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I am reading the paper Slightly Superexponential Parameterized Problems at the moment and have two questions about it:
First question: The paper gives a proof of the following statement
Theorem 2.1: Assuming ETH, there is no $ 2^{o(klogk)}$ time algorithm for $ k \times k$ -Clique.
They prove this statement by sophisti... |
There is a number of methods of calculations among which are functions, differentiation and integration.
Application of Integrals is applied in various fields like Mathematics, Science, Engineering etc. For the calculation of areas, we use majorly integrals formulas. So let us give here a brief introduction on integral... |
Summary:
The expansion is around branch point hence the result is not unique! The result for $c>0$ and $x$ approaching $0$ along real axis is at the end.
Note: Version 11.3 is used! Details:
The problem stems from the fact that you are expanding about the branch point of square root for $c>0$. It is easy to see this as... |
$15.0~\mathrm{mL}$ of $1.4~\mathrm{M}\ \ce{HCl}$ was mixed with $1.00~\mathrm{g}$ of limestone (impure $\ce{CaCO3}$) until all the solid had dissolved. The solution was then transferred to a conical flask and made up to $200~\mathrm{mL}$ with water. A $20.0~\mathrm{mL}$ portion was then neutralised by $8.50~\mathrm{mL}... |
Overview
We give a short introduction to neural networks and the backpropagation algorithm for training neural networks. Our overview is brief because we assume familiarity with partial derivatives, the chain rule, and matrix multiplication.
We also hope this post will be a quick reference for those already familiar wi... |
Introduction
In this post, we derive the batch MLE procedure for the GARCH model in a more principled way than the last GARCH post. The derivation presented here is simple and concise.
The general GARCH model is defined as follows. \begin{align} V_1 &\sim \mu \\ X_n &\sim \NPDF(0,V_n) \label{GARCHobs} \\ V_n &= c + \su... |
While playing around with complete and incomplete zeta functions I found a nice formula which to my knowledge was not discussed in MSE.
Here it is
$$\sum_{k=2}^\infty (\zeta(k)-1) = 1\tag{1}$$
and its generalizaton
$$\sum _{k=2}^{\infty }\left( \zeta (k)-\left(1+\frac{1}{2^k}+\frac{1}{3^k}+...+\frac{1}{m^k}\right)\righ... |
I came across this question in a textbook and after a full day of going over it and consulting friends none of us can figure out why a particular approach to this question doesn't yield the correct answer.
The question
A light elastic string of natural length $0.2m$ has its ends attached to two fixed points $A$ and $B$... |
Learning Objectives
To convert a value reported in one unit to a corresponding value in a different unit.
The ability to convert from one unit to another is an important skill. For example, a nurse with 50 mg aspirin tablets who must administer 0.2 g of aspirin to a patient needs to know that 0.2 g equals 200 mg, so 4 ... |
Determine the behavior of the following sequences and calculate if there is a possible upper and lower bound.
a) $$a_n=\dfrac{8n}{1-2n}$$
b) $$b_n=\dfrac{2n}{1+n^2}$$
c) $$c_n=\dfrac{n^2+2}{-n-1}$$
Development:
a) The sequence is not constant since $$a_1=-8$$ and $$a_2=-\dfrac{16}{3}$$.
To verify if the solution is inc... |
I'm trying to figure out some details about involutions of division algebra, thought maybe someone here might have a better insight.
Let $k$ be a $p$-adic or number field, and let $K=k[\sqrt{\delta}]$ be a non-trivial extension of degree $2$. For $x\in K$, let $\bar{x}$ denote the conjugate of $x$ under the non-trivial... |
I was testing the .fft package of numpy 1.16.1 in Python 3.7.2. In particular I was trying to verify that the transform resembles the analytical one for: $$f(x) = \mathrm{exp}\left[-\left(\frac{x-5}{2}\right)^{2}\right]$$
I get from Wolfram Alpha that $\hat{f} = \mathcal{F}[f]$ looks like this:
Then I tried to replicat... |
Is it ever valid to include a two-way interaction in a model without including the main effects? What if your hypothesis is only about the interaction, do you still need to include the main effects?
In my experience, not only is it necessary to have all lower order effects in the model when they are connected to higher... |
My last post dealt with interactions between atoms that were separated by a small number of chemical bonds. This post deals with the interactions between the atoms that are
not connected by chemical bonds -- the nonbonded interactions.
Standard fixed-charge force fields typically have a nonbonded potential that account... |
So far we have seen how lines and formulas can estimate outputs given an input. We can describe any straight line with two different variables:
So far we have been rather fast and loose with choosing a line to estimate our output - we simply drew a line between the first and last points of our data set. Well today, we ... |
If we use the composite trapezoidal rule, then what is the least number of divisions $N$ for which the error of the integral $\int^1_0{e^{-x}}dx$ doesn't exceed $\frac{1}{12}\times10^{-2}$.
My guess is 11 or 5. Kindly tell me which of the answer is correct?
I obtained 11 as the answer by applying the formula
$$\Big|\fr... |
Difference between revisions of "Huge"
(→$C^{(n)}$-$m$-huge cardinals: corrected)
(→$C^{(n)}$-$m$-huge cardinals: I3)
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The first $C^{(n)}$-$m$-huge cardinal is not $C^{(n+1)}$-$m$-huge, for all $m$ and $n$ greater or equal than $1$. For suppose $κ$ is the least $C^{(n)}$-$m$-huge cardinal and $j : V → ... |
Filtering time-series data can be a tricky business. Many times what seems to obvious to our eyes is difficult to mathematically put into practice. A recent technique I've been reading about is called "total variance minimization" filtering or another name would be "$ \ell_1 $ trend filtering." Another member of this f... |
I am interested in solving numerically the following mathematical problem Consider an ode of the form $$ \dot q(t) = f(q(t),t_1,\ldots, t_N),\qquad t\in [0,T], $$ where $q\in \mathbb{R}^n$ is the state and $t_i,\, i=1,\ldots N$ are real parameters such that $0\le t_1 \le \ldots \le t_N\le T$.
Moreover $f$ is defined fr... |
This question already has an answer here:
Suppose that you write something like this for your students. This is just the beginning of something I would like to write to help them with the formal definition of a limit, but I am puzzled by the first output.
formalLimit[expr_, a_, L_, ϵ_] := Module[{f}, f[x_] := expr; f[2... |
These are only going to be a soft questions. And I thought this question is also a case for MO, so I have posted a duplicate there (Does that comply with the etiquette here? In case not I am sorry.)
When looking at the Liouville function, defined as $$ \lambda(n) = (-1)^{\Omega_n},$$ where $\Omega_n$ is the total count... |
"One-Line" Proof: Fundamental Group of the Circle
Once upon a time I wrote a six-part blog series on why the fundamental group of the circle is isomorphic to the integers. (You can read it here, though you may want to grab a cup of coffee first.) Last week, I shared a proof* of the same result. In one line
. On Twitter... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
I have a regression model
$y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 +u$
It is known that sample means of both $x_1$ and $x_2$ are zero, moreover the error term is said to be homoskedastic, the standard error of regression and standard errors of OLS estimates of the slope coefficients are given. Can we say something abou... |
Assume we have two independent random samples $(X_i)_{i=1}^{n}$ and $(Y_i)_{i=1}^{m}$ where $X_i\sim\mathrm{Uniform}(0,\theta_1)$ and $Y_j\sim\mathrm{Uniform}(0,\theta_2)$. To test, at the significant level $\alpha$, $H_0: \theta_1 = \theta_2$ against $H_1:\theta_1\ne\theta_2$ using Likelihood Ratio Test, denoting by $... |
A simple construction of inertial manifolds under time discretization
1.
Research Center for Applied Mathematics, Xi'an Jiaotong University, Xi'an, 710049, China
$ T_h^0\Phi(p)=\sum_{k=1}^{\infty}R(h)^kQF(p^{-k}+\Phi(p^{-k})) $
where $p^{-k}=(S^h_\Phi)^{-k}(p)$, see [1] for detailed definition. Here we get the existenc... |
2018-09-02 17:21
Measurement of $P_T$-weighted Sivers asymmetries in leptoproduction of hadrons / COMPASS Collaboration The transverse spin asymmetries measured in semi-inclusive leptoproduction of hadrons, when weighted with the hadron transverse momentum $P_T$, allow for the extraction of important transverse-momentu... |
You can resolve this by logical calculus only. Using standard notation, $\land$ is the "logical and", $\lor$ is the" logical or", and $\lnot$ is negation. Let's use the variables $t,s,m,b,c$ to represent different people being the culprit.The first line can be written : $(\lnot c \land \lnot s )\lor( c \land s)$ (one o... |
I have done this proof in my blog
Since I already have the code for the equations, I'm reproducing it here.
We have to prove that
$$F_{a-1, N-a} = \frac{MST}{MSE} = \frac{\frac{SST}{a-1}}{\frac{SSE}{N-a}} \tag{1}$$
reduces to
$$t_{k}^2 = \frac{(\bar{y}_{1.} - \bar{y}_{2.})^2}{S_{p}^2(\frac{1}{n_{1}} + \frac{1}{n_{2}})}... |
Search
Now showing items 1-1 of 1
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... |
Search
Now showing items 21-30 of 167
Anisotropic flow of charged hadrons, pions and (anti-)protons measured at high transverse momentum in Pb-Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV
(Elsevier, 2013-03)
The elliptic, $v_2$, triangular, $v_3$, and quadrangular, $v_4$, azimuthal anisotropic flow coefficients are measur... |
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∑i=0∞∑j=0∞∑k=0∞13i 3j 3k,i≠j≠k\large \sum_{i=0}^{\infty} \sum_{j=0}^{\infty} \sum_{k=0}^{\infty} \dfrac{1}{3^i \ 3^j \ 3^k}, \quad i≠j≠ki=0∑∞j=0∑∞k=0∑∞3i 3j 3k1,i=j=k
Find the value of the above triple summation. If your answer comes in form of ab\dfrac{a}{b}ba w... |
The standard algorithm for finding a maximum still works. Start with $a_1$ and go over the elements, if you see a larger value, update the maximum to be that value. The reason this works is that every element you skipped is smaller than at least one element, and can thus not be the maximum.To be clear, by the "standard... |
I just learned that almost %99 percent of an atom's mass comes from Strong Force Field Energy. But this energy is counted as my rest mass nevertheless. So in $ F=m.a$, should i take $m$ as rest mass (as standard description)? Or should i take $m$ as total energy that an object has? To make it more clear; if an object's... |
Training and Loss Training a model is called empirical risk minimization. Mean square error ( MSE) is the average squared loss per example over the whole dataset. To calculate MSE, sum up all the squared losses for individual examples and then divide by the number of examples:
$ MSE = \frac{1}{N} \sum_{(x,y)\in D} (y -... |
The Berlekamp-Massey algorithm and the extended Euclidean algorithm (both further extended with the Chien search and the Forney calculation of error values) for decoding BCH and RS codes (hereinafter referred to as the
decoder) have the following characteristic that is not well understood by many people:
If there is a ... |
Today we learned about filters and ultrafilters in the General Topology course. I am trying to play around with these definitions. I wish to ask a question that I am unsure about. Let us say, we have an ultrafilter $\mathcal{F}$ on the closed interval $[0, 1]$. Construct $\overline{\mathcal{F}} = \{ \overline{A} : A \i... |
Complicated resistor networks can be simplified by finding series and parallel resistor combinations within the context of the larger circuit.
Contents
Here is the example circuit we will work through together,
We see a voltage source connected to a resistor network. The two little circles near the left end represent t... |
Difference between revisions of "Mahlo"
(→$\Sigma_n$-Mahlo etc.: spiral)
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* Every Mahlo cardinal $\kappa$ is inaccessible, and indeed hyper-inaccessible and hyper-hyper-inaccessible, up to degree $\kappa$, and a limit of such cardinals.
* Every Mahlo cardinal $\kappa$ is inaccessible, and indeed hyper-in... |
Could any one give an example of a bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$?
Thank you.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community
Could any one give a... |
I'm studying Conway's functional Analysis by myself. In page 132 of his book, for showing every Closed subspace M of a reflexive Banach space X is reflexive, he says $\sigma(X,X^*)_{|_{M}}=\sigma(M,M^*)$. But I can not understand how it is. Please regard me. Thanks in advance
You can use the criterion that reflexivity ... |
Siril processing tutorial Convert your images in the FITS format Siril uses (image import) Work on a sequence of converted images Pre-processing images Registration (PSF image alignment) → Stacking Stacking
The final step to do with Siril is to stack the images. Go to the "stacking" tab, indicate if you want to stack a... |
Once we know what energy a given transition would have, we can ask, “Which transitions between energy levels or states are possible?” In answering this question, we also will learn why the longer cyanine dye molecules have stronger absorptions, or larger absorption coefficients.
Clearly the transitions cannot violate t... |
You cannot compare the values of coefficients in this way. Suppose that your response $Y$ is measured in meters, and you have two features $X_1$ and $X_2$ which are measured in seconds and hours respectively. Then your coefficients: $\beta_1$ has units meters/second and $\beta_2$ has units meters/hour - these are not c... |
The following is an exercise from Carothers'
Real Analysis:
Show that $$\int_{1}^{\infty}\frac{1}{x}=\infty$$ (as a Lebesgue Integral).
Attempt:
Let $E=[1,\infty)$.
$\int_E f=\int f\cdot \chi_E=\sup\{\int\varphi:\varphi \text{ simple }, 0\leq \varphi\leq f\}\cdot \chi_E$
I'm not sure how to find out what $\sup\{\int\va... |
We want to be fully transparent regarding the underlying calculations for the standard model types that Evidencio supports. This page lists our standard model types and the associated calculations
Linear Regression Models
Linear regression models are used to predict continuous outcomes. The prediction is estimated by:
... |
Huge cardinal Huge cardinals (and their variants) were introduced by Kenneth Kunen in 1972 as a very large cardinal axiom. Kenneth Kunen first used them to prove that the consistency of the existence of a huge cardinal implies the consistency of $\text{ZFC}$+"there is a $\omega_2$-saturated $\sigma$-ideal on $\omega_1$... |
Let $V$ be an inner product space and $(e_n)_{n=1}^{\infty}$ be an orthonormal system.
We call it complete if $\left \langle v,e_n \right \rangle=0$ for all $n$ implies $v=0$; and closed if $v=\sum_{n=1}^{\infty}\left \langle v,e_n \right \rangle e_n$ for every $v\in V$.
We've proved in class that a closed system is co... |
What's the state-of-the-art in the approximation of highly oscillatory integrals in both one dimension and higher dimensions to arbitrary precision?
I'm not entirely familiar with what's now done for cubatures (multidimensional integration), so I'll restrict myself to quadrature formulae.
There are a number of effectiv... |
When you fit a generalized linear model (GLM) in R and call
confint on the model object, you get confidence intervals for the model coefficients. But you also get an interesting message:
Waiting for profiling to be done...
What's that all about? What exactly is being profiled? Put simply, it's telling you that it's cal... |
Difference between revisions of "Vopenka"
(A start to the page: the definition & place in the hierarchy.)
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{{DISPLAYTITLE: Vopěnka's principle}}
+
{{DISPLAYTITLE: Vopěnka's principle }}
Vopěnka's principle is a large cardinal axiom at the upper end of the large cardinal hierarchy that is particularly n... |
Consider the function $f$ on $[0,1]\times [0,1]$ given by
$$f(x,y) = \frac{x^2-y^2}{(x^2+y^2)^2}, \,(x,y)\neq (0,0)$$
and $f(0,0) = 0.$
Let $M$ denote the $\sigma$-algebra of Lebesgue measuable sets and $m$ the Lebesgue measure.
In my previous question, it was shown that $f(x,y)$ is $M\times M$ measurable.
I am trying ... |
Answer
$$\cot\theta\sin\theta=\cos\theta$$
Work Step by Step
$$A=\cot\theta\sin\theta$$ - Quotient Identity: $$\cot\theta=\frac{\cos\theta}{\sin\theta}$$ Therefore, $A$ would be $$A=\frac{\cos\theta}{\sin\theta}\times\sin\theta$$ $$A=\cos\theta$$ Since no quotients appear here and all functions are of $\theta$ only, we... |
Difference between revisions of "Vopenka"
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{{stub}}
{{stub}}
+ + Revision as of 00:57, 4 February 2012 Vopěnka's principle is a large cardinal axiom at the upper end of the large cardinal hierarchy that is particularly notable for its applications to category theory. In a set theoretic setting, the mos... |
I came up with the following approximation
$$\sqrt[4]{\pi}+\frac{2}{1000}\gtrsim\frac{4}{3}$$
I don't know too much about proving an inequality like this algebraically. I was hoping for an extremely rigorous proof of this (I would definitely appreciate names of theorems). I am
just starting to self study computational ... |
$\newcommand{\HH}{\mathbb H}$$\newcommand{\RR}{\mathbb R}$$\newcommand{\ZZ}{\mathbb Z}$$\newcommand{\SL}{\mathop {\rm SL}}$
In your question $X = G \backslash \HH$ is given as a quotient. Also,$G$ is a finitely generated free group and a subgroup of $\SL(2,\RR)$.As $G$ is convex co-compact it follows that $G$ is discre... |
I'm nearly at the end of this derivation but totally stuck so I'd appreciate a nudge in the right direction
Consider a set of N identical but distinguishable particles in a system of energy E. These particles are to be placed in energy levels $E_i$ for $i = 1, 2 .. r$. Assume that we have $n_i$ particles in each energy... |
Topological Magic: Infinitely Many Primes The Basic Idea
A while ago, I wrote about the importance of open sets in topology and how the properties of a topological space $X$ are highly dependent on these special sets. In that post, we discovered that the real line $\mathbb{R}$ can either be compact or non-compact, depe... |
We show that the asynchronous push-pull protocol spreads rumors in preferential attachment graphs (as defined by Barabasi and Albert) in time \(O(\sqrt{\log n})\) to all but a lower order fraction of the nodes with high probability. This is significantly faster than what synchronized protocols can achieve; an obvious l... |
You don't need to keep chasing that one perfect strategy...
See how you can use algos to systematise your trading, remove emotions and finally
make your capital grow!
Grab your FREE Guide to Algo Trading PDF:
Anyone who’s tried pairs trading will tell you that real financial series don’t exhibit truly stable, cointegra... |
Answer
The solution set is $$\{0,\frac{\pi}{3},2\pi\}$$
Work Step by Step
$$\sin x=\sin2x$$ over interval $[0,2\pi)$ 1) In this case, only the interval for $x$, which is $[0,2\pi)$, is necessary, as you will see in step 2 that $\sin2x$ would be changed to a function of $x$ only. $$x\in[0,2\pi)$$ 2) Now consider back th... |
Difference between revisions of "Vopenka"
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In fact if Vopěnka's principle holds then there are a proper class of extendible cardinals; bounding the strength of the axiom from above, we have that
In fact if Vopěnka's principle holds then there are a proper class of extendible cardinals; bounding the str... |
This note addresses the typical applied problem of estimating from data how a target “conversion rate” function varies with some available scalar score function — e.g., estimating conversion rates from some marketing campaign as a function of a targeting model score. The idea centers around estimating the integral of t... |
I am new to ML. I am currently reading the classic book
Machine Learning in Action by Peter Harrington. In its implementation of ridge regression in P165 Listing 8.3, the book standardizes feature matrix $X$ by subtracting means of attributes and then dividing it by variances of attributes not by standard deviations of... |
The following is not particularly fast and could be more accurate but does make progress toward the goals set in the Question. To begin, consider the analytical properties of
f, as defined in the Question. By observation, it has branch points at
{I Sqrt[6/5] ξ, I Sqrt[2/5] ξ}
and their conjugates. Poles are obtained by... |
Permanent link: https://www.ias.ac.in/article/fulltext/pram/087/04/0056
We have synthesized, characterized and studied the third-order nonlinear optical properties of two different nanostructures of polydiacetylene (PDA), PDA nanocrystals and PDA nanovesicles, along with silver nanoparticles-decorated PDA nanovesicles.... |
4 Ways to Show a Group is Not Simple
You know the Sylow game. You're given a group of a certain order and are asked to show it's not simple. But where do you start? Here are four options that may be helpful when trying to produce a nontrivial normal subgroup.
Option 1: Show there is a unique Sylow p-subgroup.
This is t... |
Difference between revisions of "Vopenka"
(Added not necessarily weakly compact and external links section.)
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As stated above and from the point of view of ZFC, this is actually an axiom schema, as we quantify over proper classes, which from a purely ZFC perspective means definable proper classes.
As s... |
Current browse context:
cond-mat.dis-nn
Change to browse by: References & Citations Bookmark(what is this?) Condensed Matter > Disordered Systems and Neural Networks Title: Chaotic wave packet spreading in two-dimensional disordered nonlinear lattices
(Submitted on 20 Aug 2019)
Abstract: We reveal the generic character... |
Search
Now showing items 1-10 of 26
Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
The integrability of negative powers of the solution of the Saint Venant problem 2014 (English)In: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, ISSN 0391-173X, E-ISSN 2036-2145, Vol. XIII, no 2, p. 465-531Article in journal (Refereed) Published Abstract [en]
We initiate the study of the fini... |
The equation I am trying to solve is:
$$\lim\limits_{k \rightarrow 3} \left( \sum\limits_{n=1}^{n=k} \frac{1}{n^s}+ \frac{1}{k^{s - 1} \cdot (s - 1)}\right)=0 \tag{1}$$
The simplest possible analytic continuation of the Riemann zeta function is: $$\zeta(s)=\lim\limits_{k \rightarrow \infty} \left( \sum\limits_{n=1}^{n=... |
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x=yx=yx=y
x2=xyx^2=xyx2=xy
x2−y2=xy−y2x^2 - y^2=xy - y^2x2−y2=xy−y2
(x+y)(x−y)=y(x−y)(x + y)(x - y)= y(x - y)(x+y)(x−y)=y(x−y)
x+y=yx + y=yx+y=y
1+1=11 + 1=11+1=1
What is the fallacy?
Note by Sharky Kesa 5 years, 9 months ago
Easy Math Editor
This discussion boar... |
Background
Let's say you own a convenience store
Each day $N$ customers will visit you, where $N \in (1,7 \, billion \, humans)$
$X_i$ is the amount that each customer will spend
All the $X_i$'s are iid and also independent of $N$
Let's say you want to know the expected value of total revenue made in a day. I know the ... |
If $\exists a, b, m_1, m_2 \in \mathbb{Z}, a\equiv b\pmod {m_1}$ and $a\equiv b\pmod {m_2}$, then $\exists k \in \mathbb{Z}, a=b+{m_1m_2k\over gcd(m_1,m_2)} \implies a\equiv b\pmod L$, where $L$ is the l.c.m. of $m_1$ and $m_2$.
I am trying to derive, starting with the first part, with no success
$\exists l \in \mathbb... |
Hi: I've read this post: Uniform Circular Motion w/ Tension and Friction and helped me a lot.
I have a similar problem:
At one end of the rope ($R = 1 m$) is tied a mass ($m = 3 kg$) and the other end is attached to a spherical joint located in the center of a entirely horizontal turntable. The mass is on the turntable... |
Difference between revisions of "De Bruijn-Newman constant"
(→t>0)
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It is known that <math>\xi</math> is an entire function of order one ([T1986, Theorem 2.12]). Hence by the fundamental solution for the heat equation, the <math>H_t</math> are also entire functions of order one for any <math>t</math>.
... |
Input Inductor peak current
Q1) Can I use this formula for calculating input ripple current?
Q2) What will be the case if the input inductor is replaced with ferrite baed? I mean how can calculate the input ripple current?
Electrical Engineering Stack Exchange is a question and answer site for electronics and electrica... |
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 ... |
What was the improvement that Maxwell did to the electromagnetic field equations and why?
I understand that he combined the main equations so that you could get a wave equation for the vectors of $\bf E$ and $\bf B$ but is there anything else?
Physics Stack Exchange is a question and answer site for active researchers,... |
Show/Hide Sub-topics (O Level)
Radioactive decay refers to the process in which α-particles and β-particles are emitted by an unstable nuclei (contains too many neutrons or protons) of an element in order to form a more stable nuclei of another element.
The decaying nucleus is called the ‘parent’ nucleus; the resulting... |
In James and Stein (1961) the authors consider the following loss function for an estimator $\hat{\Sigma}$ of the covariance matrix $\Sigma$ of a multivariate normal distribution:
$$L(\hat{\Sigma}) = tr[\hat{\Sigma}\Sigma^{-1}] - \log|\hat{\Sigma}\Sigma^{-1}| - p.$$
This loss function has since been referred to as `Ste... |
1. Direct-address tables
Assume all elements’ keys are different and are from \(U={0, 1, …, m-1}\). Then the direct-address table is \(T[0..m-1]\), that is to say, the key is the index.
DIRECT-ADDRESS-SEARCH(T,k) return T[k] DIRECT-ADDRESS-INSERT(T,x) T[x.key]=x DIRECT-ADDRESS-DELETE(T,x) T[x.key]=NIL 2. Hash tables
Th... |
№ 9
All Issues On infinite-rank singular perturbations of the Schrödinger operator Abstract
Schrodinger operators with infinite-rank singular potentials $\sum^\infty_{i,j=1}b_{i,j}(\psi_j,\cdot)\psi_i$ are studied under the condition that singular elements $\psi_j$ are $\xi_j(t)$-invariant with respect to scaling trans... |
Let $F$ be a field, and let $A$ be a finite-dimensional associative $F$-algebra with multiplicative identity 1. If $M$ is a finite-dimensional module of $A$, define the character $\chi_M:A\rightarrow F$ given by $a\mapsto\mathrm{Trace}(a|_M)$.
If $\chi_i$ for $1\leq i\leq n$ are characters of pairwisely non-isomorphic ... |
I have a question regarding these strikingly similar problems with contradicting solutions. This is somewhat long, so prepare
Probblem 1
Consider a bag of ten coins, nine are fair, but one is weighted with both sides heads. You randomly select a coin and toss it five times. Let $2s$ denote the event of selecting the we... |
I just found the following Taylor series expansions around $z=0$ for the following functions:
$\displaystyle \frac{1}{z^{2}-5z+6} = \frac{1}{(z-2)(z-3)} = \frac{-1}{(z-2)} + \frac{1}{(z-3)} = \sum_{n=0}^{\infty}\frac{z^{n}}{2^{n+1}} - \sum_{n=0}^{\infty}\frac{z^{n}}{3^{n+1}} = \sum_{n=0}^{\infty}\left( \frac{1}{2^{n+1}... |
In classification problems, the usual negative log-likelihood loss function
$L(\theta)=\sum_{i=1}^N -\log(p(y_i|x_i,\theta))$
is always non-negative, since the $y_i$'s are discrete random variables and, as such, $p(y_i|x_i,\theta) \leq 1$ for all $\theta$. Therefore, the existence of a minimizer $\theta^*$ for $L(\thet... |
Today I learned about the Elliot Activation (or Sigmoid) Function. In fact, The MathWorks just included it in their most recent update to the Neural Network toolbox. The function was first introduced in 1993 by D.L. Elliot under the title A Better Activation Function for Artificial Neural Networks. The function closely... |
Yes, there is a certain sense in which your statements are true. As Mike Shulman and Qiaochu Yuan said, the strict fiber of a map cannot be defined in HoTT and doesn't make sense, but you can work from the other direction: instead of trying to associate a family of types to a map start with an arbitrary type family $P:... |
Let $E=\mathbb C/\Lambda$ be an elliptic curve,and let $D\subset E$ be a very small disc.
($D$ is round for the usual flat metric on $E$)
By the main result of [1], there exists a holomorphic immersion $f:E\setminus D \to \mathbb C$.
The image $f(\partial D)$ is a closed curve in $\mathbb C$ that self-intersects a bunc... |
title: Dependent Density Regression with PyMC3
My last post showed how to use Dirichlet processes and
pymc3 to perform Bayesian nonparametric density estimation. This post expands on the previous one, illustrating dependent density regression with
pymc3.
Just as Dirichlet process mixtures can be thought of as infinite ... |
I am reading a paper, and I came across the following definition of sinc interpolation.
Warning. I don't have a strong background in signal processing. Also, I have no clue what that bar on $\bar{F}$ means. I don't know why that would be the conjugate. Would it actually be the conjugate? Context. In this part, for a gi... |
By the result of Baker, Harman, Pintz (http://www.cs.umd.edu/~gasarch/BLOGPAPERS/BakerHarmanPintz.pdf), for any sufficiently large $x$ the interval $[x-x^{21/40},x]$ contains a prime number. This result implies the asymptotic $p(x)=x+O(x^{21/40})$ where the function $p(x)$ assigns to each real number $x$ the smallest p... |
There is a known mathematical question here: you are given a unitvector, lying on the $(n-1)$-sphere in $\mathbb{R}^n$, $v\in S^{n-1}$, and you wouldlike to associate with each such vector a frame in the tangent bundleof $S^{n-1}$ at $v$. This is a map $S^{n-1}\to \mathrm{F}S^{n-1}$ fromthe sphere to its frame bundle, ... |
Regularization using methods such as Ridge, Lasso, ElasticNet is quite common for linear regression. I wanted to know the following: Are these methods applicable for logistic regression? If so, are there any differences in the way they need to be used for logistic regression? If these methods are not applicable, how do... |
Difference between revisions of "Shrewd"
(→Properties: i.e. stationary)
(→Properties: for every class $\mathcal{A}$,)
Line 19: Line 19:
* If $κ$ is $\mathcal{A}$-$δ$-shrewd and $0 < η < δ$, then $κ$ is $\mathcal{A}$-$η$-shrewd. This is a difference between the properties of shrewdness and indescribability.
* If $κ$ is ... |
Learning Outcomes Recognize central limit theorem problems
The
central limit theorem for sample means says that if you keep drawing larger and larger samples (such as rolling one, two, five, and finally, ten dice) and calculating their means, the sample means form their own normal distribution (the sampling distributio... |
When class-conditional distributions are gaussian with equal covariance matrices, the optimal decision boundary is a hyperplane. This is the core concept behind Linear Discriminant Analysis (LDA).
For any data point $x$, the probability that $x$ comes from class $\omega_1$ is:
$P(x|\omega_1) \sim N(\mu_1,\Sigma) = (2\p... |
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Help me evaluate the infinite series of
1+2+3+4+5+......543\displaystyle 1 + \sqrt {2 + \sqrt[3] {3+ \sqrt[4] {4 + \sqrt[5] {5 +......}}}}1+2+33+44+55+.......
Note by Bryan Lee Shi Yang 4 years, 6 months ago
Easy Math Editor
This discussion board is a place to di... |
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