class ActivityRegularization: Layer that applies an update to the cost function based input activity. Python keras. The layer has three modes, it works just like PositionEmbedding in expand mode: import keras from keras_pos_embd import TrigPosEmbedding model = keras. Dropout regularization is a computationally cheap way to regularize a deep neural network. A Keras model as a layer. Instead, after we create the model and load it up with the ImageNet weight, we perform the equivalent of top layer truncation by defining another fully connected sofmax ( x_newfc. optimizers, and tf. Basically; I'm implementing this facial point paper for work; and it uses spatial softargmax (just a layer that takes in a stack of images a lot like this - and it returns the most "intense part" of the image (so just the x,y coordinates of the white blob). In this tutorial we are using the Sequential model API to create a simple CNN model repeating a few layers of a convolution layer followed by a pooling layer then a dropout layer. We can clearly see that the sentences are of different length. non_trainabe_weights（列表）和self. Introduction to Variational Autoencoders. In this lab, you will learn how to build a Keras classifier. Keras Conv2D and Convolutional Layers. resnet50(pretrained=False) a. The network largely consists of convolutional layers, and just before the final output layer, global average pooling is applied on the convolutional feature maps, and use those as features for a fully-connected layer that produces the desired output (categorial or. layers import Dense. ∙ 0 ∙ share Implementing artificial neural networks is commonly achieved via high-level programming languages like Python and easy-to-use deep learning libraries like Keras. Keras example — using the lambda layer. This layer applies multiplicative zero-centered gaussian noise to the layer input. Also, calculate the shape (width, height, depth) of the output of each layer. Keras was developed with a focus on enabling fast experimentation, supports both convolution based networks and recurrent networks (as well as combinations of the two), and runs seamlessly on both CPU and GPU devices. We will use the LSTM network to classify the MNIST data of handwritten digits. It is limited in that it does not allow you to create models that share layers or have multiple inputs or outputs. ConvNets are powerful due to their ability to extract the core features of an image and use these features to identify images that contain features like them. Python keras. Understand Grad-CAM in special case: Network with Global Average Pooling¶. Based on the implicit function theorem, the EMD can be inserted as a layer into the network for end-to-end training. Use pencil and paper!. TensorFlow Python 官方参考文档_来自TensorFlow Python，w3cschool。 下载w3cschool手机App端 请从各大安卓应用商店、苹果App Store. Keras documentation. VGG-Face model. Masking()。. The elements of the output vector are in range (0, 1) and sum to 1. I guess the stride should be 0 but I’ve no idea about the value of kernel_size. It might have an individual integer. Here we will see what we need to do in code to implement it. Keras forked into tf. layers import CuDNNLSTM, Dense, Dropout, LSTM from keras. If you cannot find it in that folder, then it is residing at "channels_last". MaxPooling1D layer; MaxPooling2D layer. It takes as input a list of tensors of size 2, both of the same shape, and returns a single tensor, (inputs[0] - inputs[1]), also of the same shape. layers: Can be a list of Keras tensors or a list of layer instances. keras Classification Metrics. SimpleRNN()。. of: 'sum', 'mul', 'concat', 'ave', 'cos', 'dot', 'max'. Dropout(p) Applies Dropout to the input. get_weights()的形状相同. 3) - Duration: 14:39. Keras API reference / Layers API / Pooling layers Pooling layers. LSTMCell(units, activation=‘tanh’, recurrent_activation=‘sigmoid’, use_bias=True. It does not handle itself low-level operations such as tensor products, convolutions and so on. This layer applies multiplicative zero-centered gaussian noise to the layer input. In this case, a hidden layer of 10 nodes with sigmoid activation will be used. Pre-trained models and datasets built by Google and the community. Let’s say:. optimizers import Adam. Python keras. Dropout layer. trainable_weights中。其他的属性还包括self. l1 ( 10e-5 ))( input_img ) decoded. models import model_from_json, Model def build_tower ( input_layer , features_nr , shape , tower_nr ,. Among the layers, you can distinguish an input layer, hidden layers, and an output layer. Keras layers and models are fully compatible with pure-TensorFlow tensors, and as a result, Keras makes a great model definition add-on for TensorFlow, and can even be used alongside other TensorFlow libraries. class AbstractRNNCell: Abstract object representing an RNN cell. This is a tutorial of how to classify the Fashion-MNIST dataset with tf. These software libraries come pre-loaded with a variety of network. Note that this tutorial assumes that you have configured Keras to use the TensorFlow backend (instead of Theano). Introduction Deep learning is one of the most interesting and promising areas of artificial intelligence (AI) and machine learning currently. You can read this paper which two loss functions are used for graph embedding or this article for multiple label classification. models import Sequential from keras. Things to try: I assume you have a test program that uses your customer layer. The LSTM layer has different initializations for biases, input layer weights, and hidden layer weights. Third, Fourth and Fifth Layers:. This demonstration utilizes the Keras framework for describing the structure of a deep neural network, and subsequently leverages the Dist-Keras framework to achieve data parallel model training on Apache Spark. It ranges from 1 to 0 (no error), and returns results similar to binary crossentropy # define custom loss and metric functions. In the context of artificial neural networks , the rectifier is an activation function. Introduction to Variational Autoencoders. Keras implements a pooling operation as a layer that can be added to CNNs between other layers. Flatten ()) # takes our 28x28 and makes it 1x784 model. 池化层 MaxPooling1D层 keras. json) file given by the file name modelfile. In this tutorial we are using the Sequential model API to create a simple CNN model repeating a few layers of a convolution layer followed by a pooling layer then a dropout layer. Setup import tensorflow as tf from tensorflow import keras from tensorflow. For instance, the vector which corresponds to state 1 is [0, 1, 0, 0, 0] and state 3 is [0, 0, 0, 1, 0]. Here is a dice loss for keras which is smoothed to approximate a linear (L1) loss. sum(axis=-1, keepdims=True). In Keras, this can be done by adding an activity_regularizer to our Dense layer: from keras import regularizers encoding_dim = 32 input_img = Input ( shape = ( 784 ,)) # add a Dense layer with a L1 activity regularizer encoded = Dense ( encoding_dim , activation = 'relu' , activity_regularizer = regularizers. word vectors after embedding) in each. To learn classification with keras and containerizing it, we will devide this task in 7 simple parts- Introduction with Keras Learning to program with Keras Multiclass classification with keras Layers and Optimization Saving model and weights Creating docker file for application Pushing to Dockerhub Introduction Keras is a deep learning API written in Python, running […]. Linear (a simple linear layer that computes w^Tx + b) and nn. mode = TrigPosEmbedding. Keras Tuner found a better model with 100% accuracy (+20%) and only 24M parameters (-45%) Dataset is small so there is a possibility of overfit despite using augmented icons in training. The one word with the highest probability will be the predicted word – in other words, the Keras LSTM network will predict one word out of 10,000 possible categories. layers: Can be a list of Keras tensors or a list of layer instances. Typically you will use metrics=['accuracy']. LSTMCell 在整个时间序列输入中处理一个步骤，而 tf. The example below illustrates the skeleton of a Keras custom layer. Keras forked into tf. Keras provides both the 16-layer and 19-layer version via the VGG16 and VGG19 classes. Click here for more details on the Sequential model. Lambda keras. In this article, we will learn to conduct fire and smoke detection with Keras and deep learning. 3 filter layers in each convolution Conclusion. LSTMCell(units, activation=‘tanh’, recurrent_activation=‘sigmoid’, use_bias=True. Masking(mask_value=0. Tensors, tf. With great advances in technology and algorithms in recent years, deep learning has opened the door to a new era of AI applications. You can get started with Keras in this Sentiment Analysis with Keras Tutorial. From Keras, import the Sequential model as well as the Dense, Dropout and the Activation layers. The output Softmax layer has 10 nodes, one for each class. Can anyone explain how to get the activations of intermediate layers in Keras? keras. kerasはシンプルに記述できるので、わかりやすいです。 これができたら、Neural Network Consoleで設計検討したものを、kerasのモデルに置き換えて、学習させて、Tensorflow. A tensor, the sum of the. These examples are extracted from open source projects. 2 With tuple. Company running summary() on your layer and a standard layer. Let’s say:. R defines the following functions: layer_add layer_subtract layer_multiply layer_average layer_maximum layer_minimum layer_concatenate layer_dot keras source: R/layers-merge. Note how the output layer creates 3 output values, one for each Iris class (versicolor, virginica or setosa). Keras provides a powerful abstraction for recurrent layers such as RNN, GRU and LSTM for Natural Language Processing. models import Sequential from keras. keras/keras. 3 filter layers in each convolution Conclusion. import keras. get_weights()：返回层的权重（numpy array） layer. class AdditiveAttention.
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# Tag Info

## Hot answers tagged potential

2

The "direct" formula is $$V(r)=\frac{1}{4\pi\epsilon_0}\int\frac{dQ}{\lvert \vec{r}-\vec{R} \rvert}=\frac{1}{4\pi\epsilon_0}\iint_{sphere}\frac{\sigma(\vec{R})dS}{\lvert \vec{r}-\vec{R} \rvert}.$$ Now, think carefully about what the $\frac{1}{\lvert \vec{r}-\vec{R} \rvert}$ means---it is the reciprocal of the distance from an arbitrary point on the surface ...

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As you've worked out, since $v=0$ then the kinetic energy must also be zero. Potential energy is a little more dubious. At school you are usually taught that the gravitational potential energy is $E=mgh$ but that's not quite right; this equation is the work that you must do to lift an object of mass $m$ a height $h$ or, equivalently, the work done by ...

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The electric potential can be negative. Both in difference and absolutely if you have chosen a gauge. To see that this must be so, just replace the charge distribution (not the test charge, all the others...) with one that has the opposite sign.

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Make make an analogy between gravitational potential energy, which is easy to visualize, and electrical potential energy. By doing this all the knowledge they have about a simpler subject will help them understand a more complicated one. Hold a ball and drop it. Draw what happened on the board, showing that the more potential (voltage) the fastest the ball ...

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Eigenstates aren't the only allowed physical states. It's a postulate of quantum mechanics that the most general quantum state can be written as a superposition of eigenstates of some operator (the Hamiltonian for instance). For instance $\Psi(x)=\sum_nc_n\psi_n(x)$ is a general quantum state for a particle in a box, where $\psi_n(x)$ are the energy ...

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It actually is the very essence of the QM. In short, when we observe a superposed state, the probability of observing specific eigenvalue is the square of the norm of the corresponding eigenstate in the superposed state. And this is more like a postulate, rather than a mathematical derivation. For example, particle in a box has discrete eigenvalues, bounded ...

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For an infinite well (actually infinitely high barriers) the probability to find an electron in the barrier vanishes. Therefore the wavefunction in the barrier has to be 0. For barriers with a finite height, the commonly used, but actually wrong boundary conditions require the wavefunction and the first derivative to be continuous. This relies on the wrong ...

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Electric fields produces a difference of potential on two points with different distances of the field source. Magnetic fields induces current on a closed loop if the loop is not on parallel in relation of the lines of field and the magnitude of the field does have to change (you have to have a flux). If you have a magnetic field interfering on your ...

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You will have to use Kirchoff's law to get the answer. How can some of positive numbers be zero? No, the sum of all charges will be zero while that of positive plate will be finite. Now the net sum would be zero since charge is conserved on the system having all the right plates. Use Kirchoff's Loop Law and Kirchoff's current law to find charges and ...

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I believe you are confusing the work done by the electric field with the work done on the particle. By the electric field: The radial force of the electric field is always pointing outwards, and the displacement of the charge in this case is going inward. Thus, the integral you've specified will be negative. That is, the work done by the electric field is ...

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Imagine you have a point charge inside the conducting sphere. Obviously, since the electric field inside the sphere is zero (as you state), there is no force on the charge, so no work done. Therefore the potential is constant. So far so good. Now as we approach the boundary, we can imagine moving an infinitesimal amount to go from $r = R - \delta r$ to $r = ... 1 As wiki says "The effective potential (also known as effective potential energy) is a mathematical expression combining multiple (perhaps opposing) effects into a single potential." Basically the concept of the effective potential simplifies the equations of motion and simplifies their analysis. 1 This is just the line integral which gives you the electric potential in two dimensions due to a charge distribution of one or more closed loops, i.e. closed charged wires. The logarithm is coming from the solution of laplace equation in two dimensions, replacing the$\frac{1}{|\vec{x} - \vec{x}'|}$of three dimensions, and$f(w)$is just the charge density ... 1 Modern electronic devices like quantum well lasers, resonant tunneling diodes, quantum cascade lasers and detectors heavily rely on the spatial and energetic position of such bound states. This defines their transport and optical properties. On a separate notice: any well, no matter how shallow or narrow, has at least one bound state. 1 If some charge is given to a conductor then its potential will be remain same through out the region, because work done on every charge is same. 1 There are two important points to keep in mind when working through this problem. (1) Since the Hamiltonian for the system changes suddenly, the wavefunction just after the change is the same as the wavefunction just before the change. (2) Then energy eigenstates after the change are different from the energy eigenstates after the change. It follows that, ... 1 What is potential energy truly? It depends on the circumstances. When you compress a spring it's stress in the bonds or electromagnetic field between the atoms. IMHO at the fundamental level it's essentially spatial stress. That might sound unfamiliar, but it shouldn't, because the stress-energy-momentum tensor "describes the density and flux of energy and ... 1 The three directions$x$,$y$and$z$are separable for the particle-in-a-box problem - the behaviour in each is independent of that in the others. Thus, each direction when separately considered only gives the contribution to the energy due to the limits of the box, or equivalently, the 'part' of the wavefunction, in that direction. In the case of$l_z ...

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# Puzzles

## Double derivative

What is
$$\frac{d}{dy}\left(\frac{dy}{dx}\right)$$
when:
(i) $$y=x$$
(ii) $$y=x^2$$
(iii) $$y=x^3$$
(iv) $$y=x^n$$
(v) $$y=e^x$$
(vi) $$y=\sin(x)$$?
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MathSciNet bibliographic data MR2264675 (2007j:51014) 51M10 (51M25 53C65) Cho, Yunhi; Kim, Hyuk Volume of $C\sp {1,\alpha}$$C\sp {1,\alpha}$-boundary domain in extended hyperbolic space. J. Korean Math. Soc. 43 (2006), no. 6, 1143–1158. Article

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# Calc - conditional formatting prob after update

I have just today upgraded from 5.1.6.2 to the latest version for windows - sorry don't have number as on another machine elsewhere atm.

I have a spreadsheet with extensive use of number formats as styles including N° of decimal places, e.g: formula is if value of C1=1 then apply 2 decimal places to 5 place number in target cell. All was working fine until I upgraded and now the decimal place change no longer works. I have messed around with this so much that I have just cleared out all direct and conditional formatting and started again from scratch (leaving the styles as they were)....now I can't reproduce the same result no matter the direct format of the target cell. Other aspects of the same style work fine such as cell background colour and font effect.

I have just now tried to get this to work on my machine with the 5.1.6.2 but with the same result.

So, my condition is C1=1 with the style to be applied as number of decimal places....I have tried changing the direct format from number to general with no decimal places to the max 5 but no joy.

I feel there must be something very basic that I'm missing but I can't see it.

EDIT: I have uploaded a sample as an attachment to my original question - which I hope will clarify things. To keep clutter to a minimum I have applied the conditional formatting to only the cells G3:G4 and H3:H4 using both a text cell and a number as examples of what isn't happening.

The specific result that I really want is that all numbers take the number of decimal places from column D where "FX" should result in a 5 decimal place number in the target cell and "IND" a two decimal place one. In my earlier functioning version, I was using 5 decimal places by default which were then modified by the condition Dx="IND" to a 2 decimal one.

C:\fakepath\SS_Cond_Format_Prob.ods

edit retag close merge delete

I assume, there's no way to figure out your problem without having an anonymized example of your file (and conditional formatting). Please consider to upload a sample file ...

( 2019-07-16 11:40:46 +0200 )edit

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Hello,

please see the reworked file - I've cleared all formattings on range G3:H14 and added the following "Conditional Formattings"

Condition 1: Formula is: $D3="FX" Template: Green_5_DP Condition 2: Formula is: $D3="IND" Template: Green_2_DP
Range: G3:H14

Note: The "\$" is required to keep the absolute reference to column D

C:\fakepath\ConditionalFormats.ods

You may have some interfering Conditional Formattings - check in Format -> Conditional -> Manage .... I have also deleted any existing Conditional Formatting definitions here prior to starting over.

Tested with:

Version: 6.2.5.2, Build ID: 1ec314fa52f458adc18c4f025c545a4e8b22c159, CPU threads: 8; OS:
Linux 4.12; UI render: default; VCL: kde5; Locale: en-US (en_US.UTF-8); UI-Language: en-US,

more

Thank you so much (again) as the problem is resolved. Curiously I did establish that one of the issues was direct formats which needed to be deleted and then re-instated as before.

( 2019-07-16 15:02:04 +0200 )edit

Hello, nice to hear that it works.

( 2019-07-16 15:11:09 +0200 )edit

I have already tried clicking on these check marks but nothing seems to happen - What behaviour should I see?

( 2019-07-16 16:29:36 +0200 )edit

Mouseover the grey circle of (✔) and you'll see the colour to turn green (and an explanation). Click onto that circle and it permanently get's green. The up-arrow is to "upvote" and answer, while the down-arrow is to "downvote" a poor answer (Hopefully not the one you want to do ;-) ).

( 2019-07-16 16:43:11 +0200 )edit

Excellent! For some reason the first couple of times I clicked it stayed grey but now a beautiful grateful green :-)

( 2019-07-16 17:11:12 +0200 )edit


text:
RO  EN

## Commutator subgroup of Sylow 2-subgroups of alternating group and the commutator width in the wreath product

Authors: Ruslan V. Skuratovskii

### Abstract

It is proved that the commutator length of an arbitrary element of the iterated wreath product of cyclic groups $C_{p_i}, \, p_i\in \mathbb{N}$, is equal to 1. The commutator width of direct limit of wreath product of cyclic groups is found. This paper gives upper bounds of the commutator width $(cw(G))$ \cite{Mur} of a wreath product of groups. A presentation in the form of wreath recursion \cite{Ne} of Sylow $2$-subgroups $Syl_2A_{{2^{k}}}$ of $A_{{2^k}}$ is introduced. As a corollary, we obtain a short proof of the result that the commutator width is equal to 1 for Sylow 2-subgroups of the alternating group ${A_{{2^{k}}}}$, where $k>2$, permutation group ${S_{{2^{k}}}}$ and for Sylow $p$-subgroups $Syl_2 A_{p^k}$ and $Syl_2 S_{p^k}$. %As a result a short proof of the fact that the commutator width of Sylow 2-subgroups of alternating group ${A_{{2^{k}}}}$, %permutation group $S_{{2^{k}}}$ and Sylow $p$-subgroups of $Syl_2 A_{p^k}$, where $k>2$, $Syl_2 S_{p^k}$ are equal to 1 is %obtained. The commutator width of permutational wreath product $B \wr C_n$ is investigated. An upper bound of the commutator width of permutational wreath product $B \wr C_n$ for an arbitrary group $B$ is found.}

Kiev, 03056, Peremogy 37, KPI Igor Sikorsky Kiev
Polytechnic Institution, Ukraine.
E-mail: ,

0.17 Mb


text:
# 10.1: The Born-Oppenheimer Approximation

The Born-Oppenheimer approximation is one of the basic concepts underlying the description of the quantum states of molecules. This approximation makes it possible to separate the motion of the nuclei and the motion of the electrons. This is not a new idea for us. We already made use of this approximation in the particle-in-a-box model when we explained the electronic absorption spectra of cyanine dyes without considering the motion of the nuclei. Then we discussed the translational, rotational and vibrational motion of the nuclei without including the motion of the electrons. In this chapter we will examine more closely the significance and consequences of this important approximation. Note, in this discussion nuclear refers to the atomic nuclei as parts of molecules not to the internal structure of the nucleus.

The Born-Oppenheimer approximation neglects the motion of the atomic nuclei when describing the electrons in a molecule. The physical basis for the Born-Oppenheimer approximation is the fact that the mass of an atomic nucleus in a molecule is much larger than the mass of an electron (more than 1000 times). Because of this difference, the nuclei move much more slowly than the electrons. In addition, due to their opposite charges, there is a mutual attractive force of

$\dfrac{Ze^2}{r^2}$

acting on an atomic nucleus and an electron. This force causes both particles to be accelerated. Since the magnitude of the acceleration is inversely proportional to the mass, a = f/m, the acceleration of the electrons is large and the acceleration of the atomic nuclei is small; the difference is a factor of more than 1000. Consequently, the electrons are moving and responding to forces very quickly, and the nuclei are not. You can imagine running a 100-yard dash against someone whose acceleration is a 1000 times greater than yours. That person could literally run circles around you. So a good approximation is to describe the electronic states of a molecule by thinking that the nuclei aren't moving, i.e. that they are stationary. The nuclei, however, can be stationary at different positions so the electronic wavefunction can depend on the positions of the nuclei even though their motion is neglected.

Now we look at the mathematics to see what is done in solving the Schrödinger equation after making the Born-Oppenheimer approximation. For a diatomic molecule as an example, the Hamiltonian operator is grouped into three terms

$\hat {H} (r, R) = \hat {T}_{nuc} (R) + \dfrac {e^2}{4\pi \epsilon _0} \dfrac {Z_A Z_B}{R} + \hat {H} _{elec} (r,R) \label {10-1}$

where

$T_{nuc} (R) = -\dfrac {\hbar^2}{2m_A} \nabla ^2_A - \dfrac {\hbar ^2}{2m_B} \nabla ^2_B \label {10-2}$

and

$\hat {H} _{elec} (r, R) = \dfrac {- \hbar ^2}{2m} \sum \limits _i \nabla ^2_i + \dfrac {e^2}{4 \pi \epsilon _0} \left ( -\sum \limits _i \dfrac {Z_A}{r_{Ai}} - \sum \limits _i \dfrac {Z_B}{r_{Bi}} + \dfrac {1}{2} \sum \limits _i \sum \limits _{j \ne i} \dfrac {1}{r_{ij}}\right ) \label {10-3}$

In Equation \ref{10-1}, the first term represents the kinetic energy of the nuclei, the second term represents the Coulomb repulsion of the two nuclei, and the third term represents the contribution to the energy from the electrons, which consists of their kinetic energy, mutual repulsion for each other, and attraction for the nuclei. Bold-face type is used to represent that $$r$$ and $$R$$ are vectors specifying the positions of all the electrons and all the nuclei, respectively.

Exercise $$\PageIndex{1}$$

Define all the symbols in Equations \ref{10-1} through \ref{10-3}.

Exercise $$\PageIndex{2}$$

Explain why the factor of 1/2 appears in the last term in Equation \ref{10-3}.

The Born-Oppenheimer approximation says that the nuclear kinetic energy terms in the complete Hamiltonian, Equation \ref{10-1}, can be neglected in solving for the electronic wavefunctions and energies. Consequently, the electronic wavefunction $$\varphi _e (r,R)$$ is found as a solution to the electronic Schrödinger equation:

$\hat {H} _{elec} (r, R) \varphi _e (r, R) = E_e (R) \varphi _e (r, R) \label {10-4}$

Even though the nuclear kinetic energy terms are neglected, the Born-Oppenheimer approximation still takes into account the variation in the positions of the nuclei in determining the electronic energy and the resulting electronic wavefunction depends upon the nuclear positions, $$R$$.

As a result of the Born-Oppenheimer approximation, the molecular wavefunction can be written as a product the Born-Oppenheimer Approximation

$\psi _{ne} (r, R) = X_{ne} (R) \varphi _e (r, R) \label {10-5}$

This product wavefunction is called the Born-Oppenheimer wavefunction. The function $$X_{ne} (R)$$ is the vibrational wavefunction, which is a function of the nuclear coordinates $$R$$ and depends upon both the vibrational and electronic quantum numbers or states, $$n$$ and $$e$$, respectively. The electronic function, $$\varphi _e (r, R)$$, is a function of both the nuclear and electronic coordinates, but only depends upon the electronic quantum number or electronic state, $$e$$. Translational and rotational motion is not included here. The translational and rotational wavefunctions simply multiply the vibrational and electronic functions in Equation \ref{10-5} to give he complete molecular wavefunction when the translational and rotational motions are not coupled to the vibrational and electronic motion.

## Crude Born-Oppenheimer Approximation

In the Crude Born-Oppenheimer Approximation, $$R$$ is set equal to $$R_o$$, the equilibrium separation of the nuclei, and the electronic wavefunctions are taken to be the same for all positions of the nuclei.

The electronic energy, $$E_e (R)$$, in Equation \ref{10-4} combines with the repulsive Coulomb energy of the two nuclei, to form the potential energy function that controls the nuclear motion as shown in Figure $$\PageIndex{1}$$.

$V_e (R) = E_e (R) + \dfrac {e^2}{4\pi \epsilon _0} \dfrac {Z_A Z_B}{R} \label {10-6}$

Consequently the Schrödinger equation for the vibrational motion is

$( \hat {T} _{nuc} (R) + V (R) )_{X_{ne}} (R) = E_{ne X_{ne}} (R) \label {10-7}$

In Chapter 6, the potential energy was approximated as a harmonic potential depending on the displacement, $$Q$$, of the nuclei from their equilibrium positions.

In practice the electronic Schrödinger equation is solved using approximations at particular values of $$R$$ to obtain the wavefunctions $$\varphi _e (r,R)$$ and potential energies $$V_e (R)$$. The potential energies can be graphed as illustrated in Figure $$\PageIndex{1}$$.

The graph in Figure $$\PageIndex{1}$$ is the energy of a diatomic molecule as a function of internuclear separation, which serves as the potential energy function for the nuclei. When $$R$$ is very large there are two atoms that are weakly interacting. As $$R$$ becomes smaller, the interaction becomes stronger, the energy becomes a large negative value, and we say a bond is formed between the atoms. At very small values of $$R$$, the internuclear repulsion is very large so the energy is large and positive. This energy function controls the motion of the nuclei. Previously, we approximated this function by a harmonic potential to obtain the description of vibrational motion in terms of the harmonic oscillator model. Other approximate functional forms could be used as well, e.g. the Morse potential. The equilibrium position of the nuclei is where this function is a minimum, i.e. at $$R = R_0$$. If we obtain the wavefunction at $$R = R_0$$, and use this function for all values of $$R$$, we have employed the Crude Born-Oppenheimer approximation.

Exercise $$\PageIndex{3}$$

Relate Equation \ref{10-7} to the one previously used in our description of molecular vibrations in terms of the harmonic oscillator model.

In this section we started with the Schrödinger equation for a diatomic molecule and separated it into two equations, an electronic Schrödinger equation and a nuclear Schrödinger equation. In order to make the separation, we had to make an approximation. We had to neglect the effect of the nuclear kinetic energy on the electrons. The fact that this assumption works can be traced to the fact that the nuclear masses are much larger than the electron mass. We then used the solution of the electronic Schrödinger equation to provide the potential energy function for the nuclear motion. The solution to the nuclear Schrödinger equation provides the vibrational wavefunctions and energies.

Exercise $$\PageIndex{4}$$

Explain the difference between the Born-Oppenheimer approximation and the Crude Born-Oppenheimer approximation.


text:
# area of the shaded area of the circle.

• October 22nd 2010, 10:39 PM
ejaykasai
area of the shaded area of the circle.
The center C of the larger circle lies on another circle whose diameter coincides with the chord AB of the larger circle. Find the area of the shaded region if the length AB measures 10cm.

http://i1209.photobucket.com/albums/.../Photo0267.jpg
• October 22nd 2010, 11:39 PM
CaptainBlack
Quote:

Originally Posted by ejaykasai
The center C of the larger circle lies on another circle whose diameter coincides with the chord AB of the larger circle. Find the area of the shaded region if the length AB measures 10cm.

http://i1209.photobucket.com/albums/.../Photo0267.jpg

What have you tried, where are you stuck?

Post what you have done.

CB
• October 23rd 2010, 06:31 AM
ejaykasai
i got the area of the half circle which is 1/2 pi r^2 but then i don't know how to get the area of the segment to minus it on the half area of the circle.
• October 23rd 2010, 06:57 AM
HallsofIvy
Since AB, of length 10cm, is a diameter, the radius of the smaller circle is 5 cm. That tells you that the segment from O to P, the center of the smaller circle, is 5 cm. Now, Look at the right triangle formed by OAP. It has legs of 5 and 5 so you can find the length of OA, a radius of the larger circle.
• October 23rd 2010, 01:37 PM
Soroban

Since $\angle AOB$ is inscribed in a semicircle: $\angle AOB = 90^o.$

As HallsofIvy pointed out: . $PA = PO = PB = 5$

You can now find the area of sector $AOB$ of the large circle
and the area of right triangle $AOB$,
then determine the area of the unshaded segment.


text:
# PHYSICS HWK. Problem-Stuck?

1. Sep 8, 2004

### shawonna23

In a football game a kicker attempts a field goal. The ball remains in contact with the kicker's foot for 0.050 s during which time it experiences an acceleration of 390 m/s2. The ball is launched at an angle of 54° above the ground. Determine the horizontal and vertical components of the launch velocity.

vx = ? m/s
vy = ? m/s

2. Sep 8, 2004

### Tide

I think this should be in the homework section.

3. Sep 9, 2004

$$a = \frac{v - v_o}{t}$$
$$390m/s^2 = \frac{v - 0m/s}{0.050s}$$

I think you know how to do the rest. If you dont, ask away.

4. Sep 11, 2004

### shawonna23

Can u show me how to do the rest of the problem so I can make sure that I'm doing the problem the correct way.

5. Sep 11, 2004

### Tide

Why don't you show us what you're doing then I'm sure someone will be happy to check your work.

6. Sep 11, 2004

### HallsofIvy

Staff Emeritus
Personally, I wouldn't trust an answer given by anyone stupid enough to fall for that!


text:
It is currently 17 Dec 2017, 15:18

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What is the remainder when the positive integer n is divided by 6?

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What is the remainder when the positive integer n is divided by 6? [#permalink]

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What is the remainder when the positive integer n is divided by 6?

(1) n when divided by 12 leaves a remainder of 1
(2) n when divided by 3 leaves a remainder of 1
[Reveal] Spoiler: OA

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Re: What is the remainder when the positive integer n is divided by 6? [#permalink]

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03 Dec 2017, 09:07
Bunuel wrote:
What is the remainder when the positive integer n is divided by 6?

(1) n when divided by 12 leaves a remainder of 1
(2) n when divided by 3 leaves a remainder of 1

(1) n/12 = 12q + 1/12: so n could be {1,13,25,37...} and the numbers in this set divided by 6 all give a remainder of 1. sufficient.
(2) n/3 = 3q + 1/3: so n could be {1,4,7,10,13...} and the numbers in this set divided by 6 give a remainder of 1 or 4. not suf.
(A) is the answer.

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Re: What is the remainder when the positive integer n is divided by 6? [#permalink]

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03 Dec 2017, 09:20
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Bunuel wrote:
What is the remainder when the positive integer n is divided by 6?

(1) n when divided by 12 leaves a remainder of 1
(2) n when divided by 3 leaves a remainder of 1

Target question: What is the remainder when the positive integer n is divided by 6?

Statement 1: n when divided by 12 leaves a remainder of 1
USEFUL RULE #1: "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

No onto the question...........
Statement 1 does not tell us the quotient, so let's just say that n divided by 12 equals k with remainder 1
So, we can write: n = 12k + 1, where k is some integer
We can also write 12k a different way: n = (6)(2)(k) + 1
Or n = (6)(2k) + 1
As you can see, (6)(2k) is a multiple of 6, which means (6)(2k) + 1 is ONE MORE than a multiple of 6
So, when (6)(2k) + 1 (aka n) is divided by 6, the remainder must be 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n when divided by 3 leaves a remainder of 1
USEFUL RULE #2: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

So, for statement 2, some possible values of n are: 1, 4, 7, 10, 13, 16, 19, 22, etc.
Let's TEST some values...
Case a: If n = 1, then the remainder is 1, when n is divided by 6
Case b: If n = 4, then the remainder is 4, when n is divided by 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

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Re: What is the remainder when the positive integer n is divided by 6? [#permalink]

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03 Dec 2017, 23:38
From 1) we know $$\frac{n}{12} = x + \frac{1}{12}$$ so adjusting it to become $$n = 12x + 1$$ if we let $$x = 0$$ then$$n = 1$$, plug in in the question stem $$\frac{1}{6}$$ remainder is 1, if we let $$x = 1$$, then $$n = 13$$, plug in $$\frac{13}{6} = 2 \frac{1}{6}$$ another remainder of 1 and so it goes. A is sufficient.

From 2) $$\frac{n}{3} = x + \frac{1}{3}$$ so adjusting it to become $$n = 3x + 1$$ if we let $$x = 0$$ then $$n = 1$$, plug in in the question stem $$\frac{1}{6}$$ remainder is 1, if we let $$x = 1$$, then $$n = 4$$, plug in question stem $$\frac{4}{6}$$ a remainder of 4. Because we get two different answers it is insufficient.

The answer is A

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Re: What is the remainder when the positive integer n is divided by 6?   [#permalink] 03 Dec 2017, 23:38
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text:
# Dummy/baseline models for time series forecasting

I am working on an evaluation of time series forecasting models in Python, more specifically with statsmodels, scikit-learn and tensorflow. I think it makes sense to first compare the model performance to a set of "trivial" models.

• What are examples of such baseline models typically used?
• Are there existing implementations? (E.g., is there something analogous to scikit-learn DummyClassifier for time series forecasts?)


text:
# Axiom

An axiom is a statement that mathematicians assume to be true. Choosing to assume different axioms leads to different systems of mathematical logic and to different theorems being provable.

For example, the statement $a \times b = b \times a$ for real numbers $a$ and $b$ is an axiom (one of the field axioms of real numbers). However, this statement does not hold true for any objects; for matrices, not only is this not an axiom, it is not true.

Another example is the axiom of mathematical induction: $F(0) \wedge \forall n(F(n) \Longrightarrow F(n + 1)) \Longrightarrow \forall k F(k)$. This says that if $F(0)$ is true and $F(n)$ implies $F(n + 1)$ for all $n$, then $F(k)$ is true for every nonnegative integer $k$. This statement is not something we prove. Rather, it is something that we assume to be true about the integers in order to prove other statements. It is possible to develop different axiomatizations of arithmetic which lack the axiom of mathematical induction, but these are generally much weaker systems (that is, fewer statements are provable).

In geometry, we sometimes use the word postulate instead of axiom.


text:
# File extensions related to LaTeX, etc

In addition to the .tex and .dvi or .pdf files, TeX/LaTeX/ConTeXt produces and uses lots of other files. What do they do? Which ones are used to create the document and which ones are automatically created by the compiler. What files can I safely delete?

.fd = Font definition; used in generating the output.

.bst = BibTeX Style File (e.g., a certain journal's preferred Bibliography layout settings); used by BibTeX when generating the bibliography.

.aux = LaTeX auxiliary file; created when LaTeX is run, these contain information LaTeX records which is then used by either BibTeX or LaTeX itself on later runs (e.g., about cross-references), and can contain other things as well. This file is created by running LaTeX but also used the next time LaTeX is run. It can be deleted, but then you may need to run multiple times in the future to regenerate it.

.bbl = Bibliography; this is what is outputted by BibTeX for insertion into LaTeX the next time LaTeX is run.

.blg = Bibliography (BibTeX) log -- just like .log but for BibTeX; generated by BibTeX and can be safely deleted if there's no need to check it for errors.

.brf = BackReference file for the backref package, I think. I'm not very familiar with these, but I suspect they're created by LaTeX when a file using that package is compiled.

.cls = Documentclass (like article, or report - if you have them cluttering up your folders, you must use a lot of custom classes for individual journals or universities, etc.) This is obviously used to generate the output.

.dtx = Documented source file; can be used to generate a LaTeX package or other file along with its associated documentation.

Of these, .aux and .blg can be safely deleted. Probably .bbl too if you don't mind rerunning BibTeX and have access to the .bib files needed. The rest should not be deleted but maybe moved somewhere more appropriate. In particular .fd, .cls, and .dtx are better taking up space on a (personal) TeX tree, not in the folder of the document you're working on.

• Thanks very much. Actually, I forgot another extension which is .lbl. Could you please edit your answer to tell me what it is? – Rafid Dec 26 '10 at 16:50
• I'm afraid I don't know what a .lbl file is. Probably something specific to a package, like .brf, and the letters suggest something having to do with labels. What packages are you using for things like that? Almost all of these are plain text files, so you could open it and see what's inside. – frabjous Dec 26 '10 at 17:19

# General

## Manually created

• .tex: The document itself
Created by you.

## Automatically created

• .aux: An auxiliary file that saves information for the creation of ToC, references, indices, bibliographies and other things like that. It is reread in the next compiling to create the ToC, references etc.
Created by (pdf/xe/lua)(la)tex

• .toc: An auxiliary file that stores the Table of Contents, read in on subsequent runs to create the actual ToC.
Created by (pdf)latex, xe(la)tex.

• .lof: An auxiliary file that stores the List of Figures, read in on subsequent runs to create the actual LoF.
Created by (pdf)latex, xe(la)tex.

• .lot: An auxiliary file that stores the List of Tables, read in on subsequent runs to create the actual LoT.
Created by (pdf)latex, xe(la)tex.

• .log: Stors all messages of the compilation, like errors and warnings. It’s used by most Editors / LaTeX IDEs to show the errors in you document.
Created by (pdf)latex, xe(la)tex.

• .pdf: The common output format for your document.
Created by pdflatex, xelatex, ps2pdf, dvipdf.

# Bibliographies

## Manually created

• .bib: The data base file containing your bibliography entries.
Created by you.
• .bst: BibTeX style file.
• .bbx: A biblatex bibliography style.
Created by users.
• .cbx: A biblatex cite style.
Created by users.

## Automatically created

• .bbl: bibliography environment, generated by BibTeX.
This is what the call to bibtex produces and what is included into your document by the \bibliography command.
• .blg: bibtex and biber log file.
Created by bibtex/biber.
• .bcf: biblatex control file.
• .run.xml: biber XML file.
• -blx.bib: biblatex control file.

## beamer special files

In addition to the standard .aux, .log, and .toc files, a beamer document will also create the following auxiliary files:

• .nav: contains the information needed for the navigation bar hyperlinks.

• .vrb: will contain the verbatim material when fragile (containing verbatim material) frames.

• .snm: will contain information that will be used by \pgfimage to include actual slides when using the beamerarticle package.

• .out: contains information about the sectional units that will be used to write the outlines.

# General Layout and Package files

## Manually created

• .cls: Class files containing settings for you document and providing the basic macros for the mark up, e.g \section.
Created by users or latex with an ins file.

• .def: Collection of a list of similar definitions, that would make a sty file long and unreadable. See What does the .def file do?, and When to use ".sty" extension and when to use ".def".

• .dtx: Source file containing template files, like classes and styles and their documentation.
Created by users.

• .ins: installation file to extract template files out of a dtx file. Created by users.

• .sty: Style file containing macro definitions and other extensions for your document. Created by users or latex with an ins file.

## Automatically created

• These are not templates! – Joseph Wright May 14 '12 at 7:00
• @JosephWright: Maybe it’s the wrong word, I’m no native speaker. Pleas change it if you find a better title :-) – Tobi May 14 '12 at 7:27

Some further extension you might encounter depending on what packages you are using:

• .soc - package changes
• .fdb_latexmk - compile tool latexmk
• .fls - running latex with \$ latex -recorder
• .spl - documentclass elsarticle (Elsevier journals)
• .auxlock - tikzlibrary external
• .xwm - package xwatermark

I think you don't need to worry about files other than *.tex, *.cls and *.sty.

1. *.tex is the extension for input files in which you put your document content and format. You can have more than one input file for your project. But only one input file can contain \documentclass call. The input file contains \documentclass call is called as your main input file.

2. *.cls is the extension for documentclass containing layout settings and commands. There are many documentclass, such as article, book, minimal, report, etc. From within your main input file, you call this document class using the command \documentclass{book}, for example. Calling \documentclass{book} means you want to create a book project. In book project, you will have some settings such as chapter, section, subsection, subsubsection, frontmatter, mainmatter, backmatter, etc. Other documentclass also has different settings.

3. *.sty is the extension for package containing class-agnostic commands. There are many packages. Each provides different purposes and works indendepently. For example, if you want to draw Euclid diagram for your project, you can use pst-eucl.sty. From within your main input file, you call this package by using \usepackage{pst-eucl}.

As the rule of thumbs: You may accidently lose files other than your input files, image files, data files. If you lost *.cls and *.sty, download again from the internet. If you lost *.aux, just compile again your input file.

• I don't understand why someone wouldn't need to worry about .bst or .fd files, etc. Deleting those could definitely cause problems. – frabjous Dec 26 '10 at 15:58
• @frabjous. I don't say the other files are not important. :-) – xport Dec 26 '10 at 16:02
• @frabjous: I would read "don't worry about them" as "leave them be: don't try to understand what's going on with them, for now, just treat them as part of the magic of TeX", certainly not as "they're not important; you may as well delete them"! – Peter LeFanu Lumsdaine Dec 26 '10 at 21:04
• Fair enough! Just so long as it is clear, which it wasn't to me, and may not have been to others. (It is now, thank!.) – frabjous Dec 26 '10 at 22:06
• What about .bst's? – einpoklum Sep 16 '17 at 9:35

# ConTeXt MkIV related files:

## User-Input Files

• .tex: For content and typesetting instructions.
• .cld: For ConTeXt Lua Documents
• .xml: For XML data (related: .xhtml)

## Macro package files

• .mkiv: Code for MkIV
• .mkvi: Code for MkIV written with named variables \def\macro#{val1}#{val2} rather than \def\macro#1#2, etc.)
• .lua: Lua code for MkIV
• .lfg: Goodies for fonts (used for creating virtual fonts and changing parameters defined in fonts)

• .mpiv: Metapost code for MkIV

## Automatically generated

• .tuc: Data stored for multiple passes, ToC, etc.
• .log: Log file

You can safely delete the .tuc and .log files. These can be automatically deleted if you run

context --purgeall

# Related questions

The following is a list of most of the common file extensions used for UNIX (La)TeX files and what they mean. They are in the order in which you are likely to come across them rather than alphabetic order.

• .tex: denotes a source file for any flavour of TeX.

• .cls: denotes a LaTeX 2e class file.

• .clo: denotes a LaTeX 2e class option file. usually options associated with a class are defined in a .cls file, but occasionally they are defined in separate .clo files.

• .sty: denotes a LaTeX (or AmS-TeX) package/style file. LaTeX 2.09 made no distinction between classes and packages ... all such files were style files - hence the suffix. LaTeX 2e has retained the suffix for what it now terms as packages.

• .log: denotes a log file for any flavour of TeX.

• .aux: denotes an auxiliary file. generated by running latex (or etex) on a source file. It typically contains information latex needs on a second pass to construct \refs and \cites and information that bibtex needs to construct a .bbl file.

• .toc: denotes a table of contents file. generated by latex when the source file contains the line \tableofcontents.

• .lot: denotes a list of tables file. generated by latex when the source file contains the line \listoftables (Similar to a .toc file.)

• .lof: denotes a list of figures file. generated by latex when the source file contains the line \listoffigures (Similar to a .toc file.)

• .bib: denotes a BibTeX source file. such files contain the database from which the .bbl bibliography file is generated.

• .bst: denotes a BibTeX style file. the style in which bibtex presents the .bbl bibliography file.

• .bbl: denotes a (La)TeX bibliography file. usually generated by bibtex.

• .blg: denotes a BibTeX log file.

• .idx: denotes a MakeIndex index source file. contains \indexentry commands generated by a first pass of a TeX source file through a flavour of TeX.

• .ist: denotes a MakeIndex style file. needed only when the default manner in which makeindex processes an .idx file needs to be over-ridden, e.g. when makeindex is used for generating a .gls glossary file.

• .ind: denotes a (La)TeX index file. usually generated by makeindex.

• .ilg: denotes a MakeIndex log file.

• .glo: denotes a MakeIndex glossary source file. contains \glossaryentry commands generated by a first pass of a TeX source file through a flavour of TeX.

• .gls: denotes a TeX glossary file. usually generated by makeindex, which needs an appropriate .ist file to over-ride the MakeIndex defaults that produce indexes.

• .glg: denotes a MakeIndex glossary log file.

• .dtx: denotes a file containing (La)TeX package(s)/class(es) together with its documentation. Running (La)TeX on the file usually generates the .dvi documentation. An accompanying .ins file calls docstrip.tex to strip the (La)TeX package(s)/class(es) from the .dtx file and sometimes also a .drv file.

• .ins: denotes a (La)TeX install file. Running (La)TeX on the file strips package or class files from accompanying .dtx files(s).

• .drv: denotes a (La)TeX driver file. Sometimes stripped from a .dtx file by running (La)TeX on an .ins file. Running (La)TeX on the .drv file generates the .dvi documentation.

## Files generated by some other packages

### changebar

• .cb2: Coordinates of "points" in the text for beginning and ending stretches marked by a change-bar on the side.
• .cb: Some other kind of history / points file (package documentation is not very clear about it)

In addition to all the other answers mentioned here, I'd like to add the extensions mtc[0-9] and ptc to the list here.

Files with these extension names are created by the titletoc package, usually used in books and long articles to obtain a toc within each chapter.

I guess they stand for mini toc (with the suffix denoting chapter number) and partial toc (i.e. the global toc that gets continuously updated during the build process as each chapter is getting built).

# (r)(e)ledmac/(r)(e)ledpar files

.1, .1R, .2, .2R file storing metadata about line break and critical notes. One by \beginnumbering...\endnumbering .eledsec1, .elesdec2 etc. File for the eledsection and related commands .Aend, .Bend, .Cend etc. File for the endnotes of series A, B, C etc.