情報で捉える生物学入門#2 【生物学のための情報理論入門】
WEB4 days ago · 情報を確率変数の実現値であると定義すると、情報を定量化した 自己情報量. I (x) I (x) は以下の式で表される。 I (x) = -\log_2 p (x) I (x) = −log2p(x) 情報量は驚きの程度を表す量ともいわれ、確率が低い事象が起こったときほど情報量が多くなる。 よって、犬がヒトをかんだも情報量は高くないが、ヒトが犬をかむと情報量が高い。 (ちなみに …
制約x^2+y^2-1＝0の下で目的関数h (x,y)=xy+xの極値を求め ...
WEB4 days ago · 制約x^2+y^2-1＝0の下で目的関数h (x,y)=xy+xの極値を求めることを考える。 （1） この制約を満たす点の軌跡、および目的関数の値を一定にする (x,y)組み合わせの軌跡を描きなさい 上記の問題についての解説に「図から双曲線xy+x=kが円x^2+y^2=1と接するときに極値（k＞0のとき極大，k＜0のとき極小）を ...
【️数学】合成関数の微分の問題です。 (f (g (h (x))))' を求めよ ...
WEB1 day ago · 関数 y=tan^2 2x (タンジェント二乗2x)の微分のやり方を教えてください。 計算したら y’= 2tan 2x / cos^2 2x になってしまいます。答えは4sin2x / cos^3 2x となってました。
Entropy (information theory) - Wikipedia
WEB6 days ago · In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable , which takes values in the alphabet and is distributed according to , the entropy is. where denotes the sum over the variable's possible values.
微分 - Wikipedia
WEB4 days ago · ごく単純な関数については、上記の説明が微分係数の具体的な値について十分な示唆を与えるのは確かだ。たとえば 一次関数 f(x) = Ax + B を考えると、そのグラフは直線なので、「 x = a における接線」もその直線自身であると考えるのが妥当だろう。
Information theory - Wikipedia
WEB4 days ago · Information theory is the mathematical study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. [1] : vii The field, in applied mathematics, is at the intersection of probability theory, statistics, …
Convolution - Wikipedia
WEB6 days ago · The term convolution refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The integral is evaluated for all values of shift, producing the convolution function.
8.3: Properties of Green's Functions - Mathematics LibreTexts
WEB5 days ago · Differential Equation: ∂ ∂x(p(x)∂G(x, ξ) ∂x) + q(x)G(x, ξ) = 0, x ≠ ξ. For x < ξ we are on the second branch and G(x, ξ) is proportional to y1(x). Thus, since y1(x) is a solution of the homogeneous equation, then so is G(x, ξ). For x > ξ we are on the first branch and G(x, ξ) is proportional to y2(x).
MATHEMATICA TUTORIAL, Part 1.3: Runge--Kutta 2
WEB5 days ago · Using a uniform grid of points xn = x0 + nh, with fixed step size h, we write down the Taylor series formula for y (x+h): y(x + h) = y(x) + hy. (x) + h2 2 y ″ (x) + Ch3 + ⋯, where C is a constant expressed through the third derivative of y (x) and the other terms in the series involve powers of h greater than 3.
MATHEMATICA TUTORIAL, Part 1.2: Solving First Order ODEs
WEB5 days ago · You can pin down a specific solution by using the Mathematica command /. (ReplaceAll). This means that Mathematica assigns y [x] to be the general solution (because it contains an arbitrary constant) to the given differential equation.
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