title

[ihaveaplan]

Lynn the Hacker👩‍💻, Drug Dealer🤏, and Heavy Smoker🚬 (2)

야심차게 집을 나선 린이 온 곳은 바로 델 솔 밸리, 심월드의 할리우드같은 곳입니다. 셀럽들이 약 많이 한다는건 공공연한 사실이죠?

도착하자마자 또 한번 빨아주시네요. 재활원에 보내야할 것 같아요~^^

쨋든 좆목질을 시작해봅시다

저 장미꽃뿌리기는 린이 클라이언트(호구)로 점찍은 심에게만 하는 특별한 행동입니다. 뭣도 모르고 좋아하는것좀 보새요?

성공적인 고객 유치 후 흥에 겨워 춤을 추는데... 추면서도 담배를 피네요 ㅎ; 하나만 해라

그래도 고객 두명을 유치하고 1000시몰을 벌었습니다. 하지만 아직 택도 없죠.

그래서 린은 무리수를 둡니다. 집앞에서 열린 어린이들 축제에 온 것입니다~~^^

설마 돈에 눈이 먼 린이 파릇파릇한 어린이심에게까지 약을 팔려는 걸까요..?😬😱

아! 다행히 그건 아닌가봅니다. 가서 엄마데려와~ 라고 하네요^^

애새끼 상대하다 급격히 배가고파진 린..

뭔가 시켜먹네요 옆에 랜덤심 cc헤어 차고있는거 킹받음

맛대가리가 존나 없나본데요?ㅋ

먹고있으니 앞에 누군가 동석을 합니다!

......... 

깨진 노즈 프리셋이 하나 있었는데 그걸 차고있었나봐요....

하지만 우리 린이는 적어도 피부색으로 차별을 하진 않습니다❗

인간이라면 누구나 공평히 약을 접할 기회를 가져야죠

화려한 언변으로 미스블랙씨를 고객으로 유치하는데 성공하고..

옆에 누군가 또 옵니다.

바로 또 다른 호구죠. 장미꽃으로 맞아줍시다.

코카인에 대한 열띤 토론을 하다보니 구경꾼이 많이 생겼네요~

이 아이는 청소년이 되면 린을 다시 찾아오기로 했습니다😉

무리수를 둔 것치곤 나름 고객을 많이 확보했네요 ㅎㅎ 

다음화엔 개같이 코카인을 팔아치워봅시다😘

[ihaveaplan]

Lynn the Hacker👩‍💻, Drug Dealer🤏, and Heavy Smoker🚬 (1)

⚠️주의! 범죄자 비행청소년의 이야기를 다루고 있습니다.

+ 글쓴이 화나있음

여기 시작부터 손목에 쇠고랑을 차는 청소년이 있다 ❗❓❓

바로 우리 주인공 린입니다 성씨따윈 없어요

이 개성강하신 분은 swat에서 나오셨다는데 눈썹만 하얀게 킹받지 않나요 ㅎ?

이 아이는 우선 해커인데요

부업으로 딥웹에서 마약도 팔고 있습니다. 꽤 쏠쏠하지만 가끔 저렇게 쇠고랑차고 잡혀간다는게 함정이죠.. 상품배송중인 모습입니다~^^

추가로 개꼴초라 툭하면 담배피는데 참.. 폐암 엔딩은 원치 않는데 말이죠

린이 잡혀간새 집앞에서 수다떨고있는 SWAT팀. 직무유기 아닌가요?

조사받고 돌아온 린. 갖고있던 약 다 뺏기고 개빡쳐서 어디론가 전화를 하네요

전화받고 달려온 저 뒤에 계신분.. 많이 피곤해보이시는데

그새 담배피우는 린. 언젠가 버릇을 고쳐놔주겠습니다.

이 분으로 말할거같으면 집주인이자 코카인 공급처. 이름은 왠지모르지만 안가르쳐줘서 그냥 집쥔언니라고 한다는 컨셉입니다. 뺏긴만큼 다시 수급하네요^^

미자한테 약을 팔아도 나름 좋은 어른이란건가요? 집에 뭐가 고장나면 봐주기도합니다

꼴받는건 맨날 시도는 하는데 한번도 제대로 고친적 없습니다

대타 등장. 얘 이름은 볼프강인데 린 친구에요

깔끔히 고쳤네요. 집주인 뭐했노...

이 둘은 볼프강이 린한테 약을 사며 친해졌습니다

평소라면 공과 사 얄짤없겠지만 저 와꾸를 보새요. 친해지고싶었을겁니다...

혈기왕성한 때라 그런지 가끔 이런짓저런도 하는데 둘은 ✌친구 ✌ 가 맞습니다!

그나저나 약을 다뺏겨서 다시 샀더니 개털이됐습니다.

저정도면 많은거 아니냐구요? 툭하면 쥐도 나오고 고장나는 저 집은 꼴에 역세권이라고 월세만 6000시몰입니다. 개처럼 벌어야 쫓겨나지 않습니다.

조실부모하고 혼자 자란 린이 범죄까지 저질러가며 돈을 버는덴 이유가 있었던 것입니다..😫

그럼 돈을 벌러 출동해볼까요..^^;

[ihaveaplan]

Computer Vision 2.2.2

(2) Sobel Filter in y-axis

(3) Averaging filter

We can smooth out image noise by performing a weighted average in a local area.

5) The Concept of Origin

A 1 * 2 kernel filter H whose origin (the position of the kernel which is determining the location of the output pixel) is on the left (marked by the dot).

H=[1•−1]

Another 1 *2 kernel filter H whose origin is now on the right.

H=[1−1•]

Convolve them to an Image I = [10 20 10 30 40], the first gives [−10 10−20−10 unknown] and the second (how scipy works with mode='same') gives [unknown−10 10−20−10]. With an odd number of elements, origin is in the middle.

6) Formula

- Given an image I and a template M.

- For simplicity, ignore the edge of the image and suppose a template with an odd number of elements.

- M is represented by a (2N+ 1)×(2N+ 1) matrix1,and that these are indexed from -N to N, so that the center eement of M is M(0, 0)

- Then we can write:

7) Code

8) Dealing with the boundaries of the image

- Make the output array smaller than the input array - miss off a few rows and columns so that the mask never has to go over the edge of the input array.

- 'Wrap round' the input array, so that the right edge joins the left and the top joins the bottom - this is not usually a good idea, but fits in with a computational method for doing convolutions called the Fourier transform.

- Assume the input array is surrounded by zeroes.

- Assume the left-hand column of the input is repeated to the left as far as necessary, and the same for other boundaries.

- Assume the data are reflected in the boundaries of the input array.

*The first and last of these are generally the nicest. The Matlab function convolve2 allows you to specify these as options (valid and reflect).

2. Convolution and Correlation

- Convolution and correlation are not the same.

- Convolution is a filtering operation (like detecting high freqeuncy spatial content to expose edges):

- Convolution templates have a flipped mask compared to correlations.

- The reason for the flip is that masks can be convolved together to make new masks.

- Correlation looks at how similar two signals or patterns are:

- Do not flip the mask.

[ihaveaplan]

Computer Vision Week 2.2.1

Overview

1. Convolution and its usage

2. How to contruct edge dectors and averaging filters using convolution

1. Convolution

- Convolutions are a fundamental and powerful operation in signal/image processing.

- Some form is used in almost every computer vision application.

- Convolution has been hypothesised as a good model of low-level biological visual processing.

- Convolutional Neural Networks (CNNs) are a big part of the recen wave of deep learning, and the convolutional part has enabled impressive results on a variety of tasks.

1) Usage

Simple hand-defined convolutional filters can be used to accomplish:

- Edge detection

- Image denoising

- Edge enhancement/sharpening

- Object localisation

2) What is it?

- A convolution can be thought of as concurrently applying a local function to parts of the image.

- Unlike the pixelwise operations we saw before, this looks at a group of pixels in a neighbourhood.

- The manner in which this function is applied to the image is sometimes called a sliding window, as the function only sees a small portion of the image at a time.

- Convolutions are trivially parallellised, which is one reason for their continuing success.

This little array is known by various names:

- Mask

- Weight array

- Operator

- Kernel filter

To use it, we must flip it over to make a template:

3) Code

A = [19 24 22 10 3 20 22 4 19 14]

convolve with template [-1, 1]

# Note that the template is flipped

scipy.signal.convolve(A, [1, -1], mode='valid')

Output:

([ 5, -2, -12, -7, 17, 2, -18, 15, -5])

4) Horizontal Differencing

- [-1, +1] gives a first order apporximation of the derivative (rate of change) of the image (in the x-direction) using finite differences.

- i.e. It measures the strength of vertical edges.

- Mathematically, it is approximating the derivative at the point in-between the 2 pixels.

5) 2D Templates

- Templates are not restricted to being 1-dimensional, they can be 2D as well.

- All this menas is that our convolution function operates oen neighbours in both x and y.

(1) Sobel Filter in x-axis

- Provides a mechanism for reducing noise:

a) In python

from scipy.signal import convolve2d

sobel_x_kernel = [[-1, 0, +1], [-2, 0, +2], [-1, 0, +1]]

sobel_x_img = convolve2d(img_gray, sobel_x_kernel, 'same')

# 'same' refers to the padding

[ihaveaplan]

Computer Vision Week 2 - 3

3. Colour images Colour is represented in a variety of ways, some complex. A common approach is to split the image into red, green and blue components. Adjustments may need to be made both when the image is acquired and when it is displayed.

Image operations can be applied to each of the colour planes separately, or in some cases combined operations can be devised.

1) Colour Spaces

- Several standardised colour spaces have been developed to represent images.

- Each of which ahs different usages.

- Most common to work with is RGB.

- Ohters such as hue saturation value (HSV) and LAB distinguish between colour information, and brightness (which encodes most of the structure).

(1) Colour Spaces - LAB

(2) Colour Spaces - RGB

[ihaveaplan]

Computer Vision Week 2 - 2

plot_im_hist(pow(img_gray, 1.0./1.1))

c) Using histogram to stretch the gray scale:

We can use a tailored curve from input to output to make the output have a flat histogram: that is, with about the same number of pixels at each gray level. This gives high visibiity for most of the detail in the image. In Matlab, histeq does this.

(a) Histogram Equalised

cv2.equalizeHist

• Why Histogram Equlisation?

- It doesn't necessarily make better looking photos, but it improves the global contrast.

- This means that more details may become visible in the image.

- It doesn't discriminate between image noise and true signal, so it could have adverse effects.

- The operation is invertible so the original values are recoverable.

- It's not used that much in deep learning based vision systems, but still is used as a pre-processing step for many systems.

d) Thresholding: a very non-linear operation

Thresholding compares the gl at each pixel with a number called the threshold. If the gl is greater than the threshold, the corresponding pixel in the output is set to 1; otherwise, it is set to 0. We might choose the threshold by looking at the histogram.

Thresholding is often most useful when applied to the output of some other image processing operation, rather than directly to the original image.

2. Dynamic Range

- The ratio between the highest and lowest values that can be described.

- In photography, this corresponds to the range of luminance visible in the image.

- Typically, we are interested in detail within the middle range of luminance, and can compress shadows and highlights.

- By playing with more localised contrast controls, we can create the appearance of high dynamic range on screens and printed images.

[ihaveaplan]

Computer Vision Week 2 - 1

Overview

1. Image histograms

2. Simple operations on inidivdual pixels

INTRO

Data Scaling:

- Sometimes it can be useful to rescale the pixel intensities, e.g. to make them between 0 and 1.

- This means that the numbers need to be converted from a unit 8 to a floating point.

- Always keep in mind the original data precision (discretized into 256 bins.)

- Scaling the data will also scale the summary statistics.

1. Histogram

- Summary statistics are naturally limited in what they can represent.

- A more flexible description: histogram

- Histogram split a data space into discrete bins (value ranges), and count the number of occurences in each bin.

1) Operation

(1) How to use in python

- Each pixel falls within one of the bins, and we plot the count of pixels in each bin.

plt.hist(img_gray.flatten(), normed=True, bins=10)

- Changing the number of bins:

plt.hist(img.gray.flatten(), normed=True, bins=30)

2) Usage

- Histograms provide a global description of the ocntents of an image.

- They sumamrise how much of which colour is in the image.

- They throw away all of the spatial relationships, i.e. patterns and textures.

(1) Histogram as Features

- Can be used as features for certain tasks: e.g. differentiating images of sandy beaches from snowy hills.

(2) Adjusting Images

a) Changing gray levels

- Division:

plot_im_hist(img_gray / 2.0)

- Multiplication:

plot_im_hist(img_gray * 2.0)

- Contrast:

plot_im_hist((img_gray - np.mean(img_gray)) * 2.0 + np.mean(img_gray))

- Drawing image and histogram:

def plot_im_hist(img_compressed):

plt.subplot(1, 2, 1)

plt.imshow(img_compressed, cmap='gray', vmin=0, vmax=255)

plt.axis('off')

plt.subplot(1, 2, 2)

plt.hist(img_compressed.flatten(), np.linspace(0, 255, 20), normed=True)

plt.show()

b) Non-linear changes to the gray-levels

- Gamma-correction: Raising the gray levels to a power to expand some parts of the gray-level scale at the expense of others.

* .^ operator raises to a power.

plot_im_hist(pow(img_gray, 1.1))

[ihaveaplan]

Acquired Intelligence & Adaptive Behaviour Week 3 - 3

Overview

1. What is evolution

2. Evolutionary Algorithms

3. Related terminology and concepts

- Fitness function

- Genotype and phenotype

4. Artificial Evolution vs Design

5. Examples

*References

- blog

- An Introduction to Genetic Algoirthms - Melanie Mitchell

1. Evolution

- For evolution to occur, you need a population of individuals that:

- has variation

- undergoes selection

- reproduces with heredity

1) Artificial Evolution

The main idea of artificail evolution is to simulate the imortant parts of evolution, to 'harness the creative power of evolution'. To get the computer to build such things, we have to build things beyond design. -> Intelligent behaviour rather than intelligent solutions

2) Evolution -> Evolutionary Algorithm

- In natural evolution, the accumulation of beneficial mutations can reproduce better adapted organisms.

- An evolutionary algorithm (EA), also known as a genetic algorithm (GA) is an attempt to capture this 'improvement of a system' that is the result of natural evolution.

3) Evolutionary Algorithm

- Simulates a population of 'individuals' that:

- reproduce with heritability

- are mutated to produce variation

- are selected on some measure of fitness

*Example:

- Evolution (directed accumulatio nof blind variation) is quite different form rational desgin.

- Human desgin tends to break systems down into components. These are themselves then broken down into subcomponents etc., until basic components are understood. (e.g. modern aeroplane or space craft design)

(1) Advantages

- They introduce different biases than those in place in typical human design.

- Allow us to consider alternative ways to 'solved a problem', other than how a human might have.

- Can be used to automate design:

- Engine design

- Scheduling problems

- Container load optimisation

(2) Different Biases

- Unlike typical human design, GAs are not biased against 'cheap tricks' - i.e. non-intuitive short-cuts to solving problems for hierarchical desgin.

- But they have their own biases.

- There must be an evolutioanry path to any solution given by a GA. (Consider how a bacterium could not evolve in one step (generation) into an elephant.)

- The biases of GAs are not easy to identify. They are influenced by how the genotype is related to the phenotype, how mutation takes place - lots of different, subtle things.

*Engine Design example:

(3) Genotype / Phenotype

- Genotype: the genetic materail, passed down from one generation to the next the order of the nucleotide on DNA, e.g. AGGCACATT...

- Phenotype: what undergoes selection, 'what the genotype codes for'. Typically the body and the brain in artificial evolution.

(a) In Engineering

- Genotype: (the encoding of the information) the angle of each aerofoil. E.g. g0 = [a1 a2 a3 a4 ... a8]

- Phenotype: (what the information encodes) the shape of the wing

(4) Fitness

- In the natural world, the fitness of an organism is determined by many complex interacting factors: predator, prey coevolution, sexual selection, competition with ocnspecifics, luck, etc.

- But evolution =/= evolutionary algorithms. In GAs, there is often a clearly deifned 'fitness function' guidign evolution towards a predetermined objective.

*Fitness in the aerofoil model is the amount of drag on the wing due the airflow.

(5) Evolutionary Strategy

*pseudo code:

[ihaveaplan]

Acquired Intelligence & Adaptive Behaviour Week 3 - 2

e) What are they good for?

- Powerful because the dynamics allows a form of memory and processing sequences of input.

- Language

e.g. I L O V E Y O U

i1 i2 i3 ...

f) How to train?

- Backpropagation through time

- Trian with BP through each time update

- Only works for small networks and has lots of problems

3) Attractor Neural Network

- Get rid of the complicated dynamics

- Symmetrical connected node gets rid of chaotic dynamics a leave just multiple fixed points

- Good for pattern completion

4) Echo state machines

- Weakly connected node exhibit only asingle fixed point attractor

- Use the transient dynamics to process

- Good time series analysis

*These models are more appropriate models of the brain which also is recurrent and show very rich dynamics. More biologically plausible than FFNN.

[ihaveaplan]

Acquired Intelligence & Adaptive Behaviour Week 3 - 1

Overview

1. From feed forward to recurrent neural networks

2. Building a recurrent neural network (RNN)

3. Dynamics in RNNs

4. Training RNNs

Recap

- Old fashioned AI is symbolic

- GOFAI and Connectionism are static

- In feed-forward NNs, input at time t maps to output at time t+1. -> static

*Coherent behaviour emerges only from the dynamic interaction between brain/body and environment.

1. Recurrent Neural Networks

- Dynamics reverberates around cycles in the network.

1) Formulation

(1) Feed-forward NN

(2) Recurrent NN

- yi(t+1) = Denotes the value yi in the next timestep.

- wij (weight) = Denotes the strength of a connection from afferent neuron j to efferent nueron j is described by the varaible, wij.

- θi (bias) = Implemented for each by adding the parameter θ from the value of y at the afferent node, j.

- F (transfer function) = Sigmoid usually, alternatives: log-simoid, tan-sigmoid

- Ii (input) = Can be any node, denoted by the input function Ii(t).

a) How to simulate them?

b) Fixed points

*Converges to 0 when the weights are too small.

c) Cyclic Behaviour

d) Complex Cycles or Chaotic behaviour

[ihaveaplan]

The Fundamentals of Machine Learning Week 2 - 2

- mean distance (mean deviation):

*Standard deviation is easier to work with mathematically than mean distance

3. Multivariate Probability Distributions

- Multivariate means multi-dimensional, i.e. 2 or more random variables.

- Multivariate integral of probability density function to get probability a sample will lie within a certain region.

1) Covariance and Correlation

Covariance:

Correlation:

*Reference: https://youtu.be/KDw3hC2YNFc

4. Common Distributions

1) Uniform Distribution

- Has the same probability for each point. Thus, probability is governed by the range of the data R and pdf p(x) = 1/R, which equals 0.1 in the example below:

2) Gaussian Distribution

- Governed by mean μ and variance σ^2 with pdf:

*There are binomial, multinomial, Poisson distributions etc.

5. Central Limit Theorem

- The distribution of the sum or the mean of N i.i.d (independent identically distributed) random variables becomes increasingly Gaussian as N grows.

- Example: N uniform [0, 1] random variables. The distribution of the sample mean:

*As you increase N, the probability distribution of X itself becomes Gaussian.

-> The larger the sample size becomes, the more perfect normal distribution you get.

*Reference: https://www.youtube.com/watch?v=JNm3M9cqWyc

6. Multivariate Gaussian Distribution (normal distribution)

Single normal random variable with mean  μ and standard deviation σ:

*Reference: https://www.youtube.com/watch?v=JjB58InuTqM

1) Properties of the Gaussian (Normal)

- Sum of Gaussians is Gaussian

- Conditional densities are Gaussian

- Linear transformation is Gaussian

- Limit of binomial and Poisson distributions in certain cases is Gaussian

7. Conditional Probabilities

- P(A|B) read as ‘probability of A given B’

1) Independence

- Two variables X and Y are independent if for each x and y:

- Independent variables have zero covariance/correlation

- However, zero covariance/correlation does not imply independence.

2) Bayes Theorem

(1) Bayes Theorem and Classification

[ihaveaplan]

The Fundatmentals of Machine Learning Week 2 - 1

Overview

1. Probability density functions

2. Properties & parameters of probability distributions

3. Multivariate probability distributions

4. The normal distribution

5. Conditional probabilities and Bayes Theorem

INTRO

Why is probability densitiy destimation useful in ML?:

- A lost easier to classify data if you have the underlying distributions.

- Build up a probability distribution from previous instances.

- See where a new test case lies on the distribution and infer how likely it is to belong to the same class.

- Understand how distribution from two or more classes overlaps, to inform choice of machine learning algorithm.

- See how distribution fits with assumptions of chosen model/algorithm.

1. Probability Density Functions

1) Probability Theory

2) Probability Density Functions

Function known as a probability density function (pdf):

*The higher the probability density at x and around x, the more likely that the value of a datapoint will be close to x.

- Area under the curve gives the probability so if pdf is p(x),

- Area under the whole curve must sum to 1.

2. Properties / Parameters of Distributions

- Distributions and pdfs are often described/specified by parameters, commonly mean and variance.

- The mean is the usual average, also known as the expected value E(x) of <X>:

- Variance governs the spread of the data and is the square of the standard deviation. It is given by the expected square of the deviation from the mean:

- Other notations

- Example:

Fair 6-sided dice: P(X=1) = P(X=2) = ... = P(X = 6) = 1/6

[ihaveaplan]

Acquired Intelligence & Adaptive Behaviour Week 2 - 3

- For each new data batch:

- Set all gradients to zero (optimizer.zero_grad())

- Update the model (optimizer.step())

9) Testing the model

MNIST comes with a testing dataset.

10) Application

Backpropagation updates the weights and biases a little bit each time, so we need to train for multiple epochs.

[ihaveaplan]

Acquired Intelligence & Adaptive Behaviour Week 2 - 2

(2) Creating a predict function

- We will use 2 layers and rectified linear unit (ReLU) as an activation function:

- input size: how many pixels are the MNIST examples? (28 * 28 = 784)

- output size: how many labels are there? (10)

- hidden size: how many hidden units do we want? (no correct answer)

(3) Training data and batches

- In deep learning (and machine learning in general), we have a training dataset

*A list of inputs and desired outputs (e.g. images and their true labels)

- Rather than training on a single input and output at a time, we use batches of examples

*These are all passed through the nerual network at once

4) Loading MNIST

We need to convert the images into vectors:

5) Error function

- E(^y, y)

- Returns a single number

- The goal of learning is to minimise this function

6) Getting gradients with automatic differentiation

- For each weight and biases (θ), we want to find:

*α = learning rate

- Automatic differentiation by calling backward on the result of the loss function

7) Backward()

Calling backward automatically calculates the derivative of the error function with respect to each parameter and stores it in the grad field.

8) Updating the model

- Backward calculates only the gradients, we need to update the weights and biases.

- Use Pytorch optimisers

(1) Optimiser

- lr = α

- SGD = Stochastic Gradient Descent

[ihaveaplan]

Acquired Intelligence & Adaptive Behaviour Week 2 - 1

Overview

1. Automatic differentiation packages

2. Setup with Pytorch

3. Basic operations

4. Creating a model

5. Creating a predict function

6. Training data and batches

7. Defining error function

8. Getting gradients with automatic differentiation

9. Update the model

10. Testing

11. Example with MNIST

INTRO

Deep Learning

- On a theoretical level, powered by backpropagation algorithm

- On a practical levell, powered by automatic differentiation libraries

*These implement the backpropagation algorithm automatically.

1. Backpropagation

- A dataset of input-output pairs (xi, yi)

- A function (e.g. neural network) which computes ^y = fθ(x)

*This function has some parameters (e.g. weights and biases) θ

- An error function E(^y, y)

*Change the parameters so that the error function goes down.

2. Pytorch

- An open source automatic differentiation library for Python

- Provides the building blocks needed for implementing backpropagation, and automatically computes the derivative

1) Importing

import torch

import torch.nn as nn

import torch.optim as optim

from torch.utils.data import DataLoader

from torchvision import datasets, transforms

2) Basic operations: Tensor

The basic building block of Pytorch is the Tensor class.

*Tensor is a multi-dimensional array of numbers.

(1) Ways to create tensors:

- torch.rand(2, 4, 5)

- torch.zeros(4, 2, 3)

- torch.ones(4, 2, 3)

- torch.from_numpy(numpy_array)

- torch.tensor(my_list_of_numbers)

(2) Tensors work with most basic python operations:

3) Creating a neural network

- At the most abstract level, a neural network (NN) is a function which takes an inputs and returns an output (e.g. inputs = images, outputs = labels)

- NNs are composed of layers

*Each layer has weights W and biases b and performs the following operation:

- Usually use multiple layers (hence deep learning) with some non-linear function applied in between:

(1) Creating one in Pytorch

- Create the weights and biases using tensors

- Use one of the predefined classes nn.Linear which performs: