327 Matching Annotations
  1. Mar 2023
    1. 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 \(e\).

  2. Apr 2022
  3. Jul 2021
  4. bafybeic2mwwizbcleyp2to22xtg7gutywzhoiwxcbuumkhpxugdnbaswoq.ipfs.localhost:8080 bafybeic2mwwizbcleyp2to22xtg7gutywzhoiwxcbuumkhpxugdnbaswoq.ipfs.localhost:8080
    1. 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
      
    2. 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
      
  5. May 2021
  6. bafybeidej4tasx6dk67t6srmq5fhdy32z26kyrsweo2nskxx7eds6y2bgm.ipfs.localhost:8080 bafybeidej4tasx6dk67t6srmq5fhdy32z26kyrsweo2nskxx7eds6y2bgm.ipfs.localhost:8080
  7. bafybeidej4tasx6dk67t6srmq5fhdy32z26kyrsweo2nskxx7eds6y2bgm.ipfs.localhost:8080 bafybeidej4tasx6dk67t6srmq5fhdy32z26kyrsweo2nskxx7eds6y2bgm.ipfs.localhost:8080
    1. second order central difference $$ \frac{\partial \phi}{\partial x} = \frac{\phi{i+1} - \phi{i-1}}{2\Delta x} $$

      $$ \frac{\partial^2\phi}{\partial x^2} = \frac{\phi_{i+1} - 2\phi + \phi_{i-1}}{\Delta x^2} $$

  8. bafybeicq7ssvd6yyrdzgs4bpby23imx7vdxhb55w7hmt7zu7m2n6ybmnly.ipfs.localhost:8080 bafybeicq7ssvd6yyrdzgs4bpby23imx7vdxhb55w7hmt7zu7m2n6ybmnly.ipfs.localhost:8080
    1. So the local truncation error for Crank-Nicolsonformula is and the global truncation error

      local truncation error $$ O(\Delta t^3) $$ global truncation error $$ O(\Delta t^2) $$

  9. bafybeifdxtggnhokzsb6hg4ve3sijpewdbwc4fxo56mhc5e6ockfih6rvy.ipfs.localhost:8080 bafybeifdxtggnhokzsb6hg4ve3sijpewdbwc4fxo56mhc5e6ockfih6rvy.ipfs.localhost:8080
    1. 4th order Runge Kutta

      4th order Runge-Kutta $$ \begin{aligned} k_1 & = f(t_n, x_n) \ k_2 & = f\left(t_n + \frac{\Delta t}{2} , x_n + \frac{\Delta t}{2} k_1\right)\ k_3 & = f\left(t_n + \frac{\Delta t}{2} , x_n + \frac{\Delta t}{2} k_2\right)\ k_4 & = f\left(t_n + \Delta t, x_n + \Delta t k3\right)\ x{n+1} & = x_n + \left(\frac{1}{6}k_1 + \frac{1}{3}(k_2+k_3) + \frac{1}{6}k_4\right)\Delta t \end{aligned} $$

    2. 2nd order Runge Kutta

      2nd order Runge-Kutta $$ \begin{aligned} k_1 & = f(t_n, x_n) \ k_2 & = f(t_n + \Delta t , x_n + \Delta t k1)\ x{n+1} & = x_n + \left(\frac{1}{2}k_1 + \frac{1}{2}k_2\right)\Delta t \end{aligned} $$

    3. 2nd order Runge-Kutta $$ \begin{aligned} k_1 & = f(t_n, x_n) \ k_2 & = f(t_n + \Delta t , x_n + \Delta t k1)\ x{n+1} & = x_n + \left(\frac{1}{2}k_1 + \frac{1}{2}k_2\right)\Delta t \end{aligned} $$

    1. Derivedoperators

      $$ [a]\varphi \equiv \neg \langle a\rangle\neg \varphi $$

      $$ x\models \langle a\rangle\top \Leftrightarrow \exist_{x'} x\overset{a}{\to} x' \land x'\models \top $$

      $$ \begin{aligned} x\models [a]\perp & \Leftrightarrow \forall_{x'} x\overset{a}{\to} x' \Rightarrow x'\models\perp \\ & \Leftrightarrow x\overset{a}{\nrightarrow} \end{aligned} $$

  10. bafybeicq7ssvd6yyrdzgs4bpby23imx7vdxhb55w7hmt7zu7m2n6ybmnly.ipfs.localhost:8080 bafybeicq7ssvd6yyrdzgs4bpby23imx7vdxhb55w7hmt7zu7m2n6ybmnly.ipfs.localhost:8080
    1. source $$ f(x+h) = f(x) + f'(x)h + \frac1{2}f''(x)h^2 +\frac1{6}f'''(\xi_3)h^3,\f(x-h) = f(x) - f'(x)h + \frac1{2}f''(x)h^2 -\frac1{6}f'''(\xi'_3)h^3\ f'(x) \approx \frac{f(x+h)-f(x-h)}{2h} $$

  11. bafybeiakog6znbrgrydmhpruc5nzmoreo2gg7dwtpfvgxnelgbgcxuit3a.ipfs.localhost:8080 bafybeiakog6znbrgrydmhpruc5nzmoreo2gg7dwtpfvgxnelgbgcxuit3a.ipfs.localhost:8080
    1. A (2, 5)

      $$A(2,5) = A(1,A(2, 4)) = 2^{2^{(2^{16})}}$$

      $$\Longleftarrow A(2,4) = A(1, A(2,3)) =2^{(2^{16})}$$

      $$\begin{aligned} \Longleftarrow A(2,3) = A(1, A(2,2)) = 2^{16} \end{aligned} $$

      $$\begin{aligned} \Longleftarrow A(2,2) &= A(1, A(2,1)) \\ & = A(1, A(1, 2)) \\ & = A(1, 4) = 16 \end{aligned} $$

  12. bafybeiax3vr6i7wslj3n5rckyvavow3p2myxquup4cismrern5p6nxjapi.ipfs.localhost:8080 bafybeiax3vr6i7wslj3n5rckyvavow3p2myxquup4cismrern5p6nxjapi.ipfs.localhost:8080
    1. $$ \begin{align} \hat{\bar{x}}_k = {\color{red} F} \bar{x}_{k-1} \\ \hat{P}_k = {\color{red} F}P_{k-1}{\color{red} F^\intercal} + {\color{red} Q} \\ K = \hat{P}_k{\color{red} H^\intercal}({\color{red} H}\hat{P}_k{\color{red} H^\intercal} + {\color{red} R})^{-1}\\ \bar{x}_k = \hat{\bar{x}}_k + K(\bar{z}_k - {\color{red} H}\hat{\bar{x}}_k) \\ P_k = (I-K{\color{red} H})\hat{P}_k \end{align} $$

    2. 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

    Annotators

    1. This current is

      $$ \begin{aligned} i_a &= \sum_y(v_a-v_y)C_{ay} \\ & = v_a\sum_yC_{ay} - \sum_y v_yC_{ay} \\ & = C_a v_a - \sum_y v_y P_{ay} C_a \\ & = C_a (1 - \sum_y P_{ay} v_y) \end{aligned} $$

  13. Apr 2021
  14. Jun 2019
    1. 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

    Tags

    Annotators

    Annotators

    Annotators

  15. May 2019
    1. 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

    1. 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.

    Annotators

  16. Mar 2019
  17. Feb 2019
  18. Oct 2018
    1. 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

    1. In certain databases the key values may be points in some multi-dimensional space

      what is the best data structure for such search problems?

  19. Sep 2018
  20. people.inf.ethz.ch people.inf.ethz.ch
  21. Aug 2018
  22. Jul 2018
    1. 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

    1. 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
      
  23. Jun 2018
  24. May 2018
    1. 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)

      • 第一阶段(古世纪--18世纪中叶): Aristotle, Problems of Machines
    1. The chapter 2 (Multilayer Networks) gives a overview of the most prominent <s>convolutional network architectures</s> multilayer architectures.

    1. 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.

      PT42

    1. 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.

      PT315

    1. 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

    2. 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 $$ \ln p_l(i,x) = \ln e_l(i) + \max_k(\ln pk(j, x-1) + \ln p{kl}) $$

  25. Apr 2018
    1. 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:

      1. 将文字当为一般对象采用一般对象的检测范式, 对多方向文字处理有问题
      2. 分割出文字区域再进行复杂的后期处理
  26. Mar 2018
    1. 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

  27. eigen.tuxfamily.org eigen.tuxfamily.org
    1. 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