hockey
曲棍球
hockey
曲棍球
plausible
看似合理
prominent
重要的
endorsements
支持,赞同
Given a set of points \(S = {x_i, y_i | i = 1,2, \dots, N}\) determine the minimum number \(n\) subset \(S_1,S_2,\dots, S_n\) where on each of them the data points are approximated by a polynomial of order at most \(m-1\) with an error norm less than a prespecified quantity \(e\).
Statute
法令
pub game
酒吧游戏
linear combination of theksolutions
解的线性组合
omogeneous linearrecurrence relation
齐次线性递归
non-homogeneous linearrecurrence relation
非齐次线性递归
derivative
形式幂级数的导数
quotient formal powerseries
形式幂级数的商不一定存在
formal power series
形式幂级数
multiplication rule
形式幂级数的乘法规则
generating function
生成函数
characteristic polynomial
特征多项式
FCFS
same as SJF
response time
t0 t1 P cpu queue
0 1 P2 busy
1 2 - cs [P1]
2 7 P1 busy
7 8 - cs [P4,P5,P3]
8 10 P4 busy
10 11 - cs [P5,P3]
11 14 P5 busy
14 15 - cs [P3]
15 19 P3 busy
total response time: (1-0) + (7-2) + (10-4) + (14-7) + (19-8) = 30
response time
t0 t1 P cpu queue
0 1 - cs [P2]
1 2 P2 busy
2 3 - cs [P1]
3 6 P1 busy
6 7 - cs [P4,P1,P5]
7 9 P4 busy
9 10 - cs [P1,P5,P3]
10 12 P1 busy
12 13 - cs [P5, P3]
13 16 P5 busy
16 17 - cs [P3]
17 20 P3 busy
20 21 - cs [P3]
21 22 P3 busy
total response time: (2-0) + (12-2) + (9-4) + (16-7) + (22-8) = 40
finish time - the arrival time
turnaround time
exerted on
施加
shear stress
剪切应力
Kirchhoff's law.pdf#page=21)
Random Walks and Electric Networks
PDF.pdf)
Use forward difference approximation. Cannot use central difference approximation
Neumann 边值条件处理方式
Dirichlet boundary condition
Dirichlet 边值条件 $$ y(a) = \beta $$
Neumann boundary condition
Neumann 边值条件 $$ y'(a) = \alpha $$
Spectral collocation method
Lagrange Interpolating Polynomials
拉格朗日插值多项式
meshgrid
meshgrid
Multidimensional integration
多重积分
Gauss Elimination - Pitfalls
高斯消除法 缺陷
second order central difference $$ \frac{\partial \phi}{\partial x} = \frac{\phi{i+1} - \phi{i-1}}{2\Delta x} $$
$$ \frac{\partial^2\phi}{\partial x^2} = \frac{\phi_{i+1} - 2\phi + \phi_{i-1}}{\Delta x^2} $$
STABILITY OF CRANK-NICOLSON
稳定性
So the local truncation error for Crank-Nicolsonformula is and the global truncation error
local truncation error $$ O(\Delta t^3) $$ global truncation error $$ O(\Delta t^2) $$
ACCURACY OF CRANK-NICOLSON
精度
Crank-Nicolson
Crank-Nicolson formula
$$ x_{n+1} = x_n + \frac{\Delta t}{2}\left[f(t_n,x_n) + f(t_{n+1}, x_{n+1}) \right] $$
4th order Runge Kutta
4th order Runge-Kutta $$ \begin{aligned} k_1 & = f(t_n, x_n) \ k_2 & = f\left(t_n + \frac{\Delta t}{2} , x_n + \frac{\Delta t}{2} k_1\right)\ k_3 & = f\left(t_n + \frac{\Delta t}{2} , x_n + \frac{\Delta t}{2} k_2\right)\ k_4 & = f\left(t_n + \Delta t, x_n + \Delta t k3\right)\ x{n+1} & = x_n + \left(\frac{1}{6}k_1 + \frac{1}{3}(k_2+k_3) + \frac{1}{6}k_4\right)\Delta t \end{aligned} $$
2nd order Runge Kutta
2nd order Runge-Kutta $$ \begin{aligned} k_1 & = f(t_n, x_n) \ k_2 & = f(t_n + \Delta t , x_n + \Delta t k1)\ x{n+1} & = x_n + \left(\frac{1}{2}k_1 + \frac{1}{2}k_2\right)\Delta t \end{aligned} $$
2nd order Runge-Kutta $$ \begin{aligned} k_1 & = f(t_n, x_n) \ k_2 & = f(t_n + \Delta t , x_n + \Delta t k1)\ x{n+1} & = x_n + \left(\frac{1}{2}k_1 + \frac{1}{2}k_2\right)\Delta t \end{aligned} $$
ΣBPA
$$ \sum_{\mathrm{BPA}} = \left\{(0,0),(1,0),(+,2)\right\}\cup \left\{(a.\_,1)\mid a\in A\right\} $$
Derivedoperators
$$ [a]\varphi \equiv \neg \langle a\rangle\neg \varphi $$
$$ x\models \langle a\rangle\top \Leftrightarrow \exist_{x'} x\overset{a}{\to} x' \land x'\models \top $$
$$ \begin{aligned} x\models [a]\perp & \Leftrightarrow \forall_{x'} x\overset{a}{\to} x' \Rightarrow x'\models\perp \\ & \Leftrightarrow x\overset{a}{\nrightarrow} \end{aligned} $$
$$ [a]\varphi \equiv \neg \langle a\rangle\neg \varphi $$
satisfaction
$$ \models $$
Book
Gravity currents: a personal perspective
approximate the first derivatives
中心差分二阶导数
source $$ f(x+h) = f(x) + f'(x)h + \frac1{2}f''(x)h^2 +\frac1{6}f'''(\xi_3)h^3,\f(x-h) = f(x) - f'(x)h + \frac1{2}f''(x)h^2 -\frac1{6}f'''(\xi'_3)h^3\ f'(x) \approx \frac{f(x+h)-f(x-h)}{2h} $$
Numerical Methods for Engineers
http://www.civilittee-hu.com/uploads/1/numerical/book6th.pdf
A (2, 5)
$$A(2,5) = A(1,A(2, 4)) = 2^{2^{(2^{16})}}$$
$$\Longleftarrow A(2,4) = A(1, A(2,3)) =2^{(2^{16})}$$
$$\begin{aligned} \Longleftarrow A(2,3) = A(1, A(2,2)) = 2^{16} \end{aligned} $$
$$\begin{aligned} \Longleftarrow A(2,2) &= A(1, A(2,1)) \\ & = A(1, A(1, 2)) \\ & = A(1, 4) = 16 \end{aligned} $$
Applied Numerical Methods Using MATLAB”
https://onlinelibrary.wiley.com/doi/book/10.1002/0471705195
for each edge at most one of its endpoints is in S
independent set
$$ \begin{align} \hat{\bar{x}}_k = {\color{red} F} \bar{x}_{k-1} \\ \hat{P}_k = {\color{red} F}P_{k-1}{\color{red} F^\intercal} + {\color{red} Q} \\ K = \hat{P}_k{\color{red} H^\intercal}({\color{red} H}\hat{P}_k{\color{red} H^\intercal} + {\color{red} R})^{-1}\\ \bar{x}_k = \hat{\bar{x}}_k + K(\bar{z}_k - {\color{red} H}\hat{\bar{x}}_k) \\ P_k = (I-K{\color{red} H})\hat{P}_k \end{align} $$
Further, especially when getting into nonlinear filtering, if the state information is not perfect,but the uncertainty is set to 0 (or just too small a value) it might cause the filter to be unstable.
unstable
xk
$$\hat{\bar{x}}_k$$
incident to some vertex
vertex cover
Binary-to-Gray
Gray Code
格雷码
expression
it says expression NOT statement
Markov chain with the same boundary values.
harmonic is unique
This current is
$$ \begin{aligned} i_a &= \sum_y(v_a-v_y)C_{ay} \\ & = v_a\sum_yC_{ay} - \sum_y v_yC_{ay} \\ & = C_a v_a - \sum_y v_y P_{ay} C_a \\ & = C_a (1 - \sum_y P_{ay} v_y) \end{aligned} $$
flowing into
the current is from outside source
first->second
overwrite the value
key, Value()
insert dummy element
Node::operator new (size_t size, size_t numPointers)
A-instruction
value must be non-negative
which stores the last operationfrom thesametransaction
prevLSN
status:
事务的三种状态: 运行中, 提交中, 终止中
a sequence of log records
Log record 类型
how a database can abort a transaction
终止事务的原因:
what inequality must hold
flushedLSN
prevLSN
flushedLSN
保存在内存prevLSN
保存在 log recordpageLSN
保存在 data pagecrease by 10 each time
为什么不是连续的?
two rules
Durability
持久性
The Strategy Pattern defines a family of algorithms, encapsulates each one, and makes them interchangeable. Strategy lets the algorithm vary independently from clients that use it.
a behavioral
pattern
Favor composition over inheritance.
composition
vs inheritance
Full Speed USB connector (USB0)
J3
LPCXpresso546x8/540xx/54S0xx Board User Manual
Rev. 2.1—7th January 2019
splinters
碎片
block size
include the header and padding
The stator, or stationary part of the stepping motorholds multiple windings. The arrangement of thesewindings is the primary factor that distinguishesdifferent types of stepping motors from an electricalpoint of view.
定子上的线圈排列是步进电机电气上的主要区分因素
variable reluctance
可变磁阻
stator
定子
rotor
转子
Brushless
无刷
The ADC converts an analog input voltage to a 10-bit digital value through successive approximation.
successive approximation
The ADC contains a Sample and Hold circuit which ensures that the input voltage to the ADC is held at a constant level during conversion.
Sample and Hold
circuit.
0x08
TWSR: a START has been trasmitted.
references
?
perform several orders in as many days
一个客户在几天内可以提交多个订单
purchases
采购
swellhead
自大的
Groups
组合
singles
单曲
long play
慢转唱片
flamethrower
喷火器
gas can
汽油桶
deadly
致命的
a pit
深坑
landmines
地雷
metallic box
金属盒子
amateur
业余的
Penelope Dolittle
佩内洛普·杜立特尔
any word beginning with an upper-case letter is a Prolog variable
This is the way logical conjunction is expressed in Prolog (that is, the comma means and )
the semicolon ; is the Prolog symbol for or
how to express disjunction
the potency of a substance in inhibiting a specific biological or biochemical function
物质抑制某特定生物/生化功能的效力
inhibitory concentration
抑制浓度
kd-tree
multidimentional binary search tree (BST)
Microprocessor
MPU
In certain databases the key values may be points in some multi-dimensional space
what is the best data structure for such search problems?
arity
Argument count
it is usual to use a suffix / followed by a number to indicate the predicate’s arity
后缀 /
2.2.1 Pinhole Camera Model
$$s\tilde{\mathbf{m}} = \mathbf{A}[\mathbf{R}\ \mathbf{t}]\tilde{M}$$
2.2.2 Absolute Conic
the :- means implication, the , means conjunction, and the ; means disjunction
:-
: means implication
;
: means conjunction
,
: means disjunction
This will introduce us to the three basic constructs in Prolog: facts, rules, and queries.
facts, rules, queries
network *net = make_network(sections->size - 1);
网络层数由配置文件中的 section 数决定:
net->n = n;
get_network_output_layer
net->outputs = out.outputs;
网络的输出
train_networks
float train_networks(network **nets, int n, data d, int interval)
train_network
get_current_batch
net->subdivisions
the number of batch
in one epoch
get_current_batch
actually, that return current epoch?
Enter a directory where you’d like to store your code and run: scrapy startproject tutorial
创建一个Scrapy project
we want the attribute href
::attr(href)
How big is your cache block
Cache block size: 2 (in words) = 8 (in bytes)
How much data fits in the WHOLE cache
Capacity: 8 words = 32 Bytes
Your processor must provide the following outputs
九个输出
Your processor has 2 inputs
两个输入: 指令 和 时钟
Layer notation for convolutional neural networks
卷积神经网络结构表示
The __thiscall calling convention is used on member functions and is the default calling convention used by C++ member functions that do not use variable arguments.
成员函数使用 __thiscall
调用约定
Calling Conventions
调用约定
Qt Widgets
Qt Widgets 模块帮助索引
Qt add-ons
Qt essentials
There are a few different options to run GUI applications inside a Docker container like using SSH with X11 forwarding, or VNC but the simplest one that I figured out was to share my X11 socket with the container and use it directly.
docker run -ti --rm \
-e DISPLAY=$DISPLAY \
-v /tmp/.X11-unix:/tmp/.X11-unix \
firefox
2/3" (~ 8.8 x 6.6 mm)
海康 DS-2CD7A86F-IZ(S)
800万 2/3" CMOS ICR日夜型筒型网络摄像机<br>
镜头参数: 2.8~16mm @F1.4,水平视场角:23.8°~98.5°
math.atan(8.8 / 2 / 2.8) * 180 / math.pi * 2
Floating Point Calling Conventions
浮点参数传递方式及返回值
CPU Registers
CPU寄存器
The supported data types are as follows
数据类型
Comments
注释语句
Parameter Passing
参数传递
Floating Point Instructions
浮点指令运算
The idea of the numeric_limits<T> trait class is due to John Barton and Lee Nackman
numeric_limits<T>
计算机图形显示和图象处理的算法<br>
英文原版: Algorithms for Graphics and Image Processing <br> see here <br> 作者: Theo Pavlidis
Structural Pattern Recognition
中文翻译版为: <br>
计算机图形显示和图象处理的算法, 1987, 科学出版社
这本书涉及了许多图像处理中经典的算法, 包括:
Algorithms for Graphics and Image Processing
Theo Pavlidis' Algorithm
Countor Tracing
机器人机构学的数学基础 - 丁靖军, 刘辛军, 丁希仑, 戴建生 编著 (1-50)
第1章 绪论
1.1 机构学与机器人学的发展历史概述
机构学广义上成为机构与机器科学 (Mechanism and Machine Science)
机器人机构学的数学基础 - 丁靖军, 刘辛军, 丁希仑, 戴建生 编著 (版权页, 前言页, 目录页)
The chapter 2 (Multilayer Networks) gives a overview of the most prominent <s>convolutional network architectures</s> multilayer architectures.
49-50<br> George Polya<br>Most famous for his classical problem book (known as Polya-Szego), he is also revered as the godfather of combinatorics.
L. J. Mordell and Gabor Szego<br>Speaking of Szego, here he is (right). Mordell was a great number theorist, known for, among other things, the deep conjecture (related to Fermat's last "theorem") that was proved by Falting (#579) in 1983.
577-578<br> J. E. Taylor<br>Jean, another Council shot, works on minimal surfaces; she has been known to talk about soap bubbles, of course, and crystals too.
R. A. Askey<br>I caught Dick during a Bloomington visit in March 1984. Hist specialty is special functions, such as ultraspherical polynomials and Jocobi polynomials; a part of his work was involved in de Branges' solution of the Bieberbach conjecture.
Borodovsky & Ekisheva (2006),
Problems and Solutions in Biological Sequence Analysis
What is the probability P(S) that this sequence S was generated by the HMM model?
计算序列由模型生成的概率
Viterbi algorithm
the probability of the most probable path ending in state \(k\) with observation \(i\) is
$$ p_l(i,x) = e_l(i)\max_k(p_k(j, x-1)\cdot p_{kl}) $$
or using the log of the probabilities $$ \ln p_l(i,x) = \ln e_l(i) + \max_k(\ln pk(j, x-1) + \ln p{kl}) $$
HMM : Viterbi algorithm -a toy example
CS 20: Tensorflow for Deep Learning Research
课程时间: 1月-3月, 2018
On the "IPv4 Settings tab", select Method: "Shared to other computers"
that just works
two cate-gories.
基于深度学习的自然场景文字检测大致可分为两类:
Pieter Abbeel
Alex Berg
Johan Löfberg
YALMIP
Steven Seitz, homepage at washington
Ira Kemelmacher-Shlizerman
Richard Szeliski
David R. Musser
Dr. Xiang Gao
高翔 SLAM
This shrinkage also means that the number of position variations that are possible has shrunk a lot.
计算机视觉识别简史:从 AlexNet、ResNet 到 Mask RCNN
Mathematics of Deep Learning
Joan Bruna
Joan Bruna, new homepage at cims
视频烟雾检测研究进展
Pete Warden
You need 1,000 representative images for each class.
How many images do I need to train my classifier?
Machine Learning at UofT
a revolutionary technique(expression tem-plates,invented independently by Todd Veldhuizen-'' andDavid Vandevoorde") could be used to improve dramaticallythe runtime efficiency of high-level C++ code like sumlt.
expression templates invented independently by Todd Veldhuizen and David Vandevoorde
Beating the Abstraction Penalty in C++ Using Expression Templates,
Beating the Abstraction Penalty in C++ Using Expression Templates, Computers in Physics 10, 552 (1996)
DisambiguatedGlommableExpressionTemplates
Disambiguated Glommable Expression Templates, Computers in Physics 11, 263 (1997)
Todd Veldhuizen - Techniques for Scientific C++ (RT542.pdf)
ScienticandEngineeringC++
Barton and Nackman, Scientific and Engineering C++
MSVC (Visual Studio), 2010 and newer.
vs2010 及以上版本
Eigen is a pure template library defined in the headers
纯模板库
Using C++ Trait Classes for Scientific Computing
expres-sion templates (CIP 10:6, 1996 p. 552; CJP I 1 :3, 1997, p. 263)
Todd Veldhuizen, the co-discoverer of expres-sion templates (CIP 10:6, 1996 p. 552; CJP I 1 :3, 1997, p. 263), i now a graduate student at the Univer-sity of Waterloo.
Todd Veldhuizen 创建Blitz++ 时是滑铁卢大学的一名研究生