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# Course References, Links and Random Notes

Title: Probabilistic Reasoning and Reinforcement Learning
Info: ECE 457C - Reinforcement Learning
Instructor: Prof. Mark Crowley, ECE Department, UWaterloo

NOTE: Ignore the weekly dates, they are from a previous year

Website: markcrowley.ca/rlcourse

Link to this Gingko Tree: RL Course Links and Notes

## Course Description :

Introduction to Reinforcement Learning (RL) theory and algorithms for learning decision-making policies in situations with uncertainty and limited information. Topics include Markov decision processes, classic exact/approximate RL algorithms such as value/policy iteration, Q-learning, State-action-reward-state-action (SARSA), Temporal Difference (TD) methods, policy gradients, actor-critic, and Deep RL such as Deep Q-Learning (DQN), Asynchronous Advantage Actor Critic (A3C), and Deep Deterministic Policy Gradient (DDPG). [Offered: S, first offered Spring 2019]

# Topics

Primary Textbook : Reinforcement Learning: An Introduction
Small
: Richard S. Sutton and Andrew G. Barto, 2018 [SB]

Some topics are not covered in the SB textbook or they are covered in much more detail than the lectures. We will continue to update this list with references as the term progresses.

1. Motivation & Context [SB 1.1, 1.2, 17.6]
2. Decision Making Under Uncertainty [SB 2.1-2.3, 2.7, 3.1-3.3]
3. Solving MDPs [SB 3.5, 3.6, 4.1-4.4]
4. The RL Problem [SB 3.7, 6.4, 6.5]
5. TD Learning [SB 12.1, 12.2]
6. Policy Search [SB 13.1, 13.2, 13.5]
7. State Representation & Value Function Approximation
8. Basics of Neural Networks
9. Deep RL
10. AlphaGo and MCTS
11. Quick Overview of Other Topics:
1. MARL
2. Free Energy
3. Hierarchical RL
4. Supervised Learning for RL and Curriculum Learning

Skipped Topics:

1. POMDPs (skipped in S22)

## Basics of Probability

### ECE 657A Youtube Videos

Introductory topics on this from my graduate course ECE 657A - Data and Knowledge Modeling and Analysis are available on youtube and mostly applicable to this course as well.

Probability and Statistics Review (youtube playlist)

Containing Videos on:

• Conditional Prob and Bayes Theorem
• Comparing Distributions and Random Variables
• Hypothesis Testing

### ECE 108 YouTube Videos

For a very fundamental view of probability from another course of Prof. Crowley you can view the lectures and tutorials for ECE 108

ECE 108 Youtube (look at “future lectures” and “future tutorials” for S20): https://www.youtube.com/channel/UCHqrRl12d0WtIyS-sECwkRQ/playlists

The last few lectures and tutorials are on probability definitions as seen from the perspective of discrete math and set theory.

### Likelihood, Loss and Risk

A Good article summarizing how likelihood, loss functions, risk, KL divergence, MLE, MAP are all connected.
https://quantivity.wordpress.com/2011/05/23/why-minimize-negative-log-likelihood/

### Probability Intro Markdown Notes

From the course website for a previous year. Some of this we won’t need so much but they are all useful to know for Machine Learning methods in general.

https://compthinking.github.io/RLCourseNotes/

• Basic probability definitions
• conditional probability
• Expectation
• Inference in Graphical Models
• Variational Inference

## Basic Decision Making Models - Multiarmed Bandits

Textbook Sections: [SB 1.1, 1.2, 17.6]

### Videos

- Part 1 - Live Lecture May 17, 2021 on Virtual Classroom - View Live Here

## Markov Decision Processes

### Textbook Sections

• Markov Decision Processes
[SB 3.0-3.4]
• Solving MDPs Exactly
[SB 3.5, 3.6, 3.7]

## Dynamic Programming

Former title: The Reinforcement Learning Problem
Textbook Sections:[SB 4.1-4.4]

## Temporal Difference Learning

Textbook Sections: Selections from [SB chap 5], [SB 6.0 - 6.5]

• Quick intro to Monte-Carlo methods
• Temporal Difference Updating
• SARSA
• Q-Learning
• Expected SARSA
• Double Q-Learning

Parts:

## N-Step TD and Eligibility Traces

Textbook Sections: [SB 12.1, 12.2]

Eligibility traces, in a tabular setting, lead to a significant benefit in training time in additional to the Temporal Difference method.

In Deep RL it is very common to use experience replay to reduce overfitting and bias to recent experiences. However, experience replay makes it very hard to leverage eligibility traces which require a sequence of actions to distribute reward backwards.

## Part 1 Review

Go over any questions or open topics from first 6 weeks.

## State Representation & Value Function Approximation

### VFA Concept

A Value Function Approximation (VFA)
is a necessary technique to use whenever the size of the state of action spaces become too large to represent the value function explicitly as a table. In practice, any practical problem needs to use a VFA.

#### Benefits of VFA

• Reduce memory need to store the functions (transition, reward, value etc)
• Reduce computation to look up values
• Reduce experience needed to find the optimal value or policy (sample efficiency)
• For continuous state spaces, a coarse coding or tile coding can be effective

#### Types of Function Approximators

• Linear function approximations (linear combination of features)
• Neural Networks
• Decision Trees
• Nearest Neighbors
• Fourier/ wavelet bases

#### Finding an Optimal Value Function

When using a VFA, you can use a Stochastic Gradient Descent (SGD) method to search for the best weights for your value function according to experience.
This parametric form the value function will then be used to obtain a greedy or epsilon-greedy policy at run-time.

This is why using a VFA + SGD is still different from a Direct Policy Search approach where you optimize the parameters of the policy directly.

## Deep Learning Fundamentals

### Deep Learning

• Review, or learn, a bit about Deep Learning
• See videos and content from DKMA Course (ECE 657A)
• This youtube playlist is a targeted “Deep Learning Crash Course” ( #dnn-crashcourse-for-rl ) with just the essentials you’ll need for Deep RL.
• That course also has more detailed videos on Deep Learning which won’t be specifically useful for ECE 493, but which you can refer to if interested.

### Lect 9B - Deep Learning Introduction

In this video go over some of the fundamental concepts that led to neural networks (such as linear regression and logistic regression models), the basic structure and formulation of classic neural networks and the history of their development.

### Lect 11A - 1 - Deep Learning Fundamentals

This video goes through a ground level description of logistic neural units, classic neural networks, modern activation functions and the idea of a Neural Network as a Universal Approximator.

### Lect 11A - 1.2 - Deep Learning - Gradient Descent

In this video we discuss the nuts and bolts of how training in Neural Networks (Deep or Shallow) works as a process of incremental optimization of weights via gradient descent. Topics discussed: Backpropagation algorithm, gradient descent, modern optimizer methods.

### Lect11B - 1 - DeepLearning - Fundamentals II

In this video we go over the fundamentals of Deep Learning from a different angle using the approach from Goodfellow et. al.’s Deep Learning Textbook and their network graph notation for neural networks.

We describe the network diagram notation, and how to view neural networks in this way, focussing on the relationship between sets of weights and layers.

Other topics include: gradient descent, loss functions, cross-entropy, network output distribution types, softmax output for classification.

### Lect 11B - 2 - Deep Learning - Fundamentals III

This video continues with the approach from Goodfellow et. al.’s Deep Learning Textbook and goes into detail about computational methods, efficiency and defining the measure being used for optimization.

Topics covered include: relationship of network depth to generalization power, computation benefits of convolutional network structures, revisiting the meaning of backpropagation, methods for defining loss functions

### Lect 11B - 3 - Deep Learning - Regularization

In this lecture I talk about some of the problems that can arise when training neural networks and how they can be mitigated. Topics include : overfitting, model complexity, vanishing gradients, catastrophic forgetting and interpretability.

### Lect 11B - 4 - Deep Learning - Data Augmentation and Vanishing Gradients

In this video we give an overview of several approaches for making DNNs more usable when data is limited with respect to the size of the network. Topics include data augmentation, residual network links, vanishing gradients.

#### Tags

[SB 13.1, 13.2, 13.5]

• Policy Gradients
• Actor-Critic

### Policy Gradient Algorithms

Some of the posts used for lecture on July 26.

### Actor-Critic Algorithm

Very clear blog post on describing Actor-Critic Algorithms to improve Policy Gradients
https://www.freecodecamp.org/news/an-intro-to-advantage-actor-critic-methods-lets-play-sonic-the-hedgehog-86d6240171d/

### Cutting Edge Algorithms

Going beyond what we covered in class, here are some exciting trends and new advances in RL research in the past few years to find out more about.
PG methods are a fast changing area of RL research. This post has a number of the successful algorithms in this area from a few years ago:
https://lilianweng.github.io/lil-log/2018/04/08/policy-gradient-algorithms.html#actor-critic

### A3C/A2C Resources

• Blog from OpenAI introducing their implementation for A3C and analysis of how a simpler, non-parallalized version they call A2C is just as good:
• The original A3C paper from DeepMind:
• Good summary of these algorithms with cleaned up pseudocode and links:

## Evaluating RL Algorithms and Double DQN

• discussion of evaluation metrics for RL algorithms
• training hyper-parameters vs. algorithm parameters
• Double DQN bringing back the Double-Q-Learning idea and giving it new life to solve optimism bias

Note: the content listed in LEARN for the S22 offering are being updated more frequently and consistently with content than this list.

## Advanced Policy Gradient Methods using Trust Regions

• Trust Region Methods
• TRPO
• PPO

## DPG, DDGP and SAC

### Hypothesis: Original DDPG Paper - Lillicrap, ICLR, 2016

https://hyp.is/go?url=https%3A%2F%2Farxiv.org%2Fpdf%2F1509.02971.pdf&group=DM67BYBG

## Looking Ahead with Tree Search - MCTS and AlphaGo

• Monte-Carlo Tree Search (MCTS)
• How AlphaGo works (combining A2C and MCTS)

## RL Next Steps

• An overview next steps in learning more about RL research and applications
• Keep Reading: Conferences
Going Beyond: MARL, Hierarchical RL, Supervised and Curriculum Learning
• Find out about Big New Ideas: LeCun, DeepMind, OpenAI, Friston
• Get Involved: Competitions and OpenSource
• You can find the slides here: RL Next Steps

## Review and End of Classes

Week 13

See the RL Next Steps tree for what was discussed in class July 22, 2022.

## Final Exam

See LEARN for more information.

# E7 Elevator Pitch

## Defining the MDP

### States

• Elevators : $e_i\in E$ : $i \in \mathcal{R} \in[1,7]$
• Floors : $f \in \mathcal{Z} \in [1,8]$
• Location : $L(e_i) : E \rightarrow f$ - which floor is the elevator on?
• Outside Button: $b\in B^f_{i,dir} \in \{0,1\}; dir\in {up, down}$
• Movement: $M(e_i): E\rightarrow \{up, stopped,down\}$
• Doors: $G(e_i,f): E \times f \rightarrow \{closed, closing, opening, open\}$
• Next Floor: $NL(e_i) : E \rightarrow f \cup {stopped}$ - the next floor the elevator will arrive at, if the elevator is not currently moving, then this returns “stopped”.

### Actions

In general: move the elevators, open/close the doors in order to maximize your objective function

At every moment the system can take any of the following actions, we can assume they only happen one at a time

• Do nothing

• Open a door/Close a door : set $G(e_i,f)$

• Move an elevator up/down from current floor : set $M(e_i)$

• Stop an elevator at the current floor it is moving towards using $NL(e_i)$

## Dynamics

• Define dynamics

# Questions

## Does the system need to remember that it just closed a door?

• Should we define actions to be “close door and move to floor f”?

## How would Exploration/Exploitation Work in This Domain?

• how long are you willing to annoy users to get the information you need?
• can we build a simulator for this system?

# Primary References for Course

[SuttonBarto2018] - Reinforcement Learning: An Introduction. Book, free pdf of draft available.
http://incompleteideas.net/book/the-book-2nd.html

# Additional Resources

## Other Useful Textbooks

[Dimitrakakis2019] - Decision Making Under Uncertainty and Reinforcement Learning

http://www.cse.chalmers.se/~chrdimi/downloads/book.pdf
[Ghavamzadeh2016] - Bayesian Reinforcement Learning: A Survey. Ghavamzadeh et al. 2016.
https://arxiv.org/abs/1609.04436

## Deep Q Network vs Policy Gradients - An Experiment on VizDoom with Keras

A nice blog post on comparing DQN and Policy Gradient algorithms such A2C.
https://flyyufelix.github.io/2017/10/12/dqn-vs-pg.html

## Open AI Reference Website

This website is a great resource. It lays out concepts from start to finish. Once you get through the first half of our course, many of the concepts on this site will be familiar to you.

### Key Papers in Deep RL List

https://spinningup.openai.com/en/latest/spinningup/keypapers.html

### Fundamental RL Concepts Overview

The fundamentals of RL are briefly covered here. We will go into all this and more in detail in our course.
https://spinningup.openai.com/en/latest/spinningup/rl_intro.html

### Family Tree of Algorithms

Here, a list of algorithms at the cutting edge of RL as of 1 year ago to so, so it’s a good place to find out more. But in a fast growing field, it may be a bit out of date about the latest now.
https://spinningup.openai.com/en/latest/spinningup/rl_intro2.html

## Reinforcement Learning Tutorial with Demo on GitHub

This is a thorough collection of slides from a few different texts and courses laid out with the essentials from basic decision making to Deep RL. There is also code examples for some of their own simple domains.
https://github.com/omerbsezer/Reinforcement_learning_tutorial_with_demo#ExperienceReplay

# Old Topics Archive

Other resources connected with previous versions of the course, I’m happy to talk about any of these if people are interested.

## Bayes Nets (dropped)

### Tools

SamIam Bayesian Network GUI Tool

Other Tools

### References

Some videos and resources on Bayes Nets, d-seperation, Bayes Ball Algorithm and more:
https://metacademy.org/graphs/concepts/bayes_ball

## Primary References for Probabilistic Reasoning (mostly dropped)

[Ermon2019] - First half of notes are based on Stanford CS 228 (https://ermongroup.github.io/cs228-notes/) which goes even more into details on PGMs than we will.

[Cam Davidson 2018] - Bayesian Methods for Hackers - Probabilistic Programming textbook as set of python notebooks.
https://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/#contents

[Koller, Friedman, 2009] Probabilistic Graphical Models : Principles and Techniques
The extensive theoretical book on PGMs.
https://mitpress.mit.edu/books/probabilistic-graphical-models


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20 Jan 2021

Angle at circumference: Angles subtended by the same chord are equal. You know that, when two lines are parallel, then a transversal gives rise to equal corresponding angles, equal alternate interior angles, and co-interior angles being supplementary. Alternate angles on parallel lines are equal. Stay Home , Stay Safe and keep learning!!! Co-interior angles add up to 180°. Share with your friends. The following figures give the some examples of co-interior angles. We are told in the question that . Euclid's Proposition 28 extends this result in two ways. Axiom 3: If a transversal intersects two parallel lines, then each pair of corresponding angles is equal. When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent. Co-interior angles add up to 180°. How to identify Alternate Interior Angles? ∴ x + 44° = 180° [Co-interior angles] ⇒ x = 180° – 44° ⇒ x = 136° Question 7. If it is stated as a 'regular octagon', the interior angles will all be the same (135 degrees in the case of an octagon). Alternate Interior Angles Equal Means Parallel Lines Theorem Solved 1 The Alternate Interior Angle Theorem States If 1 The Alternate Interior Angle Theorem States If Chegg Com Alternate Interior Angles Examples Geometry Concepts You READ Shower Curtains Bed Bath And Beyond. Example 7. In this section we will discuss about exterior and interior angles of triangle … The non-parallel case. In the above-given figure, you can see, two parallel lines are intersected by a transversal. … When a transversal intersects two lines, the two lines are parallel if and only if interior angles on the same side of the transversal and exterior angles on the same side of the transversal are supplementary (sum to 180°).. The Z-shape shows alternate interior angles. E-learning is the future today. The lines make a Z shape which can also be back to front. The lines make a Z shape. Is it necessary that each of these angles will lie a right angle? They are called co-interior angles or allied angles. Conversely, If any two lines are cut by a transversal such that Properly aligned spreaders should create equal angles. When 2 lines are cut by a third line that is a transversal, then the angle between the pair of lines on the same side of transversal are called co-interior angles. Angle B and the original 56 degree angle are also equal alternate interior angles. Here, Exterior angles are ∠1, ∠2, ∠7 and ∠8 Interior angles are ∠3, ∠4, ∠5 and ∠6 Corresponding angles are always equal. Hence, it is proved that the opposite angles of a parallelogram are equal. You may have guessed that exterior angles are on the outside of a triangle, but it's a little more specific than just that.An exterior angle must form a linear pair with an interior angle.This means that the exterior angle must be adjacent to an interior angle (right next to it - they must share a side) and the interior and exterior angles form a straight line (180 degrees). The interior angles will always add up to 1080 degrees, but the angles do not have to have the same value. To help you remember: the angle pairs are on Alternate sides of the Transversal, and they are on the Interior of the two crossed lines.. Note The interior angles only add to 180° when the triangle is planar, meaning it is lying on a flat plane. (butterfly shape) Opposite angles of cyclic quadrilateral: Equal: Exterior angle of cyclic quadrilateral: The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle. Checking for parallel lines. Allied (or co-interior) angles are supplementary. (Click on "Alternate Interior Angles" to have them highlighted for you.) In the above diagrams, d and e are Justify your answer. A bevel gauge, though primarily a carpenter’s tool, can be handy to have aboard. Are co interior angles equal? Step 2: Concentrate on first. Therefore, $${\angle 1}$$ and $${\angle 2}$$ are co-interior angles and they are supplementary. Therefore, ∠B = ∠D and ∠A=∠C. Vertically opposite angles are always equal. Example, if you want to have equal angles, you have to have a shape that has equal sides. Alternate Interior Angles Definition. We can see that the angle marked is corresponding to the angle of . We know that alternate interior angles are equal. An introduction to alternate, corresponding and co-interior angles in parallel lines. Because the interior angles always add to 180°, every angle must be less than 180° The bisectors of the three interior angles meet at a point, called the incenter, which is the center of the incircle of the triangle. Alternate angles are equal. In illustration one of the example section above, LINE 1 and LINE 2 are parallel and both interior and exterior angles on the same side of the transversal are … Exterior Angle Theorem – Explanation & Examples. Covid-19 has led the world to go through a phenomenal transition . $(1)$ Suppose Co-interior property is known then the sum of angles on the same side is $180^\circ$ if one angle is $\theta$ then the co-interior angle is $180^\circ-\theta$ then the corresponding angles must equal by using linear pair property. If the lines AB and CD are parallel, then it is obvious that the co-interior angles are not equal but it turns out that they are supplementary , that is, their sum is 180 ° . These angles are called alternate interior angles. By ASA congruence criterion, two triangles are congruent to each other. The Alternate Interior Angles Theorem states that. Use the information given in the diagram to find: a. u b. v c. w d. x e. y. One way to find the alternate interior angles is to draw a zig-zag line on the diagram. Alternate angles are equal. ∠1 = ∠4 ∠2 = ∠3. j 1 k 5 180° Corresponding angles are equal. Then one of the alternate angles is an exterior angle equal to the other angle which is an opposite interior angle in the triangle. It can be used to verify, compare, and transfer angles, or bevels. So, we all know that a triangle is a 3-sided figure with three interior angles. The angles which are formed inside the two parallel lines, when intersected by a transversal, are equal to its alternate pairs. In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Share 1. Solution: Key Terms. The Consecutive Interior Angles Theorem states that if two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. If the lines are parallel then they add up to to 180. But there exist other angles outside the triangle which we call exterior angles.. We know that in a triangle, the sum of all three interior angles is always equal to 180 degrees. This contradicts Proposition 16 which states that an exterior angle of a triangle is always greater than the opposite interior angles. The two angles lie on the inside of a pair of parallel lines. Co-interior angles on parallel lines add up to . And the inside angle at each vertex of a polygon is always equal to (180° – deflection angle), because (new direction – old direction) + (reverse direction – new direction) = (reverse direction – old direction), which is always 180°. e 5 f g 5 h The lines make an F shape. Why is the sum of the interior angles of a triangle equal to 180? The Co-interior angles also called as consecutive angles or allied interior angles. co- interior angles are on a straight line and add up to 180 degrees. In the case of rigging, a bevel gauge can be used to compare the angle formed by the shroud and the spreader both above and below the spreader. Step 3: Use the corresponding angles. View solution. You will be able to identify different angle pairs, and then use your knowledge to help you work out unknown angles in geometric figures. ... Alternate angles. Question 8. As you move A or B, you will see that the interior angles add to … This video is an explanation of the types of angles formed by a TRANSVERSAL line through two PARALLEL lines. When the two lines being crossed are Parallel Lines the Alternate Interior Angles are equal. If A, B and C are interior angles of a ΔABC then cos(B+C/2) is equal to - 29254289 Exterior and Interior Angles of Triangle. Drag point P or Q to make the lines non-parallel. This holds true for any 'regular' polygon. Two angles are said to be Co-exterior angles if they are exterior angles and lies on same side of the transversal. If the transversal cuts across lines that are not parallel, the interior angles still add up to a constant angle, but the sum is not 180°. You will come to understand what is meant by vertically opposite angles, corresponding angles, alternate angles and co-interior angles. Solution: No, because each of the two adjacent angles will be right angles only if they will form a linear pair. Co-interior Angles Finally, in each diagram below, the two marked angles are called co-interior angles and lie on the same side of the transversal. So in the below figure ( ∠4, ∠5) , ( ∠3, ∠6) are Co-interior angles or consecutive angles or allied interior angles. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length.The rhombus is often called a diamond, after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a … Two adjacent angles are equal. What is the sum of angles at a point? Exterior Angle Property of a Triangle An exterior angle of a triangle is always equal to the sum of the opposite interior angles. So, by the Alternate Interior Angles Theorem, the lines cut by the transversal must be parallel. An octagon is an eight-sided polygon. Lines and Angles Parallel Lines And A Transversal. Angles around a point add up to 360°. Parallel Lines. Same-Side Interior Angles: In geometry, same-side interior angles are angles that are formed when two lines are cut by a transversal, such that they are inside the lines and they are both on … If b + c = 3 a then cot 2 B ⋅ cot 2 C has the value equal to? 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format: plain


text:
Opuscula Math. 26, no. 1 (2006), 5-12

Opuscula Mathematica

# Bounds on the 2-domination number in cactus graphs

Mustapha Chellali

Abstract. A $$2$$-dominating set of a graph $$G$$ is a set $$D$$ of vertices of $$G$$ such that every vertex not in $$S$$ is dominated at least twice. The minimum cardinality of a $$2$$-dominating set of $$G$$ is the $$2$$-domination number $$\gamma_{2}(G)$$. We show that if $$G$$ is a nontrivial connected cactus graph with $$k(G)$$ even cycles ($$k(G)\geq 0$$), then $$\gamma_{2}(G)\geq\gamma_{t}(G)-k(G)$$, and if $$G$$ is a graph of order $$n$$ with at most one cycle, then $$\gamma_{2}(G)\geqslant(n+\ell-s)/2$$ improving Fink and Jacobson's lower bound for trees with $$\ell>s$$, where $$\gamma_{t}(G)$$, $$\ell$$ and $$s$$ are the total domination number, the number of leaves and support vertices of $$G$$, respectively. We also show that if $$T$$ is a tree of order $$n\geqslant 3$$, then $$\gamma_{2}(T)\leqslant\beta(T)+s-1$$, where $$\beta(T)$$ is the independence number of $$T$$.

Keywords: 2-domination number, total domination number, independence number, cactus graphs, trees.

Mathematics Subject Classification: 05C69.

Full text (pdf)

• Mustapha Chellali
• University of Blida, Department of Mathematics, B.P. 270, Blida, Algeria


text:
# Could you please answer it please with show work thanks QUESTION 1 Parametric equations and a...

###### Question:

with show work
thanks

QUESTION 1 Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion. x = 36+ 2 y = 6t. Stse y=x2 1++++
Entire parabola, left to right (from second quadrant to origin to first quadrant) Entire parabola, bottom to top from fourth quadrant to origin to first quadrant) x=y2 kit Entire parabola, top to bottom (from first quadrant to origin to fourth quadrant) yox? Entire parabola, right to left from first quadrant to origin to second quadrant)

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text:
# XSweet Core

The purpose of XSweet Core is to extract the underlying XML from Word documents (.docx) into valid, clean, and reusable HTML. XSweet Core extracts and saves “important” information from the .docx, such as:

• Font type and size
• Formatting, including bold, italic, underlining, text justification (left, right, center), subscript/superscript, etc.
• Paragraph indentation
• Endnotes and footnotes
• Outline and list levels

After initially extracting selected information, XSweet Core removes the (voluminous) extra noise in the XML, combines similar tags, abstracts away inline or repetitive formatting where possible, and rewrites word-specific feature implementations for HTML (e.g. notes, lists).

From an inscrutable mess comes good, clean, and human readable HTML.

## Pipeline#

Initial extraction is achieved by running the docx-extract/EXTRACT-docx.xsl sheet, which in turn runs the following sequence of steps:

1. docx-extract/docx-html-extract.xsl
• which also runs docx-extract/docx-table-extract.xsl
2. docx-extract/handle-notes.xsl
3. docx-extract/scrub.xsl
4. docx-extract/join-elements.xsl
5. docx-extract/collapse-paragraphs.xsl

Running the EXTRACT-docx.xsl sheet has exactly the same effect as running these five sheets in sequence, using each step’s output as the input for the next.

Next, list-promote/PROMOTE-lists.xsl creates HTML representations of lists.

The math sheet, xsweet_tei_omml2mml.xsl captures math and equations added in Word.

Finally, run html-polish/final-rinse.xsl for additional cleanup to the HTML file.

Note that the outputs of all of these steps technically produce XHTML, not true HTML. This is expedient for chaining transformation steps into a pipeline. You may want to serialize to HTML5 as the final step (see html5-serialize.xsl, although it is not recommended to do so until all other desired transformations are finished.

## Initial extraction#

##### docx-html-extract.xsl#

This sheet does the heaving lifting of extracting information from the MS Word XML. Contents are extracted from the body of the .docx. Information from headers and footers is not currently extracted.

### File structure#

The contents of the HTML body section are wrapped in the following section containers:

•
: the main content of the file
•
: wraps all endnotes
•
: wraps all footnotes

### Formatting#

There is a surprising amount of redundant and conflicting information in Word’s XML, so it’s important to choose the right level from which to extract properties. Many properties can be specified either on the paragraph level or the text run level.

XSweet extracts the following properties from the paragraph-level (from inside <w:pPr> paragraph properties tags):

• Named Word styles
• MS Word outline level
• MS Word list level

Other formatting information specified on the paragraph level is ignored, as it is unreliable and often overridden by properties specified on the text run level (<w:rPr>). The following are extracted from the run level:

• Font family
• Font size
• Text alignment
• Font color
• Italicization, bolding, underline, sub- and superscript

Unless formatting in Word is achieved by applied styles (see below), formatting is extracted inline or as element-level CSS (
).

Inline elements preserved in HTML:

• Bold
• Italic
• Underline
• Subscript
• Superscript
• Line breaks

CSS properties captured include:

• font font-family
• font size font-size
• font-weight:boldnormal
• font-style: italic, normal
• text-decoration: underline, none
• font-variant: normal or small-caps
• text alignment text-align: left, right, center
• indentation text-indent, padding-left, padding-right
• margins margin-top, margin-bottom, margin-left, margin-right
• color color

The following pseudo-properties are also extracted:

• list level -xsweet-list-level: used for list extraction
• outline level -xsweet-outline-level: used to aid in heading detection

Be aware that XSweet extracts only what information is present in the Word XML. Some information, such as font type and size, etc., is not always explicitly defined in the XML. Word applies formatting from the default Normal style when no other style is specified. This can lead to some minor formatting inconsistencies.

#### Word styles#

Word styles are referenced by name inside the Word file’s main document.xml file, and defined in the styles.xml file in the same directory, which contains style formatting and property information. XSweet’s initial extraction captures applied Word styles as CSS class attributes, and extracts the relevant information from styles.xml into a CSS

Chapter Two

...

Note that formatting information is often repeated: both inline as style and from class - there is analytical value to having the CSS inline (e.g. for heading promotion.

Where they exist, hyperlinks from the Word document are preserved and passed through to the HTML as s. Link text formatting is preserved.

Internal-to-Word bookmarks are also extracted, although without additional processing (not provided by XSweet), they are merely placeholders and are removed during Editoria Typescript.

### Tables#

Tables are created by the docx-table-extract.xsl sheet. This sheet is invoked from inside the docx-html-extract.xsl sheet. It recreates Word tables in HTML, capturing:

• horizontal and vertical cell text alignment
• horizontally and vertically merged cells

Word table:

HTML recreation:

### Notes#

In the handle-notes.xsl step, both endnotes and footnotes are added to the end of the HTML document and linked to the note callouts in the text. Notes come from the MS Word document’s endnotes.xml and footnotes.xml files.

Endnotes and footnotes are indexed separately. Endnotes are listed first, referenced as sequential integers. Footnotes are ordered as alphabetical callouts (a-z, aa, ab, etc.), and listed at the end of the HTML file after endnotes.

Endnote and footnote references are normalized and dynamically ordered by this step, by order of appearance. For example, even if the first endnote in Word references is labeled “2”, the converted HTML will renumber it to “1”. Notes that are never referenced in the text are removed.

Endnotes are placed inside a
. Footnotes are placed inside a
. The extracted syntax is as follows:

1
 endnote

a
 footnote

The above code is the result of the docx-extract/handle-notes.xsl step. In the initial extraction, the  and  are left empty. The handle-notes.xsl step assigns each note sequential references.

### Images#

The initial extraction sheet (docx-extract/docx-html-extract.xsl) will insert image references to the location of the unzipped file. This feature relies on image files being available locally, with paths assembled assuming you’ve used the XSweet_runner_scripts and have left the source files and unzipped .docx directory in their original location.

## Further cleanups#

##### docx-extract/scrub.xsl#

Previous steps generally pass elements through, even if they haven’t seen them before. This step removes these extra tags as unhelpful for our purposes unless they are explicitly caught and passed through. Examples of tags removed include:

• position
• iCs
• lang
• vertAlign
• noProof
• kern

Empty inline elements are removed, as is formatting applied to whitespace only, such as tabs and spaces. CSS style properties are normalized and put in a consistent order.

##### docx-extract/join-elements.xsl#

This step combines strings of elements into one element when:

• More than one element of the same type occurs in a row, and
• The two tags have similar style attributes

This step does not combine runs of
s,
s, or <tab>s.

Example:

Part I: United and Divided

becomes

Part I: United and Divided

##### docx-extract/collapse-paragraphs.xsl#

In this step, inline formatting gets copied to the paragraph level wherever possible. Elements that contain only formatting information that can be expressed on the paragraph level are removed after the formatting has been moved (see the span in the example below). Example:

blue bold text

becomes

bold blue text

Note that inline styling information isn’t removed even if it is copied to a higher level. This allows maximum flexibility for further transformation, at the cost of a bit more “noise” in the HTML.

## Lists#

Lists are promoted according to the xsweet-list-level property, extracted from the MS Word <w:ilvl w:val=[integer]> property. Each list item becomes a
 with  a
 inside it. XSweet currently extracts all lists as unordered lists.

##### PROMOTE-lists.xsl#

A wrapper that runs mark-lists.xsl then itemize-lists.xsl in sequence

##### mark-lists.xsl#

Wraps elements that have the xsweet-list-level property in a wrapper to mark them as lists, grouping and nesting according to xsweet-list-level value.

##### itemize-lists.xsl#

Adds the
 and
 wrappers to the lists marked by the previous step.

Example mark-lists.xsl input:

top-level list item

nested list item

mark-lists.xsl output:

<xsw:list xmlns:xsw="http://coko.foundation/xsweet" level="0">

top-level list item

<xsw:list level="1">

nested list item

</xsw:list>
</xsw:list>

itemize-lists.xsl output:

top-level list item

nested list item

### Math#

##### xsweet_tei_omml2mml.xsl#

XSweet captures equations created with Word’s built-in equation tool (Office MathML format) and passes them through to the HTML as standard MathML. This features should “just work” with MS Word-native equations.

Not all browsers treat MathML exactly the same, but Javascript libraries such as MathJax can be used to standardize equation appearances. Also note that math in Word comes in many formats, not all of which are supported (LaTeX, MathType, images, etc.).

Math in Word:

Extracted MathML in Firefox:

### Final Rinse#

##### html-polish/final-rinse.xml#

The last step in the XSweet pipeline targeting HTML (except serialization to HTML if desired):

• Removes redundant inline tags (e.g. , , ) that are expressed instead as CSS style attributes
• Inserts placeholder comments into empty
s and
s to ensure they are retained
• Removes extraneous noise from endnote and footnote references
• When possible, removes redundant styling repeated on child elements

##### css-abstract#

An XSL sheet that attempts to abstract style information specified on HTML tags into classes with similar formatting. This sheet is experimental and not actively maintained. For our purposes, it turns out having style information specified at a lower level enables much better analysis in other steps (e.g. heading promotion).

##### html-analysis.xsl#

This sheet produces an analysis of the HTML document, including a tree structure and a count of the HTML elements.

### Serialization#

##### html-polish/html5-serialize.xsl#

Serializes an input into valid HTML5. The primary benefit is to help normalize errors that may have occurred in the conversion wherever possible. For example, this can catch orphaned closing HTML tags without an opening counterpart and insert one, preventing errors.

##### html-polish/xhtml-serialize.xsl#

serializes an input using XML syntax and HTML tags, nominally XHTML. As such it is syntactically well-formed, “standalone”, and suitable for further processing using an XML parser (although not necessarily valid to any particular XHTML schema).

##### produce-plaintext/plaintext.xsl#

This step simply reads an HTML or XML file in and output the contents as plain text.


text:
# Rational Numbers

Rational numbers are integers plus fractions.

In other words number is rational, if it can be written as fraction $\frac{{p}}{{q}}$ (we know that every integer ${m}$ can be written as fraction $\frac{{m}}{{1}}$).

So, -4, -10, 0, 2, 23, $-\frac{{4}}{{5}}$, $-{3}\frac{{2}}{{5}}$, $-\frac{{15}}{{7}}$, $\frac{{2}}{{3}}$, $\frac{{9}}{{4}}$, ${5}\frac{{10}}{{11}}$ are all rational numbers.

Thus, rational numbers include

Set of rational numbers, i.e. group of rational numbers, is denoted by $\mathbb{Q}$.


text:
# Goodness of fit test - overview

This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the right-hand column. To practice with a specific method click the button at the bottom row of the table

Goodness of fit test
Binomial test for a single proportion
Independent variableIndependent variable
NoneNone
Dependent variableDependent variable
One categorical with $J$ independent groups ($J \geqslant 2$)One categorical with 2 independent groups
Null hypothesisNull hypothesis
• H0: the population proportions in each of the $J$ conditions are $\pi_1$, $\pi_2$, $\ldots$, $\pi_J$
or equivalently
• H0: the probability of drawing an observation from condition 1 is $\pi_1$, the probability of drawing an observation from condition 2 is $\pi_2$, $\ldots$, the probability of drawing an observation from condition $J$ is $\pi_J$
H0: $\pi = \pi_0$

Here $\pi$ is the population proportion of 'successes', and $\pi_0$ is the population proportion of successes according to the null hypothesis.
Alternative hypothesisAlternative hypothesis
• H1: the population proportions are not all as specified under the null hypothesis
or equivalently
• H1: the probabilities of drawing an observation from each of the conditions are not all as specified under the null hypothesis
H1 two sided: $\pi \neq \pi_0$
H1 right sided: $\pi > \pi_0$
H1 left sided: $\pi < \pi_0$
AssumptionsAssumptions
• Sample size is large enough for $X^2$ to be approximately chi-squared distributed. Rule of thumb: all $J$ expected cell counts are 5 or more
• Sample is a simple random sample from the population. That is, observations are independent of one another
• Sample is a simple random sample from the population. That is, observations are independent of one another
Test statisticTest statistic
$X^2 = \sum{\frac{(\mbox{observed cell count} - \mbox{expected cell count})^2}{\mbox{expected cell count}}}$
Here the expected cell count for one cell = $N \times \pi_j$, the observed cell count is the observed sample count in that same cell, and the sum is over all $J$ cells.
$X$ = number of successes in the sample
Sampling distribution of $X^2$ if H0 were trueSampling distribution of $X$ if H0 were true
Approximately the chi-squared distribution with $J - 1$ degrees of freedomBinomial($n$, $P$) distribution.

Here $n = N$ (total sample size), and $P = \pi_0$ (population proportion according to the null hypothesis).
Significant?Significant?
• Check if $X^2$ observed in sample is equal to or larger than critical value $X^{2*}$ or
• Find $p$ value corresponding to observed $X^2$ and check if it is equal to or smaller than $\alpha$
Two sided:
• Check if $X$ observed in sample is in the rejection region or
• Find two sided $p$ value corresponding to observed $X$ and check if it is equal to or smaller than $\alpha$
Right sided:
• Check if $X$ observed in sample is in the rejection region or
• Find right sided $p$ value corresponding to observed $X$ and check if it is equal to or smaller than $\alpha$
Left sided:
• Check if $X$ observed in sample is in the rejection region or
• Find left sided $p$ value corresponding to observed $X$ and check if it is equal to or smaller than $\alpha$
Example contextExample context
Is the proportion of people with a low, moderate, and high social economic status in the population different from $\pi_{low} = 0.2,$ $\pi_{moderate} = 0.6,$ and $\pi_{high} = 0.2$?Is the proportion of smokers amongst office workers different from $\pi_0 = 0.2$?
SPSSSPSS
Analyze > Nonparametric Tests > Legacy Dialogs > Chi-square...
• Put your categorical variable in the box below Test Variable List
• Fill in the population proportions / probabilities according to $H_0$ in the box below Expected Values. If $H_0$ states that they are all equal, just pick 'All categories equal' (default)
Analyze > Nonparametric Tests > Legacy Dialogs > Binomial...
• Put your dichotomous variable in the box below Test Variable List
• Fill in the value for $\pi_0$ in the box next to Test Proportion
JamoviJamovi
Frequencies > N Outcomes - $\chi^2$ Goodness of fit
• Put your categorical variable in the box below Variable
• Click on Expected Proportions and fill in the population proportions / probabilities according to $H_0$ in the boxes below Ratio. If $H_0$ states that they are all equal, you can leave the ratios equal to the default values (1)
Frequencies > 2 Outcomes - Binomial test
• Put your dichotomous variable in the white box at the right
• Fill in the value for $\pi_0$ in the box next to Test value
• Under Hypothesis, select your alternative hypothesis
Practice questionsPractice questions


text:
# The volume of a right circular cone is $9856 \mathrm{~cm}^{3}$.

Question.

The volume of a right circular cone is $9856 \mathrm{~cm}^{3}$. If the diameter of the base is $28 \mathrm{~cm}$, find

(i) height of the cone

(ii) slant height of the cone

(iii) curved surface area of the cone

$\left[\right.$ Assume $\left.\pi=\frac{22}{7}\right]$

Solution:

(i) Radius of cone $=\left(\frac{28}{2}\right) \mathrm{cm}=14 \mathrm{~cm}$

Let the height of the cone be h.

Volume of cone $=9856 \mathrm{~cm}^{3}$

$\Rightarrow \frac{1}{3} \pi r^{2} h=9856 \mathrm{~cm}^{3}$

$\Rightarrow\left[\frac{1}{3} \times \frac{22}{7} \times(14)^{2} \times h\right] \mathrm{cm}^{2}=9856 \mathrm{~cm}^{3}$

$h=48 \mathrm{~cm}$

Therefore, the height of the cone is $48 \mathrm{~cm}$.

(ii) Slant height ( $l$ ) of cone $=\sqrt{r^{2}+h^{2}}$

$=\left[\sqrt{(14)^{2}+(48)^{2}}\right] \mathrm{cm}$

$=[\sqrt{196+2304}] \mathrm{cm}$

$=50 \mathrm{~cm}$

Therefore, the slant height of the cone is $50 \mathrm{~cm}$.

(iii) CSA of cone $=\pi r$

$=\left(\frac{22}{7} \times 14 \times 50\right) \mathrm{cm}^{2}$

$=2200 \mathrm{~cm}^{2}$

Therefore, the curved surface area of the cone is $2200 \mathrm{~cm}^{2}$.

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text:
## The Annals of Statistics

### Adapting to unknown sparsity by controlling the false discovery rate

#### Abstract

We attempt to recover an n-dimensional vector observed in white noise, where n is large and the vector is known to be sparse, but the degree of sparsity is unknown. We consider three different ways of defining sparsity of a vector: using the fraction of nonzero terms; imposing power-law decay bounds on the ordered entries; and controlling the p norm for p small. We obtain a procedure which is asymptotically minimax for r loss, simultaneously throughout a range of such sparsity classes.

The optimal procedure is a data-adaptive thresholding scheme, driven by control of the false discovery rate (FDR). FDR control is a relatively recent innovation in simultaneous testing, ensuring that at most a certain expected fraction of the rejected null hypotheses will correspond to false rejections.

In our treatment, the FDR control parameter qn also plays a determining role in asymptotic minimaxity. If q=lim qn∈[0,1/2] and also qn>γ/log(n), we get sharp asymptotic minimaxity, simultaneously, over a wide range of sparse parameter spaces and loss functions. On the other hand, q=lim qn∈(1/2,1] forces the risk to exceed the minimax risk by a factor growing with q.

To our knowledge, this relation between ideas in simultaneous inference and asymptotic decision theory is new.

Our work provides a new perspective on a class of model selection rules which has been introduced recently by several authors. These new rules impose complexity penalization of the form 2⋅log(potential model size/actual model sizes). We exhibit a close connection with FDR-controlling procedures under stringent control of the false discovery rate.

#### Article information

Source
Ann. Statist., Volume 34, Number 2 (2006), 584-653.

Dates
First available in Project Euclid: 27 June 2006

https://projecteuclid.org/euclid.aos/1151418235

Digital Object Identifier
doi:10.1214/009053606000000074

Mathematical Reviews number (MathSciNet)
MR2281879

Zentralblatt MATH identifier
1092.62005

Subjects
Primary: 62C20: Minimax procedures
Secondary: 62G05: Estimation 62G32: Statistics of extreme values; tail inference

#### Citation

Abramovich, Felix; Benjamini, Yoav; Donoho, David L.; Johnstone, Iain M. Adapting to unknown sparsity by controlling the false discovery rate. Ann. Statist. 34 (2006), no. 2, 584--653. doi:10.1214/009053606000000074. https://projecteuclid.org/euclid.aos/1151418235

#### References

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• Birgé, L. and Massart, P. (2001). Gaussian model selection. J. Eur. Math. Soc. 3 203--268.
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• Donoho, D. L. and Johnstone, I. M. (1994). Minimax risk over $\ell_p$-balls for $\ell_q$-error. Probab. Theory Related Fields 99 277--303.
• Donoho, D. L. and Johnstone, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 90 1200--1224.
• Donoho, D. L., Johnstone, I. M., Hoch, J. C. and Stern, A. S. (1992). Maximum entropy and the nearly black object (with discussion). J. Roy. Statist. Soc. Ser. B. 54 41--81.
• Donoho, D. L., Johnstone, I. M., Kerkyacharian, G. and Picard, D. (1995). Wavelet shrinkage: Asymptopia? (with discussion). J. Roy. Statist. Soc. Ser. B 57 301--369.
• Efron, B. (1986). How biased is the apparent error rate of a prediction rule? J. Amer. Statist. Assoc. 81 461--170.
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• Hochberg, Y. and Tamhane, A. (1987). Multiple Comparison Procedures. Wiley, New York.
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• Huang, J. and Mumford, D. (1999). Statistics of natural images and models. In Proc. IEEE Computer Society Conference on Computer Vision and Pattern Recognition 1 541--547.
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• Johnstone, I. M. and Silverman, B. W. (2004). Needles and straw in haystacks: Empirical Bayes estimates of possibly sparse sequences. Ann. Statist. 32 1594--1649.
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• Pollard, D. (1984). Convergence of Stochastic Processes. Springer, New York.
• Ruderman, D. L. (1994). The statistics of natural images. Network: Computation in Neural Systems 5 517--548.
• Sarkar, S. K. (2002). Some results on false discovery rate in stepwise multiple testing procedures. Ann. Statist. 30 239--257.
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• Seeger, P. (1968). A note on a method for the analysis of significances en masse. Technometrics 10 586--593.
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• Simes, R. (1986). An improved Bonferroni procedure for multiple tests of significance. Biometrika 73 751--754.
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text:
How do you simplify 5sqrt8+2sqrt18?

Sep 5, 2017

Arrange the equation. The answer is $16 \sqrt{2}$

Explanation:

$\sqrt{25 \times 8} + \sqrt{4 \times 18}$

$= \sqrt{100 \times 2} + \sqrt{36 \times 2}$

$= 10 \sqrt{2} + 6 \sqrt{2}$

$= 16 \sqrt{2}$

$16 \sqrt{2}$


text:
发布时间: 2018-06-16 摘要点击次数: 全文下载次数: DOI: 10.11834/jig.170481 2018 | Volume 23 | Number 6 图像分析和识别

 收稿日期: 2017-08-23; 修回日期: 2017-12-19 基金项目: 国家自然科学基金面上项目（61672202）；中国博士后基金项目（2014M561817） 第一作者简介: 杨娟(1983-), 女, 讲师, 2012年于合肥工业大学获计算机应用技术专业博士学位, 主要研究方向为深度学习、智能信息处理等。E-mail:yangjuan@hfut.edu.cn. 中图法分类号: TP391 文献标识码: A 文章编号: 1006-8961(2018)06-0837-09

# 关键词

Fine-grained car recognition method based on region proposal networks
Yang Juan, Cao Haoyu, Wang Ronggui, Xue Lixia, Hu Min
School of Computer and Information, Hefei University of Technology, Hefei 230009, China
Supported by: National Natural Science Foundation of China (61672202)

# Abstract

Objective Over the past few decades, studies on visual object recognition have mostly focused on the category level, such as ImageNet Large-scale Visual Recognition Challenge and PASCAL VOC challenge. With the powerful feature extraction of convolutional neural networks (CNNs), many studies have begun to focus on challenging visual tasks aimed at the subtle classification of subcategories, which is called fine-grained visual pattern recognition. Fine-grained car model recognition is designed to recognize the exact make, model, and year of a car from an arbitrary viewpoint, which is essential in intelligent transportation, public security, and other fields. Research on this field mainly includes three aspects: finding and extracting features of discriminative parts, using the alignment algorithm or 3D object representations to eliminate the effects of posture and angle, and looking for powerful feature extractors such as CNN features. The three methods presented have various degrees of defect, the bottleneck of most part-based models is accurate part localization, and methods generally report adequate part localization only when a known bounding box at test time is given. 3D object representations and many other alignment algorithms need complex preprocessing or post-processing of training samples, such as co-segmentation and 3D geometry estimation. Currently, methods based on CNNs significantly outperform those of previous works, which rely on handcrafted features for fine-grained classification, but the location of objects is essential even at test time due to the subtle difference between categories. These methods are difficult to apply in real intelligent transportation because a video frame in a real traffic monitoring scenario typically shows multiple cars in which each car object and parts cannot be assigned with a bounding box. To solve these problems, the present study proposes a fine-grained car recognition method based on deep fully CNNs called region proposal network (RPN), which automatically proposes regions of discriminative parts and car objects. Our method can be trained in an end-to-end manner and without requiring a bounding box at test time. Method RPN is a type of fully CNN that simultaneously predicts object bounding box and scores at each position, which has made remarkable achievements in the field of object detection. We improve RPN with an outstanding deep CNN called deep residual network (ResNet). First, the deep convolution feature of the image is extracted by the ResNet pipeline. Then, we slide a small network over the convolutional feature map and each sliding window is mapped to a low-dimensional vector. The vector is fed into a box-regression layer and box-classification layer; the former outputs the probability of a region, which includes an object, whereas the latter outputs the coordinates of the region by bounding-box regression. Finally, these object regional candidates obtain the specific category and corrected object position through the object detection network and the final recognition result through the non-maximal suppression algorithm. To quickly optimize the model parameters, we use the ImageNet pre-training model to initialize the RPN and object detection network and then share convolutional features between them through joint optimization. Result First, we verify the performance of the proposed method on several public fine-grained car datasets. Stanford BMW-10 dataset has 512 pictures, including 10 BMW serials. However, most CNNs suffered from over-fitting and thus obtained poor results due to the limit of training samples. The Stanford Cars-196 dataset is currently the most widely used dataset for fine-grained car recognition, with 16185 images of 196 fine-grained car models covering SUVs, coupes, convertibles, pickup trucks, and trucks, to name a few. Second, apart from using the public dataset, we conduct the recognition experiment under a real traffic monitoring video. Finally, we carefully analyze the misrecognized samples of our models to explore the improved room of fine-grained methods. Recognition accuracy could be significantly improved by training data augmentation, and all our experiments only use image horizontal flip as data augmentation to compare with other methods with the same standard. The recognition accuracy of this method is 76.38% in the Stanford BMW-10 dataset and 91.48% in the Stanford Cars-196 dataset. The method also achieves excellent recognition effect in a traffic monitoring video. In particular, our method is trained in an end-to-end manner and requires no knowledge of object or part bounding box at test time. The RPN provides not only an object detection network with the specific location of the car object but also the distinguishable region, which contributes to the classification. The misrecognized samples are mostly at the same makes, which have tiny visual difference. Methods based on handcrafted global feature templates, such as HOG, achieve 28.3% recognition accuracy on the Stanford BMW-10 dataset. The most valuable 3D object representations, which trains from 59040 synthetic images, achieves 76.0% less accuracy than that of our methods. The state-of-the-art method of the Stanford Car-196 dataset without bounding-box annotation is recurrent attention CNN, which is published on CVPR2017 and achieved 92.5% recognition accuracy by combining features at three scales via a fully connected layer. Experiments show that our method not only outperforms significantly traditional methods based on handcrafted feature but is also comparable with the current state-of-the-art methods. Conclusion We introduce a new deep learning method, which is used in fine-grained car recognition, that overcomes the dependence of the traditional object recognition on the object location and can realize the recognition of cars under complex scenes, such as multiple vehicles and dense vehicles with high accuracy. The findings of this study can provide new ideas for fine-grained object recognition. Compared with traditional methods, the proposed model is better in terms of robustness and practicability.

# Key words

deep learning; convolutional neural networks; car recognition; fine-grained recognition; image classification

# 0 引言

2012年，Krizhevsky等人[4]通过深层卷积神经网络大幅提高了大规模图像数据集的识别精度，此后深度学习尤其是卷积神经网络在计算机视觉各个领域逐渐成为常态。Yang等人[5]通过ImageNet预训练的深层卷积神经网络模型提取车辆特征并分类，在大型车辆数据集上取得较好的识别结果。该方法充分利用了卷积神经网络的特征提取能力，不足是没有针对细粒度分类视觉差异主要集中在局部区域的特点进行优化。Krause等人[6]通过协同分割及对齐图像寻找具有区分度的局部区域，然后通过卷积神经网络提取特征并分类。但是该方法进行了大量的预处理，过程较为复杂。上述各方法均将区域定位以及特征提取作为两个独立的过程，忽略了区域定位和特征提取之间的相关性。Fu等人[7]提出循环注意力卷积神经网络(RACNN)通过互相强化的方式对区域定位和特征表征进行学习，由粗到细地迭代生成区域注意力，通过端到端的训练方式大幅提高了细粒度分类任务的识别精度。

# 2 细粒度车型识别网络结构

Faster RCNN[13](faster regions with convolutional neural network features)是一种极为优秀的目标检测框架，其首先通过CNN提取目标的深层卷积特征，之后通过区域建议网络[13] (RPN)产生目标的区域候选及区域评分，然后通过感兴趣区域池化(ROI pooling)将目标候选区域映射到对应的卷积特征，最后通过检测网络的分类及回归得到目标的具体类别以及修正后的目标位置。由于候选区域通常较多，且存在不同程度的重叠，网络通过非极大值抑制算法(NMS)获得目标的最终位置。本文通过ResNet-101改进了原始Faster RCNN的卷积特征提取器，使得网络具有更好的识别及检测性能以适用细粒度目标识别，网络结构如图 1所示，其中RPN使用的是卷积层4_23层特征，检测网络使用的是最后一层卷积层特征。

# 2.1 RPN

RPN是一种全卷积神经网络(FCN)，相比于经典CNN，FCN没有全连接层，因此可以接受任意尺寸的输入图片，并且可以通过反向传播算法(BP)进行端到端的训练。RPN以图像卷积映像(feature maps)为输入，通过滑动窗口在特征映像中滑窗并产生窗口固定尺寸的低维特征，在每个窗口位置，通过参照框(anchors)产生多尺寸及多比例的区域建议，然后通过分类层识别该区域为目标的概率，并通过区域回归层得到目标的粗略位置。

ResNet-101接受固定输入大小为224×224像素的图片，其卷积4_23层特征大小为14×14像素，特征维度为1 024，而相应的卷积4_23层步伐大小对应为原图的16个像素。为了得到更准确的目标位置，本文将图像保持长宽比放缩，使得短边长度为600像素。

 $\begin{array}{l} L(\{ {p_i}\} , \{ {t_i}\} ) = \frac{1}{{{N_{{\rm{cls}}}}}}\sum\nolimits_i {{L_{{\rm{cls}}}}({p_i}, {p_i}^*) + } \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\frac{\lambda }{{{N_{{\rm{reg}}}}}}\sum\nolimits_i {{p_i}^*{L_{{\rm{reg}}}}({t_i}, {t_i}^*)} \end{array}$ (1)

# 2.3 非极大值抑制算法

RPN是一种滑动窗口的形式，对于同一个目标可能会产生多个候选框，NMS算法旨在去除冗余的目标框。其算法流程如下：

1) 首先遍历所有的类别，对于每一类别下的类别得分大于阈值的目标框按照得分降序排列，并舍弃其他目标框。

2) 依次选中得分最高的目标框，并计算其余的框与该框的重叠面积(IoU)，若其$U_I$大于一定的阈值，则删除该框。

3) 从未处理的框中继续选一个得分最高的目标框，重复步骤2)，直至处理完所有的目标框。$U_I$计算方法为

 ${U_{A, B}} = \frac{{s\left( {\mathit{\boldsymbol{A}} \cap \mathit{\boldsymbol{B}}} \right)}}{{s\left( {\mathit{\boldsymbol{A}} \cup \mathit{\boldsymbol{B}}} \right)}}$ (5)

# 3.1 实验细节

Stanford BMW-10数据集包含宝马10个车系的各个角度图片，每类车型训练集约25幅。由于训练样本较少，类别之间差异极小，其难度也较高。而深度学习方法通常会因过拟合而难以取得较好的识别效果。

Stanford Cars-196是目前细粒度车型识别领域使用最为广泛的数据集，该数据集包含197类常见车辆型号，涵盖轿车、SUV、货车、跑车等诸多类型共16 185幅图片。

# 3.2 BMW-10数据集实验结果

Table 1 Comparison results on BMW-10 dataset

 方法 BMW-10/% 水平翻转/% HOG [15] 28.3 - SPM [1] 52.8 66.1 BB [2] 58.7 69.3 SPM-3D-L [3] 58.7 67.3 BB-3D-G [3] 66.1 76.0 CaffeNet [14] 48.43 58.27 GoogleNet [8] - 41.34 本文方法 - 76.38

# 3.3 Cars-196实验结果

Table 2 Comparison results on BMW-10 dataset

 方法名称 识别准确率/% HAR-CNN [16] 80.8 FV-CNN [17] 85.7 DVAN [18] 87.1 FCAN [19] 89.1 B-CNN [20] 91.3 RA-CNN [7] 92.5 本文方法 91.48

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# Limit of the Euler totient function

1. Apr 22, 2013

### henpen

My question is relatively breif: is it true that

$$\displaystyle \lim_{n \rightarrow \infty}(\varphi(n))=\lim_{n \rightarrow \infty}(n) \cdot \prod_{i=1}^{\infty}(1-\frac{1}{p_i})$$
Where $p$ is prime? Pehaps $\varphi(n)$ is too discontinuous to take the limit of, but it would seem that as it increases to infinity the function should tend to infinity, with fewer anomalies.

If this were true,

$$\displaystyle \zeta(1)=\frac{1}{ \prod_{i=1}^{\infty}(1-\frac{1}{p_i})}=\frac{1}{\lim_{n \rightarrow \infty}(\frac{\varphi(n)}{n})}=\lim_{n \rightarrow \infty}(\frac{n}{\varphi(n)})$$

2. May 3, 2013

### Mandelbroth

Let $\mathfrak{P}_n$ be the set of all distinct prime divisors of a number n.
Consider that $\displaystyle \varphi(n) = n \prod_{i=1}^{\sharp\mathfrak{P}_n}\left[1-\frac{1}{p_i}\right]$, where $\sharp\mathfrak{P}_n$ is the cardinality of $\mathfrak{P}_n$ and $p_i$ is the ith element of $\mathfrak{P}_n$. As n increases, its number of prime factors tends to increase, but this trend is in no way strictly true for individual numbers. An example of a relatively large number that does not have a large number of prime factors is 87178291199, which has only one prime factor. :tongue:

Thus, using basic properties of limits, your formula should be correct.

3. May 4, 2013

### henpen

The problem I has was that if particular numbers are 'discontinuous' from the general trend, you can't take the limit, even if the general trend tends to infinity.

4. May 4, 2013

### Mandelbroth

Consider a function $f: \mathbb{R}\rightarrow\mathbb{R}\cup\left\{Tootsiepop\right\}$, where, for $x\in\mathbb{R}$, $f(x)=\left\{\begin{array} , x , x\neq2 \\ Tootsiepop , x=2 \end{array}\right.$

As x approaches 2, f(x) approaches 2. However, f(2)=Tootsiepop.

This is not a continuous function, but the limit as x approaches 2 is defined. So, I don't understand what you mean...

5. May 4, 2013

### henpen

The example cleared up a lot, thanks. I've little formal experience with limits.


text:
Tags: web pollution astinjection

Rating:

The version of flat used seems to be vulnerable to prototype pollution, and we can find information on the payloads we can use, finding an example exploiting pug.

By having the exploit at hand, we can write a simple script which will send a POST request with the required song.name in the data, as well as with our payload.

The payload itself will allow us to do _Remove Code Execution_. More to the point, we will cat the flag file into the publically available /static/js folder, so we can navigate to it after the pollution exploit.

Original writeup (https://kblagoev.com/blog/blitzprop-cyberapocalypse-2021-ctf/).