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So I've been interested in computing homotopy classes of maps $T^2=S^1\times S^1$ to $\mathbb{R}\mathbb{P}^2$. So first, we can decompose $T^2$ into a cell complex with one zero cell, $S^1\vee S^1$ and a disc $D^2$ glued down to $S^1\vee S^1$ using the commutator. Since the commutator vanishes in $\pi_1(\mathbb{R}\math... |
I recently came across this in a textbook (NCERT class 12 , chapter: wave optics , pg:367 , example 10.4(d)) of mine while studying the Young's double slit experiment. It says a condition for the formation of interference pattern is$$\frac{s}{S} < \frac{\lambda}{d}$$Where $s$ is the size of ...
The accepted answer is c... |
You actually do recover the convolution, but as it is discussed in the comments, there is a normalization issue due to discretization.
According to the documentation,
fft is implemented like this:
$$ A_k = \sum_{m=0}^{n-1} a_m \exp \{ - 2\pi i \frac{mk}{n} \} $$
with $A_k$ being the Fourier-coefficients, $a_m$ the $m$-... |
I recently came across this in a textbook (NCERT class 12 , chapter: wave optics , pg:367 , example 10.4(d)) of mine while studying the Young's double slit experiment. It says a condition for the formation of interference pattern is$$\frac{s}{S} < \frac{\lambda}{d}$$Where $s$ is the size of ...
The accepted answer is c... |
I have a stress matrix in cartesian coordinates : $\begin{pmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{pmatrix}$. How can I convert it to spherical coordinates ?
One way to conceptualize the stress matrix is to view it as a
tensor. In general, your matrix
$$T = \begin{bmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \... |
I'm working with a simple local level model in a textbook \begin{align} y_t &= \alpha_t + \epsilon_t, \qquad \epsilon_t \sim N(0, \sigma_\epsilon^2) \\ \alpha_{t+1} &= \alpha_t + \eta_t, \qquad \eta_t \sim N(0, \sigma_\eta^2) \end{align}
The conditional distribution of $\alpha_t$ given $Y_{t-1}$ (the set of all observa... |
Difference between revisions of "SageMath"
(→Install Sage package: rm section, cf. talk)
m (add note to help identify optional sagemath dependencies available through pacman)
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== Installation ==
== Installation ==
−
{{Warning|Most if not all of the [http://doc.sagemath.org/html/en/installation/standard... |
Suppose $\phi$ is a real function on $\mathbb{R}$ such that $$\phi \Bigl(\int_0^1f(x)\,dx\Bigr)\leq \int_0^1 \phi(f)\,dx$$ for every real bounded measurable function $f$. Prove that $\phi$ is then convex.
This one is in Rudin's Real and Complex Analysis, page 74, and, to be quite honest, I am unsure what my first step ... |
To answer Question 1: Yes, there do exist integrally closed abstract number rings with infinite class group.
By factorization of ideals, for $R$ to be an abstract number ring it is enough that it is a Dedekind domain with finite residue field $R/\mathfrak{p}$ at each prime $\mathfrak{p}$. Theorem B of the paper mention... |
In the previous lesson, we learned the mathematical definition of a gradient. We saw that the gradient of a function was a combination of our partial derivatives with respect to each variable of that function. We saw the process of gradient descent involves moving in the negative direction of the gradient. For example,... |
Let $L$ be the language of set theory, and for each countable ordinal $\kappa$, define $L_\kappa$ as follows: $L_0 = L$, and $L_{\alpha+1}$ is obtained by adding countably many new class constants $c_\phi$ to the signature of $L_\alpha$ to stand for each formula $\phi(x)$ of one free variable. Define $L_\alpha$ for $\a... |
The preface to Mark Srednicki's "Quantum Field Theory" says that to be prepared for the book, one must recognize and understand the following equations:
$$\frac{d\sigma}{d\Omega} = |f(\theta,\phi)|^2, \qquad (1)$$ $$a^{\dagger}|n\rangle = \sqrt{n+1} \space |n+1\rangle, \qquad (2)$$ $$J_{\pm} |j,m \rangle = \sqrt{j(j+1)... |
Blast wave attenuation by lightly destructable granular materials Abstract
Terrorist bombings are a dismal reality nowadays. One of the most effective ways for protection against blast overpressure is the use of lightly compacted materials such as sand [1] and aqueous foam [2] as a protective envelope or barrier. Accor... |
Real Analysis Exchange Real Anal. Exchange Volume 37, Number 1 (2011), 177-188. BV -Functions and Change of Variable p p Abstract
In this note we discuss some interconnections between the space \(BV_p[a,b]\) (\(1\leq p\lt\infty\)) of functions of bounded \(p\)-variation (in Wiener's sense) and the space \(Lip_\alpha[a,... |
In my story, set in the far(ish) future, humanity discovers a way to extract energy from black holes (perhaps via the Penrose process?), which sparks conflict as various factions attempt to take control over previously useless and dangerous but now suddenly valuable black holes. This energy is extremely valuable becaus... |
K C Gupta
Articles written in Proceedings – Mathematical Sciences
Volume 96 Issue 2 November 1987 pp 125-130
A theorem which reveals an interesting relationship between originals of related functions in
Volume 100 Issue 1 April 1990 pp 21-24
In this paper we evaluate the inverse Laplace transform of$$\begin{gathered} s... |
So what are spin-networks? Briefly, they are graphs with representations ("spins") of some gauge group (generally SU(2) or SL(2,C) in LQG) living on each edge. At each non-trivial vertex, one has three or more edges meeting up. What is the simplest purpose of the intertwiner? It is to ensure that angular momentum is co... |
NOTICE: Citizendium is still being set up on its newer server, treat as a beta for now; please see here for more. Citizendium - a community developing a quality comprehensive compendium of knowledge, online and free . Click here to join and contribute—free CZ thanks our previous donors. Donate here. Treasurer's Financi... |
I've tried to explain the solution using as little math as possible, and to give some intuition as to what makes it tick. Nonetheless there will be a little mathematical notation at the end.
First steps: going beyond the obvious solution in the simplest case (N=2)
The statement of the puzzle as presented here doesn't m... |
The theorem that inkspot refers to in his answer is originally from Inoue's paper
New Surfaces with No Meromorphic Functions, II which seems like a more complete reference for this question. In particular, Inoue gives an explicit example of a compact complex surface which has an analytic subvariety but no compact compl... |
I need to compute the two-sided (bilateral) Laplace transform of a
numerically given function $F$,$$I(t) = \int_{-\infty}^{+\infty} {dx} \, e^{-x} \, F(x + t) ~,$$where $F(x)$ has some sharp features, e.g., at $ x = \{ 0, x_p, \cdots \} $, has finite support, and vanishes sufficiently fast for $ x < 0 $ to prevent a di... |
Hello, Now I have a question about a formulation and want to seek for help.
For a facility location problem, I have come up with several constraints. The decision variable \(y\) is binary. But it cannot be automatically guaranteed to take on binary values, if relaxed.
The problem is described as: a network has \(n\) cu... |
The inversion barrier in $\ce{NH3}$ is approximately $5~\mathrm{kcal~mol^{-1}}$ and that of $\ce{PH3}$ is $35~\mathrm{kcal~mol^{-1}}$. This has well-known stereochemical consequences in that amines are not chiral whereas phosphines can be. How can the larger inversion barrier be explained?
Ammonia is
the classic system... |
My question concerns some nomenclature on page 4 of this paper.
I've always viewed the Fourier transform as a continuous analogue of Fourier coefficients: the Fourier coefficients usually defined by a sum, and the Fourier transform by an integral. However, a paper I'm reading doesn't seem to reflect that idea, and I'm ... |
For the backward Euler discretization in time: $$ \left( \frac{u^{(k)}-u^{(k-1)}}{\Delta t}, v\right) + a(u^{(k)},v) = \ell(v) $$
where $a(\cdot,\cdot)$ is the bilinear operator associated with the discretization in space. I’m considering linear elliptic problems in 2D. So I rearrange the above equation: $$ \left(\frac... |
№ 9
All Issues Engibaryan N. B.
Ukr. Mat. Zh. - 2014. - 66, № 8. - pp. 1092–1105
We study the problems of analytic theory and the numerical-analytic solution of the integral convolution equation of the second kind $$ \begin{array}{cc}\hfill {\varepsilon}^2f(x)+{\displaystyle \underset{0}{\overset{r}{\int }}K\left(x-t\r... |
CRC Part 1: Programmer vs Compiler
C compilers are quite intelligent when it comes to performing optimization tricks. When compiling code with something like GCC, you get man-centuries worth of optimization passes applied before seeing the output. Unfortunately, the compiler isn't always smart enough in the way we migh... |
My class was recently given an assignment by our teacher which was to find the atomic weight of Magnesium by adding $\ce{HNO3}$ and heating it until it solidified. We did it in the laboratory as an example, with $\pu{0.21g Mg}$ and found the atomic weight to be $15.272$ and the %error was $14.272$. Afterwards, he asked... |
Has something gone haywire? Let us know about it!
A for awesome Posts: 1901 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact:
I have 64-bit Golly 2.8 on Mac, and it crashes when I try to set the rule to
Code: Select all
B4c4e4c4c4c3e3c5c5e6c6e2e2c2i2n2n6n6i6i3i5a3y1e1c5k7c7e4t4q4t6k4w4i88888000005i5y3a1c1e3... |
so Im given a discrete sum $$x[n] = \sum\limits_{r=\infty}^{+\infty}\delta[n-rN]$$ how do I calculate its discrete Fourier series coefficients?
Thank you.
edit: this is what i've come to up to now:
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image a... |
Let $\mathcal{V_1}$ and $\mathcal{V_2}$ be cocomplete symmetric monoidal categories, each endowed with a cosimplicial object $\Delta^\bullet=\Delta^\bullet_{\mathcal{V}_i}:\Delta \to \mathcal{V}_i$. Denote by $|-|=|-|_{\mathcal{V}_i}:s\mathcal{V}_i\to \mathcal{V}_i$ the functor tensor product $-\otimes_\Delta \Delta^\b... |
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.'Google Translate says this means something ...
@EmilioPisanty Tough call. ... |
Quantization of the free electro-magnetic field has essential differences in comparison to quantization of say scalar or massive vector fields. In fact there are different approches to it.
One of them is a covariant approach due to Gupta and Bleuler, see Section 3-2-1 in "Quantum Field Theory" by Itzykson and Zuber. Fi... |
Given certain function $f(X)$ which is quadratic in $X\in\mathbb{R}^{n\times d}$,
$$\frac{1}{2}tr(X^TAX) - tr(Y^TBX)$$ for positive definite weighted Laplacian matrices $A, B\in\mathbb{R}^{n\times n}$, i.e. the diagonal elements are negative summation of the negative off-diagonal elements plus a constant for strict dia... |
We know that the longest common substring of two strings can be found in $\mathcal O(N^2)$ time complexity. Can a solution be found in only linear time?
Let $m$ and $n$ be the lengths of two given strings,
Linear time assuming the size of the alphabet is constant.
Yes, the longest common substring of two given strings ... |
Thank you for using the timer!We noticed you are actually not timing your practice. Click the START button first next time you use the timer.There are many benefits to timing your practice, including:
Does GMAT RC seem like an uphill battle? e-GMAT is conducting a free webinar to help you learn reading strategies that ... |
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Search for new resonances in $W\gamma$ and $Z\gamma$ Final States in $pp$ Collisions at $\sqrt{s}=8\,\mathrm{TeV}$ with the ATLAS Detector
(Elsevier, 2014-11-10)
This letter presents a search for new resonances decaying to final states with a vector boson produced in association with a... |
I want to calculate the fourier-legendre series coefficients $C_n$ of a bump function $f(x)$ defined as:
\begin{equation} f(x)= \{\begin{array}[ll] a\exp[-\dfrac{1}{0.25-x^2}] & \text{if } |x|<0.5 \\ \quad \quad \quad 0 & \text{if } |x|\geq 0.5\\ \end{array} \end{equation}
for:
\begin{equation} f(x)=\sum_{n}C_nP^m_n \e... |
I am working on generating a (complex) solenoidal vector field $\mathbf{A}$ from a prescribed (complex) vector $\mathbf{a}$ and the gradient of a scalar, $b$, such that $$\mathbf{A} = \mathbf{a} + \nabla b.$$ The condition that I require is then $$\nabla\cdot\mathbf{A} = \nabla\cdot\mathbf{a} + \nabla^2 b = 0 \qquad \L... |
The feature that makes LaTeX the right editing tool for scientific documents is the ability to render complex mathematical expressions. This article explains the basic commands to display equations.
Contents
Basic equations in LaTeX can be easily "programmed", for example:
The well known Pythagorean theorem \(x^2 + y^2... |
The answer to the connected component version is yes, though the only proof I can come up with seems like more trouble than it would've been worth in math camp homework! Two steps:
If there there are finitely many components of $S^2 \smallsetminus Z$, produce a finite-diameter bipartite tree on which the antipodal map ... |
Background
For definiteness (even though this is a categorical question!) let's agree that a
vector space is a finite-dimensional real vector space and that an associative algebra is a finite-dimensional real unital associative algebra.
Let $V$ be a vector space with a nondegenerate symmetric bilinear form $B$ and let ... |
Suppose $\Omega\subset \mathbb{R}^n$ is bounded Lipschitz domain. When $1\leq p < n$, apparently $p< p^* = np/(n-p)$, hence $$ W^{1,p}(\Omega )\subset \subset L^{p}(\Omega ), $$ and for any $u\in W^{1,p}(\Omega)$ $$ \|u\|_{L^p}\leq C \|u \|_{W^{1,p}}\;. $$ To bound using the seminorm like the following Poincare inequal... |
Suppose I have a linear system
$$ \left\lbrack \begin{array}{cc} M_1& S\\ S^{\mathrm{T}}& M_2 \end{array} \right\rbrack \left\lbrack \begin{array}{c} X\\ Y\end{array} \right\rbrack= \left\lbrack \begin{array}{c} F\\G\end{array}\right\rbrack, $$ where $M_1\in \mathrm{R}^{n\times n}$ is symmetric positive definite, $M_2\... |
Challenge
Given an integer, \$s\$, as input where \$s\geq 1\$ output the value of \$\zeta(s)\$ (Where \$\zeta(x)\$ represents the Riemann Zeta Function).
Further information
\$\zeta(s)\$ is defined as:
$$\zeta(s) = \sum\limits^\infty_{n=1}\frac{1}{n^s}$$
You should output your answer to 5 decimal places (no more, no le... |
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"""
Definition of the variance-constrained semi-grand canonical ensemble class.
"""
import numpy as np
from ase import Atoms
from ase.data import atomic_numbers, chemical_symbols
from ... |
CryptoDB Yanbin Pan Affiliation: Academy of Mathematics and Systems Science, CAS Publications Year Venue Title
2019
CRYPTO
New Results on Modular Inversion Hidden Number Problem and Inversive Congruential Generator 📺
The Modular Inversion Hidden Number Problem (MIHNP), introduced by Boneh, Halevi and Howgrave-Graham i... |
Probability Seminar Spring 2019 Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. We usually end for questions at 3:15 PM.
If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu
January 31, Oanh Nguyen, Princeton
Title:... |
I'm quite curious about this:
In a basis set (I'll just use minimal-basis STO-nG basis sets for convenience), the basis functions are written as a linear combination of primitive GTOs. Are the GTOs normalised first, like this:
$$\Psi^\mathrm{STO} = \sum_i N_i c_i \phi_i^\mathrm{GTO}$$
where $\phi_i^\mathrm{GTO}$ are un... |
I am a student studying cryptography by reading "Introduction to Modern Cryptography". I have some confusion about encryption using PRP (e.g., AES).
Briefly speaking, a keyed deterministic permutation $F_{k}$ is a strong PRP if no efficient adversary (who is given oracle access to $F_k$ and $F_k^{-1}$) can distinguish ... |
I wish to solve a coupled system of non-linear equation of this form,
$$ u_t = -(\mathcal{F})_x + f(x,u,w) \\ w_t = \mathcal{F} + g(x,u,w) $$
by stepping the equations forward in time. The first equation is the
advection-diffusion equation with non-linear reaction term, and where the flux has the definition,
$$\mathcal... |
This post is meant to teach new folks how to use MathJax and mhchem formatting on chem.SE
Getting started
On chemistry.SE, we use MathJax to format mathematical as well as chemical equations and similar expressions in questions, answers, and comments. MathJax allows us to typeset expressions using $\LaTeX$ notation.
To... |
We show that for $r$ red cards and $b$ black cards your chance of winning is $\frac{b}{r + b}$ and that this is true for all possible strategies. We do this by induction on $T = r + b$, the total number of cards left. This means we need to show that the chance to win is $\frac{b}{T}$.
For $T = 1$ you must, according to... |
I'd like to learn how the Raviart-Thomas (RT) element works. To that end I'd like to analytically describe how the basis functions look on the reference square. The goal here is not to implement it myself, but rather just to get an intuitive understanding of the element.
I'm largely basing this work off of the triangul... |
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Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
I am trying to prove the integer square root theorem $\forall x: \mathbb{N}, \exists y : \mathbb{N}((y^2 \leq x) \land (x < (y+1)^2))$ for $\lfloor \sqrt{x} \rfloor$. In words: for any natural number $x$, there exists a natural number $y$ which is the integer part of the square root of $x$. I would like to use proof by... |
Homework disclaimer...
The task:
We are using the following algorithm to solve the quadratic equation $x^2+2px+q=0$:
$x_1=|p|+\sqrt{p^2-q}\mathtt{;}$
$\mathtt{if}\,p>0\,\mathtt{then}\,x_1=-x_1\mathtt{;}$
$x_2=q/x_1\mathtt{;}$
Point out two places where running this algorithm can meet significant problems. How to mitiga... |
Published October 2001,October 2004,February 2011.
(The ideas used in this article are also used here to find the volume of a sphere and the, impressively named, mouhefanggai shape.)
You need to be familiar with the formulae for the area of a square, the area of a circle, and the volume of a cuboid. We will also use id... |
By Murray Bourne, 28 Jan 2006
How cool is this? Mathematical tattoos.
For the mathematics behind this, see fractals.
I might get one of these on my left nipple.
Juz kidding...
See the 4 Comments below.
Posted in Mathematics category - 28 Jan 2006 [Permalink]
Tags: Culture
im looking 4 a fractal tatoo artist willing to ... |
Let's split the usual time horizon $[0,T]$ like $0=T_{0}<T_{1}<\dots<T_{n}=T$ and consider the bond price $P(t,T_{i})$ for $i=1,...,n$. We assume $$\frac{dP(t,T_{i})}{P(t,_{i})}=r_{t}dt+\xi_{i}(t)dB_{t}$$ By Ito we can recall $$P(t,T_{i})=P(0,T)\exp(\int_{0}^{t}r_{s}ds+\int^{t}_{0}\xi_{i}(s)dB_{s}-\frac{1}{2}\int^{t}_{... |
Encouraged by Hilmar, I've decided to update the answer with all the steps necessary to calculate the Reverberation Time from a scratch. Presumably, it will be useful for others interested in this area. Obviously, it is the simplest approach because more advanced are definitely beyond a scope.
In the beginning, you mus... |
In Freedman and Proeyen's text on supergravity they derive the equation of motion for the gravitino using the second order formalism. However, I'm not exactly clear as to how they use partial integration and the identities given to manipulate it into the final form. They give the gravitino action as (9.1),
$$S_{3/2}=-\... |
I have implemented the Richardson extrapolation of the Euler-Maruyama method to 4th order, to estimate the moments of SDE.
The Euler-Maruyama works, and I would expect the Richardson extrapolation to work too, because when I suppress the noise contribution it gives the correct solution in the resulting ordinary differe... |
The Annals of Probability Ann. Probab. Volume 11, Number 3 (1983), 760-764. The Reliability of $K$ Out of $N$ Systems Abstract
A system with $n$ independent components which functions if and only if at least $k$ of the components function is a $k$ out of $n$ system. Parallel systems are 1 out of $n$ systems and series ... |
I tried asking a similar question in SE.Physics, and I got some information regarding the abstract side of this, but I figured I should post here to get more complete information about the numerical benefits of variational formalisms.
Assuming I am able derive a functional representation for
any dynamical system (dissi... |
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Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
Precision-Recall¶
Example of Precision-Recall metric to evaluate classifier output quality.
Precision-Recall is a useful measure of success of prediction when the classes are very imbalanced. In information retrieval, precision is a measure of result relevancy, while recall is a measure of how many truly relevant resul... |
I am puzzled by a riddle to which I have been told the answer and I have loads of difficulties to believe in the result.
The riddle goes as follows:
"imagine you are shrunk to the size of a coin (i.e. you are, say, scaled down by two orders of magnitude) but your density remains the same. You are put into a blender of ... |
Let $G_q$ be a Paley graph on $q$ vertices, where $q=1 \text{ (mod 4)}$, i.e., the vertices of $G_q$ are the elements of the finite field $\mathbb{F}_q$, and there is an edge between vertices $a,b \in \mathbb{F}_q$ if and only if $a-b$ is the square of an element in $\mathbb{F}_q$. It is known that $G_q$ is a strongly ... |
There is no non-trivial one-dimensional representation of $\mathrm{U}(1)$ on a scalar field $\mathbb{R}^4\to\mathbb{R}$, but on complex fields $\mathbb{R}^4\to\mathbb{C}$, we have the one-dimensional "phase" representations by $$\phi\mapsto\mathrm{e}^{e\mathrm{i}\chi}\phi$$for $e\in\mathbb{Z},\chi\in\mathfrak{u}(1)\con... |
I'm sorry this must be an elementary question. I spent a good deal of time searching through webs including this site for the problem but I got none.Here's the problem:Say we have a binomial tree ...
I wonder if anyone here has read the following paper by Paul Kupiec in which he approximates a loss rate distribution fo... |
The logistic map is the discrete case of the logistic equation, given by: $\frac {\mathrm{d}y}{\mathrm{d}t}=ry(1-\frac{y}{Y})$
We then approximate to deduce the discrete case:$$ \begin{align*} \frac{y_{n+1}-y_n}{\Delta t} &\approx ry_n\left(1-\frac{y_n}{Y}\right) \\ y_{n+1} &\approx r \Delta t y_n \left(1-\frac{y_n}{Y}... |
Answer
3.5 percent
Work Step by Step
We use the margin of error equation to find: $$=100\times \frac{1}{\sqrt{n}}\\ = 100 \times \frac{1}{\sqrt{800}} \\ =3.5\text{%}$$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have
24 hours to send in a draft... |
To evaluate detection performance, we plot the
miss-rate $mr(c) = \frac{fn(c)}{tp(c) + fn(c)}$ against the number of false positives per image $fppi(c)=\frac{fp(c)}{\text{#img}}$ in log-log plots. $tp(c)$ is the number of true positives, $fp(c)$ is the number of false positives, and $fn(c)$ is the number of false negat... |
Following on from the basic branching processes introduction, we now calculate the expected number of individuals at the
nth generation.
As in the above example, let $Z_n$ be the number of individuals in generation
n, and X be a random variable describing the number of offspring an individual has, with $E[X]=\mu$ and $... |
also, if you are in the US, the next time anything important publishing-related comes up, you can let your representatives know that you care about this and that you think the existing situation is appalling
@heather well, there's a spectrum
so, there's things like New Journal of Physics and Physical Review X
which are... |
I discovered that the mathematics behind the two papers are not exactly the same.
Definition of $Q$ and $N_k$ by Brown in 1991 and 1992
$Q=\frac{f_k}{\Delta f_k}=\frac{f_k}{f_{k+1}-f_k}=\frac{1}{2^{\frac{1}{b}}-1}$ ----(1A), where $b$ is the number of bins per octave.
$N_k=\frac{f_s}{\Delta f_k}=\frac{f_s}{f_k}Q$ ----(... |
To evaluate detection performance, we plot the
miss-rate $mr(c) = \frac{fn(c)}{tp(c) + fn(c)}$ against the number of false positives per image $fppi(c)=\frac{fp(c)}{\text{#img}}$ in log-log plots. $tp(c)$ is the number of true positives, $fp(c)$ is the number of false positives, and $fn(c)$ is the number of false negat... |
I am reading "Analysis, Geometry and Modeling in Finance". In section 2.10.2 which derives the quanto adjustment, it states that (in page 46) by definition the process $S_t^{d/f}S_t^f$ is the foreign asset valued in the domestic currency and therefore should be driven under $\mathbb{P}^d $ by $\frac{dS_t^{d/f}S_t^f}{S_... |
This is essentially an addition to the list of @4tnemele
I'd like to add some earlier work to this list, namely Discrete Gauge Theory.
Discrete gauge theory in 2+1 dimensions arises by breaking a gauge symmetry with gauge group $G$ to some lower
discrete subgroup $H$, via a Higgs mechanism. The force carriers ('photons... |
Cluster expansions¶
This page provides a short introduction to cluster expansions. For more extensive descriptions, please consult for example [SanDucGra84], [Wal09] or [AngMunRah19]. A simpler introduction to the subject can be found in the first part of this tutorial.
Formalism¶
In the following, we are concerned wit... |
I did cointegration test on two identical time series, and the result shows that they are not cointegrated, but intuitively, I think they are.
Can anyone share some thoughts on this? Thanks!
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It only takes a minute... |
In a scientific paper, I need for my Bachelor thesis, the differential cross section for photo pair production
$\gamma\gamma\to e^{+}e^{-}$
is given as follow:
$\mathrm{d}\sigma = \frac{r_{0}^{2}\mathrm{d}\vec{p}_{+}\mathrm{d}\vec{p}_{-}}{2\epsilon_{+}\epsilon_{-}\omega_{1}\omega_{2}(1-\cos(\theta))}(B+4A-4A^{2})\delta... |
It's well-known that in System F, you can encode binary products with the type $$ A \times B \triangleq \forall\alpha.\; (A \to B \to \alpha) \to \alpha $$ You can then define projection functions $\pi_1 : A \times B \to A$ and $\pi_2 : A \times B \to B$.
This isn't so surprising, even though the natural reading of the... |
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"""Definition of the canonical ensemble class."""
import numpy as np
from ase import Atoms
from ase.units import kB
from typing import List
from .. import DataContainer
from ..calculat... |
Let $Y$ be a smooth projective connected curve of genus $g>0$ over $\overline{\mathbf{Q}}$. Let $h_{\textrm{Fal}}(Y)$ be the Faltings height of $Y$.
Question 1. Can one classify or describe the curves $Y$ such that $h_{\textrm{Fal}}(Y) \geq 1$? Question 2. For any $g>0$, does there exist a curve $Y$ of genus $g$ such t... |
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Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
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D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
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Measurement of the top quark mass in the $t\bar t \to {\rm lepton+jets}$ and $t\bar t \to {\rm dilepton}$ channels using $\sqrt{s}=7$ TeV ATLAS data
(Springer, 2015-07)
The top quark mass was measured in the channels $t\bar{t} \to \mathrm{lepton+jets}$ and $t\bar{t} \to \mathrm{dil... |
Pentation
Penetration is Fifth of the Ackermann function. Pentation is denoted with symbol pen;
\(\mathrm{pen}_b(z)=A_{b, 5}(z)\)
where \(A_{b,5}\) is Fifth Ackermann function to base \(b\).
The explicit plot and the complex map of the natural pentation are shown in figures at right.
General properties
Pentation satisf... |
Consider the integer lattice in $2d$, namely the set $\mathbb{Z}^2 = \{(x,y): x,y\in \mathbb{Z}\}$, and let $u:\mathbb{Z}^2 \to \mathbb{R} $ be a function defined on some bounded subset of $\mathbb{Z}^2$. The discrete (graph) Laplace of $u$, denote it by $\Delta^1$, at point $(x,y)$ is defined as $$ \tag{1} \Delta^1 u(... |
The action
$\int d\theta$
has a gauge symmetry $d\theta \mapsto d\theta + df$. The gauge equivalence classes are discrete (labelled by the winding number), so the equations of motion don't say anything (and the gauge field is automatically flat for dimensional reasons).
The action is integer-valued, so you get a differ... |
Could anyone help with this question:
Edit: Reducing it to one of these options would be great!
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This question appears to be... |
At the beginning, you may start with four (component) functions $A_{\mu}(x,y,z,t)$ with $\mu=0,1,2,3$.
But then you may choose one function $\lambda(x,y,z,t)$ (pronounce "lambda") and gauge transform $A_\mu$ to$$ A'_\mu (x,y,z,t) = A_\mu (x,y,z,t) +\frac{\partial}{\partial x^\mu} \lambda $$which produces a new configur... |
I came across this expression while doing exercises and I was wondering if it was a 'real' expression.
$$\mathcal{L}=\frac{1}{2}\partial_\mu \phi \partial^\mu \phi -\frac{m^2}{2}\phi ^2 +\overline{\psi}(i\gamma^\mu\partial_\mu -M)\psi + i\lambda \phi \overline{\psi}\gamma_5\psi $$
I can recognize the first term is a ki... |
14.1. Generative Adversarial Networks¶
Throughout most of this book, we’ve talked about how to make predictions. In some form or another, we used deep neural networks learned mappings from data points to labels. This kind of learning is called discriminative learning, as in, we’d like to be able to discriminate between... |
Electronic Journal of Probability Electron. J. Probab. Volume 22 (2017), paper no. 93, 26 pp. Renormalizability of Liouville quantum field theory at the Seiberg bound Abstract
Liouville Quantum Field Theory (LQFT) can be seen as a probabilistic theory of 2d Riemannian metrics $e^{\phi (z)}|dz|^2$, conjecturally describ... |
$\begin{array}{r|lll} &\text{Name}&\text{Surname}&\text{Dessert}\\ 1&\text{Agatha}&\text{Greed}&\text{cream puffs}\\ 2&\text{Bugsy}&\text{Forager}&\text{trifle}\\ 3&\text{Delilah}&\text{Eatalot}&\text{cheesecake}\\ 4&\text{Chuck}&\text{Hunk}&\text{ice cream} \end{array}$
Four friends held a competition to see who could... |
Optimization Objective
Within supervised learning, the performance of many supervised learning algorithms will be pretty similar and when that is less more often be whether you use learning algorithm A or learning algorithm B but when that is small there will often be things like the amount of data you are creating the... |
It is easy to see that graph isomorphism(GI) is in NP. It is a major open problem whether GI is in coNP. Are there any potential candidates of properties of graphs that can be used as coNP certificates of GI. Any conjectures that imply $GI \in coNP$ ? What are some implications of $GI \in coNP$ ?
If $GI$ is in $coNP$, ... |
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