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What is the difference between logistic and logit regression? I understand that they are similar (or even the same thing) but could someone explain the difference(s) between these two? Is one about odds?
The logit is a link function / a transformation of a parameter. It is the logarithm of the odds. If we call the para... |
Today is the first in our series of blogs that will focus on different problem-solving strategies in mathematics. The strategy that we’ll look at now is simple enough at its core: if you’re stuck on a problem that involves unknowns or variables, try substituting, or “plugging”, some numbers into those letters! What num... |
We consider a smooth manifold $M$ of dimension $d$, a $C^{\infty}$ function $f:M\rightarrow \mathbb{R}$ and $p\in M$. Two charts in a neighborhood $Z$ of $p$: $\phi:U\subset \mathbb{R}^d\rightarrow Z,\phi(u)=p,\psi:V\subset \mathbb{R}^d\rightarrow Z,\psi(v)=p$ are s.t. the transition map $\tau=\phi^{-1}\circ \psi$ is a... |
QML Tutorial¶
This tutorial is a general introduction to kernel-ridge regression with QML.
Theory¶
Regression model of some property, \(y\), for some system, \(\widetilde{\mathbf{X}}\) - this could correspond to e.g. the atomization energy of a molecule:
\(y\left(\widetilde{\mathbf{X}} \right) = \sum_i \alpha_i \ K\lef... |
I'm currently studying Particle Physics and HEP and this acronym is omnipresent. I know it means
next-to-leading-order but, what is exactly the physical meaning of LO and NLO?
You say you know about Feynman diagrams, at least at tree level. So you might have seen loop diagrams, i.e. diagrams that contain a loop of inte... |
Convergence of Limsup and Liminf Theorem
Let $\sequence {x_n}$ be a sequence in $\R$.
Let the limit superior of $\sequence {x_n}$ be $\overline l$.
Let the limit inferior of $\sequence {x_n}$ be $\underline l$.
Proof Sufficient Condition
First, suppose that $\overline l = \underline l = l$.
Let $\epsilon > 0$.
$\exists... |
The Markov chain $(Xn; n\geq)$ has state-space $S = (0, 1, 2, . . .)$, with
$p_{i,0} = \frac{1}{4}$ and $p_{i,i+1} = \frac{3}{4}$ $\forall i \geq 0$, so that the transition matrix is
P =$\begin{pmatrix} \frac{1}{4} & \frac{3}{4} & 0 & 0 & ...\\\ \frac{1}{4} & 0 & \frac{3}{4} & 0 & ... \\\ \frac{1}{4} & 0 & 0 & \frac{3}... |
Examples of solving linear discrete dynamical systems
The solution to a linear discrete dynamical system is an exponential because in each time step, we multiply by a fixed number. It is easy to see what number we multiply in each time step when the dynamical system is in function iteration form. When the dynamical sys... |
Because this is a diatomic molecule, there are no group orbitals. Put another way, the group orbitals
are the molecular orbitals. Knowing the nitrogen atomic orbitals (AOs) and their irreducible representation (irrep) labels is enough.
Since we'll work in the $D_{\mathrm{2h}}$ point group, we need its character table:
... |
Quantitative Modeling for Algorithmic Traders – Primer Quantitative Modeling techniques enable traders to mathematically identify, what makes data “tick” – no pun intended 🙂 .
They rely heavily on the following core attributes of any sample data under study:
Expectation– The mean or average value of the sample Varianc... |
I'm currently reading some papers about Markov chain lumping and I'm failing to see the difference between a Markov chain and a plain directed weighted graph.
For example in the article Optimal state-space lumping in Markov chains they provide the following definition of a CTMC (continuous time Markov chain):
We consid... |
Countable models of PA fall into two categories: the standard one $(\omega, S)$ and the nonstandard ones (all the rest). The only way I've seen to construct a nonstandard model is through taking an ultraproduct or, equivalently, using the compactness theorem. My question is wether or not these are all the models there ... |
According to my revision guide baryon and mesons always interact via the strong interaction.
Does this hold for baryon-baryon interactions? meson-meson?
Thanks
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up.Sign up to joi... |
In the above example, how is it that $f^{-1}((1,3)) = (2,3]$ ? Here is my understanding, kindly correct the misconceptions. The inverse for $(2,4]$ is not defined. The inverse is as below. $$f^{-1}(y)=\begin{cases} y+1 & \text { if } y \le 2\\ 2y-5 & \text{ if } y \gt 4\\ \end{cases}$$ So, if I have to find out for exa... |
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Show that the map \(\Phi\) from the Introduction, which was roughly given by ‘Is • connected to ∗?’ is a monotone map from the preorder shown in Eq. (1.2) to \( \mathbb{B}.\)
If we apply the map "is \(\bullet\) connected to \(\star\... |
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In this chapter we learned about left and right adjoints, and about joins and meets. At first they seemed like two rather different pairs of concepts. But then we learned some deep relationships between them. Briefly:
Left adjoints ... |
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Physics of Particles and Nuclei Letters, ISSN 1547-4771, 12/2018, Volume 15, Issue 7, pp. 720 - 723
Journal Article
2. Study of the process e + e − → π + π − π 0 η in the c.m. energy rang... |
This may be a silly question, and so I apologize in advance. But it stems from a reading of section 2 (page 5) of the physics paper, "Counting chiral primaries in N=1 d=4 superconformal field theories".
My
question is: What does the representation of $U(1)$ labeled as $\frac{1}{2}$ indicate?
My question is a group-theo... |
In the comments section to Willie Wong's answer, the following Dirichlet series came up: the Riemann $\zeta$-function, Dirichlet $L$-functions, and Ramanujan's series $\sum_{n \geq 1}\tau(n) n^{-s}$, where $\tau(n)$ is the coefficient of $q^n$ in $\Delta(q) = q\prod_{n=1}^{\infty} (1-q^n)^{24}$.
First note that the $\z... |
I'm working on a homework assignment where my professor would like us to create a true regression model, simulate a sample of data and he's going to attempt to find our true regression model using some of the techniques we have learned in class. We likewise will have to do the same with a dataset he's given us.
He says... |
Korn inequality
An inequality concerning the derivatives of vector functions $f:\mathbb R^n\to \mathbb R^n$. Assuming that $f$ is continuosly differentiable, we denote by $Df$ the Jacobian matrix of its differential and by $D^s f$ its symmetric part, namely the matrix with entries \[ \frac{1}{2} \left(\frac{\partial f_... |
FBA Flux Balance Analysis
FBA has been shown to be a very useful technique for analysis of metabolic capabilities of cellular systems. FBA involves carrying out a steady state analysis, using the stoichiometric matrix for the system in question. The system is assumed to be optimised with respect to functions such as ma... |
The Annals of Statistics Ann. Statist. Volume 12, Number 3 (1984), 1100-1105. A Characterization Theorem for Externally Bayesian Groups Abstract
A contribution is made to the problem of combining the subjective probability density functions $f_1, \cdots, f_n$ of $n$ individuals for some parameter $\theta$. More precise... |
Taiwanese Journal of Mathematics Taiwanese J. Math. Volume 16, Number 4 (2012), 1531-1555. HYBRID METHOD FOR DESIGNING EXPLICIT HIERARCHICAL FIXED POINT APPROACH TO MONOTONE VARIATIONAL INEQUALITIES Abstract
Let $C$ be a nonempty closed convex subset of a real Hilbert space $H$. Assume that $F: C \to H$ is a $\kappa$-L... |
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Now showing items 1-1 of 1
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Beside the wonderful examples above, there should also be counterexamples, where visually intuitive demonstrations are actually wrong. (e.g. missing square puzzle)
Do you know the other examples?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related ... |
My best guess is that the series $$ \sum_{i=1}^n i(n-(i-1)) $$ becomes $$ 2 \Bigg[ n + 2(n-1) + ... + \frac{n}{2} \bigg(n-\bigg(\frac{n}{2}-1\bigg)\Bigg)\Bigg] $$ So the highest term is $n^2$ and there are $n$ terms. Does that mean its $O(n^3)$? That seems high. Intuitively, it seems like it should be closer to $O(n^2)... |
Someone pointed out this puzzle in Kahneman's
Thinking, Fast and Slow. I paraphrase.
A game rewards participants based on how long it takes to obtain the first heads in a toss of a fair coin. If the first toss results in heads, then the player gets reward $r(1) = \$2$. If the first heads appears only in the second toss... |
Let $X_n$ be independent Poisson random variables with $E[X_i] = \mu_i$, and let $Y_n = X_1+...+X_n$. I want to show that if $\sum_n \mu_n = \infty $ then $Y_n/E[Y_n] \rightarrow 1$ almost surly.
What I do know is that if $X_1,...$ are independent, and $E\left[X^4\right] < \infty$, then $Y_n/n \rightarrow E[X]$ a.s.* S... |
Difference between revisions of "Main Page"
(→Proof strategies)
m
Line 1: Line 1:
== The Problem ==
== The Problem ==
−
Let <math>[3]^n</math> be the set of all length <math>n</math> strings over the alphabet <math>1, 2, 3</math>. A ''combinatorial line'' is a set of three points in <math>[3]^n</math>, formed by taking... |
Trying to solve a problem I ended up working on a polynomial of degree $n-1$ in $t$, $p(t)=\sum_{k=0}^{n-1} a_k t^k$, whose coefficients are given by
$a_k=\sum_{i=1}^n\cfrac{\beta_i^k}{\prod_{j=1\\j\neq i}^n (\beta_j-\beta_i)}$
Here, $\beta_i$ are $n$ distinct positive and ordered real numbers, so that $0<\beta_1<\beta... |
The shapeUsing this, we can make a guess for how the cube might be folded:Once that fold is done, the shape looks more like this:A drawing of the finished product:And an animation of the whole process:
This seems to work:Below, I printed out the shape, and cut off the excess. The white parts are for glueing; if everyth... |
To understand the formula:
1) draw a Cartesian coordinates with a unit circle (centred at origin with a radius of 1).
2) draw a vector pointing towards 2-oclock (so we have $\theta = 30$, this is arbitrary but I prefer this 30 degree angle as I tend to confuse the sin and cos on a 45 degree angle) with a length of 1, s... |
Mohammad Shoeb
Articles written in Pramana – Journal of Physics
Volume 37 Issue 5 November 1991 pp 419-424
A one parameter, semi-empirical formula for Λ-binding energy of heavy hypernuclei in the inverse powers of core mass number (
c) has been developed in the framework of the folding model. Unlike similar calculation... |
Your statement 'For example, Na+ bonds with OH− and Cl− bonds with H+ when NaOH is dissolved in H2O' is not correct if the ions are in solution.
In an ionic solid each ion is surrounded by other ions of the same charge and those of opposite charge, in NaCl each Na$^+$ ion is surrounded by 6 Cl$^-$ and
vice versa. The i... |
I am studying Linear Discriminant Analysis (LDA). According to the formula for LDA, we are supposed to get the inverse of within group covariance. However, if $p\gg n$ (i.e., the dimension is much larger than the number of samples), what should I do?
One possibility is to regularize your estimate of the covariance matr... |
So is $\Theta$ undefined for insertion sort?
This question contains a category error. It's like saying, "I know that Donald Trump has a height of at least 5 and at most 7. So are numbers undefined for Donald Trump?
$\Theta$ is notation for expressing the growth rate of mathematical functions. "Insertion sort" is not a ... |
In general, the intensity of an electric field is given by $$ I = \frac{c\epsilon_0}{2}E_0^2 $$ where $E_0$ is the peak amplitude of the electric field. Let's say we have an electric field $$ E(t) = E_0 \sin(\omega t). $$ Without having any other potential, the electric field is connected to its corresponding vector po... |
Definition:Order Isomorphism Contents Definition
Let $\left({S, \preceq_1}\right)$ and $\left({T, \preceq_2}\right)$ be ordered sets.
Let $\phi: S \to T$ be a bijection such that:
Then $\phi$ is an
order isomorphism.
Let $\left({S, \preceq_1}\right)$ and $\left({T, \preceq_2}\right)$ be ordered sets.
Then $\phi$ is an ... |
Hydrogen iodide is a colourless gas that will decompose into colourless hydrogen gas and purple iodine gas according to the following endothermic reaction.
$$\ce{2 HI (g) <=> H2 (g) + I2 (g)}$$
A $\pu{1.0 L}$ glass container was filled with $\pu{0.60 mol}$ of hydrogen iodide gas. When equilibrium was established, there... |
Given tensor product of rank-2 Pauli matrices $\sigma^a$. Each $\sigma^a$ is related to the generator of SU(2) Lie algebra.
We know they satisfy
$$[\sigma^a, \sigma^b ] = 2 i \epsilon^{abc} \sigma^c$$
Do you know any equality/identity to simplify: $$ [\sigma^a \otimes \sigma^c, \sigma^b \otimes \sigma^d] = ? $$ also $$... |
The calculation is described in detail in the Wikipedia article on recombination.
If you consider the ionisation of hydrogen as a reaction:
$$ p + e \rightarrow H + \gamma $$
Then you can write down an expression for the equilibrium constant as a function of temperature using the Saha equation:
$$ \frac{n_pn_e}{n_H} = ... |
Split Monomorphism is Monic Theorem
Let $\mathbf C$ be a metacategory.
Let $f: C \to D$ be a split monomorphism.
Then $f: C \rightarrowtail D$ is monic. Proof
Let $g: D \to C$ be a morphism such that:
$g \circ f = \operatorname{id}_C$
which is guaranteed to exist by definition of split monomorphism.
Suppose that $x, y:... |
I have a couple questions regarding the proof of Proposition $3$ (see page $10-11$ of arxiv.org/abs/math/0102039) in Bezrukavnikov's paper "Quasi-exceptional sets and equivariant coherent sheaves on the nilpotent cone" . For simplicity, assume $G$ is simply connected, simple algebraic group (so that $G$ is its own univ... |
First of all, let me state the obvious:
After we got that out of the way we can focus on why. Phosphorus is awesome.
There are many different modifications of phosphorus in nature. With increasing thermodynamic stability they are $$\ce{P_{white} -> P_{red} -> P_{violet} -> P_{black}}.$$
Apart from this there are many l... |
The Setup
Let Greek indices be summed over $0,1,\dots, d$ and Latin indices over $1,2,\dots, d$. Consider a vector potential $A_\mu$ on $\mathbb R^{d,1}$ defined to gauge transform as$$ A_\mu\to A_\mu'=A_\mu+\partial_\mu\theta$$for some real-valued function $\theta$ on $\mathbb R^{d,1}$. The usual claim about Coulomb g... |
GTU Civil Engineering (Semester 3)
Fluid Mechanics May 2014
Fluid Mechanics
May 2014
Total marks: --
Total time: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons (2) Marks are given to the right of every question (3) Draw neat diagrams wherever necessary
(1) Assume appropriate data and ... |
Difference between revisions of "Timeline of prime gap bounds"
Line 1,043: Line 1,043:
| [http://math.mit.edu/~drew/schinzel_3473955908_80550202480.txt 80,550,202,480]* [m=5] ([http://terrytao.wordpress.com/2014/05/17/polymath-8b-xi-finishing-up-the-paper/#comment-366807 Sutherland])
| [http://math.mit.edu/~drew/schinz... |
Dynamical system definition
A dynamical system is a system whose state evolves with time over a state space according to a fixed rule.
For an introduction into the concepts behind a dynamical system, see the idea of a dynamical system.
Formal definition of dynamical system
A dynamical system is formally defined as a st... |
How large an interval with given tolerance for a Taylor polynomial?
This page treats a simple example of the first kind of questionmentioned on a previous page:‘Given a Taylor polynomialapproximation to a function, expanded at some given point, and given arequired tolerance,
on how large an interval around the given po... |
As @PaulDuBois commented, the above answer (@hjhjhj57) is incorrect for obtuse angles.
In fact, we can classify the outside of the triangle in
three regions:
1) $\alpha\geq 0$ and $\beta<0$, in which case $P$ is closest to either $AB$ or $AC$,
2) $\beta\geq 0$ and $\gamma<0$, in which case $P$ is closest to either $AB$... |
Good question! The proof given in Mohri's book indeed assumes continuity of the distribution, but this can be avoided with a finer definition of the $r_i$'s. Such a correction appears in these lecture notes who cite this paper.
Recall that you want the rectangles to be small enough, such that if $R_S$ intersects all of... |
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In this chapter we learned about left and right adjoints, and about joins and meets. At first they seemed like two rather different pairs of concepts. But then we learned some deep relationships between them. Briefly:
Left adjoints ... |
When computing special bordism groups, I often need to determine existence of (singular) smooth $4$-manifolds with fixed fundamental group and certain properties like the spin behaviour (i.e. being totally non-spin, spin or almost spin - sometimes they are denoted as odd or even manifolds).
Usually I'm able to prove ex... |
Refine Document Type Master's Thesis (5) (remove) Keywords Faculty / Organisational entity Fachbereich Mathematik (5) (remove)
Mathematische Modellierung eines Segways mit Umsetzung in der Schule als interdisziplinäre Projektarbeit (2016)
Das Ziel dieser Arbeit besteht darin, aufzuzeigen, wie eine mathematische Modelli... |
The
P-value approach involves determining "likely" or "unlikely" by determining the probability — assuming the null hypothesis were true — of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed. If the P-value is small, say less than (or equal to) \(\alpha\), the... |
I see three questions.
Question 1: Why do we care about $Set$ when we define functors $C\to Somebase$?
$Set$ is a very special category:
$Set$ is the terminal object of the category of Grothendieck topoi and geometric morphisms $Set$ is the free cocompletion of the one-object category. $Set$ is a "canonical choice" for... |
Let $H = \triangle + V(x) : \mathbb{R}^2 \rightarrow \mathbb{R}^2$. I am interested in domain decomposition for an eigenproblem involving $H$.
The lowest 1000 eigenfunctions of $H$, $ \psi_i $, can be partitioned using a region, $\Omega \subset \mathbb{R}^2$, such that each $\psi_i$ localizes either inside of $\Omega$ ... |
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Collisionless reconnection: Magnetic field line interaction
Treumann, R. A., W. Baumjohann, and W. D. Gonzalez (2... |
The
Minkowski distance is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance. Definition [ edit ]
The Minkowski distance of order
p between two points X = ( x 1 , x 2 , … , x n ) and Y = ( y 1 , y 2 , … , y n ) ∈ R n {\displaystyle X=(... |
In Peskin's book (an introduction to QFT), Page 655, the axial vector current is defined as follows, \begin{eqnarray*} j^{\mu5} & = & \text{symm }\lim_{\epsilon\rightarrow0}\bigg\{\bar{\psi}(x+\frac{\epsilon}{2})\gamma^{\mu}\gamma^{5}\exp\bigg(-ie\int_{x-\epsilon/2}^{x+\epsilon/2}dz\cdot A(z)\bigg)\psi(x-\frac{\epsilon... |
Like for $\pi$, we have an algorithm/infinite series that can give us the first 50 decimal places in about 3 terms. So if I wasn't to calculate like $ln(25551879...)$ (a really huge integer, most likely a prime), upto 100 decimal places, what will be the algorithm I should use or is used worldwide and how efficient is ... |
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Change to browse by: Bookmark(what is this?) Astrophysics > Cosmology and Nongalactic Astrophysics Title: Constraining sterile neutrino cosmologies with strong gravitational lensing observations at redshift z~0.2
(Submitted on 4 Jan 2018 (v1), last revised 9 Oct 2018 (this version, v... |
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Mon, 23 Jul 2018
The paper “Verification of Identities” (1997) of Rajagopalan and Schulman discusses fast ways to test whether a binary operation on a finite set is associative. In general, there is no method that is faster than the naïve algorithm of simply checking whether $$a\as... |
Consider $Q$ a interval in $R$. Number all the rationals in this interval. Then for rational $q_i$ consider interval $[q_j-\epsilon /2^{j+2} ,q_j+\epsilon/2^{j+2}]$. Now the whole interval lies inside the union of these intervals, sum of whose volumes is $ < \epsilon $.
Why I am getting this contradiction? I know (with... |
6.2 - Binary Logistic Regression with a Single Categorical Predictor
Key Concepts Objectives Overview Binary logistic regression estimates the probability that a characteristic is present (e.g. estimate probability of "success") given the values of explanatory variables, in this case a single categorical variable ; π =... |
I'm struggling to understand a question I've been given. The question asks: Let $\psi$ be a boolean formula in $n$ variables. There are $2^n$ different combinations of assigning values to the variables. Consider the problem of deciding whether (strictly) more than $2^{n−1}$ of these assignments satisfy the formula $\ps... |
I am having some trouble with the following:
Let $(X_1,\mathcal{F}_1,\mu_1,T_1)$ be a measure preserving dynamical system with $T_1:X_1\to X_1$ is ergodic.
Suppose $(X_2,\mathcal{F}_2,\mu_2,T_2)$ is another dynamical system and there exists some surjective function $\pi: X_2\to X_1$ such that $\pi\circ T_2=T_1\circ \pi... |
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Last time we studied meets and joins of partitions. We observed an interesting difference between the two.
Suppose we have partitions \(P\) and \(Q\) of a set \(X\). To figure out if two elements \(x , x' \in X\) are in the same par... |
Integrating the error term of a Taylor polynomial: example
Being a little more careful than for the previous example, let's keep track of the error term in the example we've been doing: we have $${1\over 1-x}=1+x+x^2+\ldots+x^n+ {1\over (n+1)}{ 1 \over (1-c)^{n+1 }}x^{n+1}$$ for some $c$ between $0$ and $x$, and also d... |
I am trying to integrate this function:
$$I = \int_{-\infty }^0 \frac{e^u}{\left(\left(e^u (u-1)+1\right) \lambda -1\right){}^2} \, du$$
and I cannot do it.
So, what I want to try to do is to expand the numerator in its Taylor series and integrate term-by-term, I.e.,
$$I = \int_{-\infty }^0 \frac{1+u+\frac{u^2}{2}+\fra... |
October 14, 2015. This is with $$ \frac{x^2 + y^2}{xy - t} = q > 0, $$which I believe to be the intent of the question.
THEOREM: $$ \color{red}{ q \leq (t+1)^2 + 1 } $$
I got some help from Gerry Myerson on MO to finish the thing. https://mathoverflow.net/questions/220834/optimal-bound-in-diophantine-representation-que... |
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Now showing items 1-9 of 9
Measurement of $J/\psi$ production as a function of event multiplicity in pp collisions at $\sqrt{s} = 13\,\mathrm{TeV}$ with ALICE
(Elsevier, 2017-11)
The availability at the LHC of the largest collision energy in pp collisions allows a significant advance in the measurement of $J/\ps... |
The idea of a probability density function An initial thought experiment
I'm thinking of a number, let's call it $X$, between 0 and 10 (inclusive). If I don't tell you anything else, what would you imagine is the probability that $X=0$? That $X=4$? Assuming that I don't have any preference for any particular number, yo... |
I'm a first time TeX user and had typed out certain (long) equations in a single column format for submission to a journal (that part worked fine). Unfortunately, I accidentally missed the fact (!) that Physical Review journals have a two column format. Directly converting to the two column format results in them spill... |
C.1 Summations and SeriesC.1 Summations and Series
Summations and Series are an important part of discrete probability theory. We provide a brief review of some of the series used in STAT 414. While it is important to recall these special series, you should also take the time to practice. For more in depth review, ther... |
An offset is generally just a coefficient set to a specific value. To get more than one offset, in general you just need to combine the different variables in a way that is consistent to get that fixed value.
In a Poisson equation if you set $Z$ as the offset (or exposure its sometimes called):
$$\log(\mathbb{E}[Y]) = ... |
Given a continuous time LTI system with impulse response $h(t)$ and determined with the transform $\mathcal{T}\{\cdot\}$, we define an input/output relationship as follows:
$$ y(t) = \mathcal{T}\{ x(t) \} $$ which can be evaluated based on the convolution integral as: $$y(t) = \mathcal{T}\{ x(t) \} = x(t) \star h(t) = ... |
Difference between revisions of "Timeline of prime gap bounds"
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127,277,395,046?# [m=5] ([http://terrytao.wordpress.com/2014/04/14/polymath8b-x-writing-the-paper-and-chasing-down-loose-ends/#comment-321171 Sutherland])
127,277,395,046?# [m=5] ([http://terrytao.wordpress.com/2014/04/14/polymath8b-x-wr... |
A family of quaternionic monodromy groups of the Kontsevich–Zorich cocycle
Institut de Mathématiques de Jussieu – Paris Rive Gauche, UMR 7586, Bátiment Sophie Germain, 75205 PARIS Cedex 13, France
For all $ d $ belonging to a density-$ 1/8 $ subset of the natural numbers, we give an example of a square-tiled surface co... |
$let\;\lambda,\mu\in\mathbb{Q}$ such that the GCD($2X^3-7X^2+\lambda X+3, X^3-3X^2+ \mu X +3)$
IS A POLYNOMIAL OF DEGREE 2.
I know this problem may seem trivial to you, but for me it seems like I just can't get it right with the greatest common divisor. I tried to use euclid's algorithm.
First I divided $\frac {2X^3-7X... |
The Standard Normal and The Chi-Square
We have one more theoretical topic to address before getting back to some practical applications on the next page, and that is the relationship between the normal distribution and the chi-square distribution. The following theorem clarifies the relationship.
\(V=\left(\dfrac{X-\mu... |
Searching online, I was not able to find construction of a confidence ellipse for $\mu$ in this case. Any help would be appreciated. Below is my attempt to construct $1- \alpha$ confidence ellipse.
(For simplicity suppose dim$(\vec{x})=2$) I try to use the fact that the statistics:
$$ T := (\overline{x} - \vec{\mu})^T ... |
Translating Code to Mathematics
Given a (more or less) formal operational semantics you can translate an algorithm's (pseudo-)code quite literally into a mathematical expression that gives you the result, provided you can manipulate the expression into a useful form. This works well for
additive cost measures such as n... |
I am trying to show that, if $X,Y$ are positive random variables, $$E((X+Y)^p)\leq 2^p\left( E(X^p)+E(Y^p)\right)$$where, if $0\leq p <1$, the $2^p$ can be replaced by $1$. I've been given the hint to think about the proof to Hölder's inequality, but I am not finding this tractable at all. Can anyone push me in the rig... |
Given Hamiltonian system with $2n$-dim phase space, if there exist $k\ge n$ independent integrals of motions then we call it integrable Hamiltonian system. The largest number of independent integrals of motions should be $2n-1$. As we know, if a Hamiltonian system is integrable, we can have action-angle variables with ... |
I am studying relativity and was working on deriving stellar aberration using relativity. My derivation is as follows:
Suppose that the observer is traveling at a velocity $v$ in the $x$-direction. Consider a light beam coming from a star to the ship's crew, which has velocity $c$ and components $u_x=c\cos\theta$ and $... |
determines the points $DFGE$ (see this post for details).
I am not sure of this claim. Therefore, I ask your advice both to assess if this is true and, otherwise,
to find the supplementary conditions needed.
Thanks for your help!
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1. Observation of a peaking structure in the J/psi phi mass spectrum from B-+/- -> J/psi phi K-+/- decays
PHYSICS LETTERS B, ISSN 0370-2693, 06/2014, Volume 734, Issue 37... |
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Thu, 26 Jul 2018
There are well-known tests if a number (represented as a base-10 numeral) is divisible by 2, 3, 5, 9, or 11. What about 7?
Let's look at where the divisibility-by-9 test comes from. We add up the digits of our number !!n!!. The sum !!s(n)!! is divisible by !!9!! if... |
In fact being able to express $B$ in that form and saying that $B$ is recursively enumerable are equivalent.
Here's a proof using Kleene Normal Form when $P$ is any partial recursive relation. First I'll show that if $B\subseteq\mathbb{N}^n$ is r.e., then there is a recursive relation $P\subseteq\mathbb{N}^{n+1}$ such ... |
The problem statement is as follows:
A triangle is dissected into six smaller triangles by its angle bisectors. Prove that the intersections of the angle bisectors of each of these smaller triangles lie on an ellipse.
Could anybody here solve it?
Mathematics Stack Exchange is a question and answer site for people study... |
I know this question has been asked previously but the answers didn't satisfy my query. Why choose gradient ascent instead of gradient descent when our aim is to minimize the cost function when we know that gradient ascent will maximize the cost function. Andrew Ng himself used gradient descent for logistic regression ... |
Directional derivative and gradient examples Example 1
Let $f(x,y) = x^2y.$ (a) Find $\nabla f(3,2)$. (b) Find the derivative of $f$ in the direction of (1,2) at the point (3,2).
Solution: (a) The gradient is just the vector of partialderivatives. The partial derivatives of$f$ at the point $(x,y)=(3,2)$ are:\begin{alig... |
Motivated by the public's desire to learn as much as possible following the occurrence of damaging events, we have developed a methodology to spatially map the probability of earthquake occurrence in the next 24 hours. We start with the simple aftershock model of Reasenberg and Jones (1989, 1990, 1994):
\[\ {\lambda}(t... |
Homology, Homotopy and Applications Homology Homotopy Appl. Volume 16, Number 1 (2014), 89-118. Holohonies for connections with values in $L_\infty$-algebras Abstract
Given a flat connection $\alpha$ on a manifold $M$ with values in a filtered $L_\infty$-algebra $\mathfrak{g}$, we construct a morphism $\mathsf{hol}^{\i... |
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The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
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Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Centers of mass (centroids)
For many (but certainly not all!) purposes in physics and mechanics,it is necessary or useful to be able to consider a physical object asbeing a mass concentrated at a single point, its
geometriccenter, also called its centroid. The centroid is essentiallythe ‘average’ of all the points in t... |
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