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t, colloid 2-droplet pair interactions, respectively; and $\Phi_{\textrm{dd}}$ is the droplet-droplet pair interaction.
The colloid-colloid pair interaction is composed of a short-ranged attractive square well and a longer-ranged repulsive Yukawa potential, $$\phi_{11}(r)=\left \{
\begin{array}{ll}
\infty & r< \sigma_{1} \\
- \epsilon_{\mathrm{SW}}
& \sigma_{1} <r< \sigma_{1}+\Delta \\
\epsilon_{\mathrm{Y}} \sigma_{1}\dfrac{e^{-\kappa \left ( r-\sigma_{1} \right )}}{r} & \textrm{otherwise,}
\end{array} \right .
\label{eqn:phic1c1}$$ $$\phi_{22}(r)=\left \{
\begin{array}{ll}
\infty & r< \sigma_{2} \\
- \epsilon_{\mathrm{SW}}
& \sigma_{2} <r< \sigma_{2}+\Delta \\
\epsilon_{\mathrm{Y}}\sigma _{2}\dfrac{e^{-\kappa \left ( r-\sigma_{2} \right )}}{r} & \textrm{otherwise,}
\end{array} \right .
\label{eqn:phic2c2}$$ and $$\phi_{12}(r)=\left \{
\begin{array}{ll}
\infty & r< \lambda \\
- \epsilon_{\mathrm{SW}}
& \lambda <r< \lambda +\Delta \\
\epsilon_{\mathrm{Y}}\lambda\dfrac{e^{-\kappa \left ( r-\lambda \right )}}{r} & \textrm{otherwise,}
\end{array} \right .
\label{eqn:phic1c2}$$ where $r$ is the the center-center distance of particles.
![Sketch of the pair interactions. (a) potentials between two colloidal particles with ${\epsilon_{\mathrm{SW}}=9k_{\textrm{B}}T}$, ${\Delta=0.09\sigma _{2}}$, $\epsilon_{\textrm{Y}}=24.6k_{\textrm{B}}T$ and (b) colloid-droplet potential at ${\sigma_{d}\left(t\right)=4\sigma_{2}}$, with $\sigma_1=1.2\sigma_2$.[]{data-label="fig:pot"}](fig2a "fig:"){width="4.25cm"} ![Sketch of the pair interactions. (a) potentials between two colloidal particles with ${\epsilon_{\mathrm{SW}}=9k_{\textrm{B}}T}$, ${\Delta=0.09\sigma _{2}}$, $\epsilon_{\textrm{Y}}=24.6k_{\textrm{B}}T$ and (b) colloid-droplet potential at ${\sigma_{d}\left(t\right)=4\sigma_{2}}$, with $\sigma_1=1.2\sigma_2$.[]{data-label="fig:pot"}](fig2b "fig:"){width="4.25cm"}
In Fig. \[fig:pot\](a), the colloid-colloid interaction potentials are plotted against the s
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a$ such that $\alpha$ ends a weak gap and $J_\a(\mathbb{R}){\vDash}\max(\b, {\gamma})<\utilde{\d}^2_1$. Notice that $f$ is $\Delta^2_1$ in codes. We define $\phi$ as follows.
\[definition of phi\] If $x\not \in S \cap \mathbb{R}$ then let $\phi(x)=\emptyset$. Suppose now $x\in S$. Let $(y_x, \P_x)$ be the pair coded by $x$. Given $\b, {\gamma}<\k$, we let $(\b, {\gamma})\in \phi(x)$ iff letting $\P=\P_x$ and $f(\b, {\gamma})=\a$ then for some $a\in \P$ the following holds in $J_\a(\mathbb{R})$:
1. $\P$ is suitable and short tree iterable,
2. $a$ is the collapse of $x(0)$,
3. $a\subseteq \l_\P\times \l_\P$,
4. there is a correctly guided short tree $\T$ with last model $\S$ such that $\pi_{\P, \S}$ exists and an $\S$-cardinal $\eta$ such that
1. $(\eta^+)^\S<\l^\S$,
2. if $\Q=\S|(\eta^+)^\S$ and $a^\Q=\pi_{\P, \S}(a){\restriction}\eta$ then $(\b, {\gamma})\in \pi_{\Q, \infty}(a^\Q)\cap rng(\pi_{\Q, \infty})$.
Given $\a<\Theta$ we let $S_a$ and $\phi_\a$ be what the above definitions give over $J_\a(\mathbb{R})$. The following lemmas establish that $\phi$ is as desired. We start with the following easy lemma.
\[easy lemma\] For each $x\in \mathbb{R}$, $\phi(x)=\cup_{\a<\k} \phi_\a(x)$.
Suppose $(\b, {\gamma})\in \phi(x)$. Then letting $\a=f(max(\b, {\gamma}), f(\b, {\gamma}))$. Then $(\b, {\gamma})\in \phi_\a(x)$. The other direction is similar.
For every $x\in \mathbb{R}$, $\phi(x)\subseteq \kappa\times \kappa$.
The claim follows from the fact that for every $\a$ and $a$, $\M_{\infty}(\a, a)\subseteq J_\a(\mathbb{R})$.
Suppose $F:\kappa\rightarrow \kappa$. Then there is $x\in dom(\phi)$ such that $\phi(x)=F$.
Fix $y$ such that $F\in \H_y$. There is then a suitable $\P$ over $y$ such that $F\in rng(\pi_{\P, \emptyset, \infty})$[^6] Notice that $\pi_{\P, \emptyset, \infty}(\l_\P)=\k$ (see Chapter 8 of [@OIMT]). Let then $a\subseteq \l_\P\times \l_\P$ be such that $\pi_{\P, \emptyset, \infty}(a)=F$ and let $x$ code the pair $(y, \P)$ such that $x(0)=a$. It is then easy to see that $\phi(x)
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tments.icmab.es/leem/siesta.
---
author:
- 'D. Kaledin[^1]'
date: '*To Yu. I. Manin, the founder, on the occasion of his 70-th birthday*'
title: Cyclic homology with coefficients
---
Introduction {#introduction .unnumbered}
============
Ever since it was discovered in 1982 by A. Connes [@C1] and B. Tsygan [@tsy], cyclic homology occupies a strange place in the realm of homological algebra. Normally in homological algebra problems, one expects to start from some data, such e.g. a topological space $X$, then construct some abelian category, such as the category of sheaves on $X$, and then define the cohomology of $X$ by computing the derived functors of some natural functor, such as e.g. the global sections functor $\Gamma(X,-)$. Admittedly, this is a modern formulation, but it had certainly been current already in 1982. Cyclic homology starts with an associative algebra $A$, and defines its homology groups $HC_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}(A)$, but there are absolutely no derived functors in sight. Originally, $HC_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}(A)$ were defined as the homology of an explicit complex, – which anyone trained to use triangulated categories cannot help but take as an insult. Later A. Connes [@C] improved on the definition by introducing the abelian category of so-called cyclic vector spaces. However, the passage from $A$ to its associated cyclic vector space $A_\#$ is still done by an explicit [*ad hoc*]{} formula. It is as if we were to know the bar-complex which computes the homology of a group, without knowing the definition of the homology of a group.
This situation undoubtedly irked many people over the years, but to the best of my knowledge, no satisfactory solution has been proposed, and it may not exist – indeed, many relations to the de Rham homology notwithstanding, it is not clear whether cyclic homology properly forms a part of homological algebra at all (to the point that e.g. in [@FT] the word “homology” is not used at all for $HC_{{\:\raisebox{1pt
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|
1.06 (0.25) 0.92 (0.17)
Nitrogen dioxide 60.05 (26.09) 46.43 (17.67)
8-hour average ozone slip in a day 74.28 (54.90) 90.24 (52.46)
Data Analysis
-------------
Since the effect of weather and air quality on respiratory conditions in humans was not instantaneous, representative lags were applied to variables based on the work done previously in this area \[[@ref3],[@ref24]-[@ref26]\]. To simplify the delayed impact of respiratory conditions, we considered a 3-day lag for all variables.
We removed records with less than 10 people on weekends to eliminate weekend effects, bringing the total number of samples collected to 559. To create a meaningful feature vector for training and cross-validation, the date field was removed to obtain a (*X*, *y*), where *X* was a matrix with the dimensions (*m* × *n* = 559 × 9) representing values of variables, and *y* was a vector of length (m=559) representing the output class of the examples (ie, events). Analysis of the data suggested that the output class was highly imbalanced with 413 examples of nonpeak and 146 examples of peak events.
Machine Learning Approaches
---------------------------
In this section the ML algorithms are presented and discussed; details of the updating and classification processes are described in the following algorithms.
### Generalized Linear Models
1. Construct the common linear model from the original training set: *f*  = *w^T^ x* + *b*, where *w* is the weight vector and *b* is the bias, both of which are only determined by the training samples
2. Identify the contact function *f* ^-1^
3. Build the GLMs:  = *f* ^-1^ (*w^T^ x* + *b*)
4. Calculate the classification on the test set
### Support Vector Machine
1. Convert the sample space into linearly separable space with polynomial core functions *K* (*x*~i~, *y*~i~)
2. Calculate the support vectors with the foll
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| 1,716
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| 1,031
| 0.795381
|
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|
$\lambda$, $L$ and their complex conjugates, the relation
\[eq:ms:8\] [( \^i[( \_iL+|\_i||[L]{} )]{}-I\_q )]{}b=0.
The vector $b$ can be identified with an eigenvector of equation (\[eq:ms:8\]). Since $b$ is known from the initial system (\[eq:SW:1\]), the equation has to be satisfied by an appropriate choice of functions $\Omega$, $\bar{\Omega}$, of wave vectors $\lambda$, $\bar{\lambda}$ and of rotation matrices $L$ and $\bar{L}$. In particular, this requires that the dispersion relation
\[eq:ms:10\] [( \^i[( \_i L+|\_i|[L]{} )]{}-I\_q )]{}=0
holds. Equation (\[eq:ms:10\]) is an additional condition on $\lambda$ and $\bar{\lambda}$, $L$ and $\bar{L}$ for the equation (\[eq:ms:8\]) to have a solution. Multiplying equations (\[eq:ms:5\]) on the left by the matrix $\Phi$, writing the matrix $\Phi$ explicitly using the notations (\[eq:ms:3\]), and then solving for ${\partial}f/{\partial}r$ and ${\partial}f/{\partial}\bar{r}$, we obtain the system
\[eq:ms:12\] =,=,
where the scalar functions $\sigma_1$ and $\sigma_2$ and their complex conjugates are defined by the equations
\[eq:ms:13\] \_1=(L b+),\_2=(L b+).
In order to ensure that system (\[eq:ms:12\]) is well-defined in the sense that it can be expressed as a system for $f$ in terms of $r$ and $\bar{r}$, we introduce the vector fields
\[eq:ms:14\] X\_a=\^i\_a(u)\_[x\^i]{},a=1,…, p-2,
where the complex coefficients $\xi^i_a(u)$ satisfy the orthogonality relations
\[eq:ms:15\] \^i\_a\_i=0,\^i\_a|\_i=0.
Next, we apply them to equations (\[eq:ms:12\]), which gives us the following conditions
&X\_a=0,\
&X\_a=0,
$a=1,\ldots, p-2$, since the vector fields $X_a$ annihilate all the functions $f(r,\bar{r})$.
#### Remark 1:
The system (\[eq:ms:12\]) for $f(r,\bar{r})$ is not necessarily integrable. However, it is possible to use the arbitrary functions defining the function $\Omega(x,u)$, the wave vectors $\lambda(u)$, $\bar{\lambda}(u)$, the vectors $\tau(x,u)$, $\bar{\tau}(x,u)$ and the matrices of rotation $L(x,u)$, $\bar{L}(x,u)$, in order to satisfy
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e way to deploy your Angular app is to use GitHub Pages.
The first step is to create a GitHub account, and then create a
repository for your project. Make a note of the user name and project
name in GitHub.
Then all you need to do is run ng build --prod --output-path docs
--base-href PROJECT_NAME, where PROJECT_NAME is the name of your project in GitHub. Make a copy of docs/index.html and name it
docs/404.html.
Commit your changes and push. On the GitHub project page, configure it
to publish from the docs folder.
And that's all you need to do! Now you can see your page at
https://USER_NAME.github.io/PROJECT_NAME/.
You can also use angular-clip-ghpages, a full featured package that
does this all this for you and has extra functionality.
Q:
Nest URIs but not controllers or views in AngularUI Router
Using AngularUI Router I want to nest some URIs but not their views or controller actions.
For example, I would like these URIs:
/things - lists the recent things.
/things/:x - shows the details of thing with id x.
If I use the "Nested States & Views" from the wiki then I have to actually nest the "list of things" and "show single thing" views, which happen to be unrelated. Moreover, the "show single thing" scope will have the "list of things" even though it will not need them.
If I use the "Nested States & Views" from the README then I've got a separate /things/list URI instead of plain old /things like I want.
It seems like I want a separate "list" (or "index") state that resolves to the base URL for an otherwise nested state but without passing on the view and actions to child states. Is this possible?
A:
Rather than using nested routes, I recommend specifically declaring the url; however, you could also use an absolute route - '^/things/:x'.
Using the routes you provided in your question, here is an example of how you could possibly go about it.
DEMO (with code): http://plnkr.co/edit/sxOeCBipiQS7AOt4Ax4L?p=preview
DEMO (without code, shows route urls): http://run.plnkr.co/uT4PLYDqk8ItzqaK/#/t
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. I am also very grateful to Professor P. V. Giaquinta for continuous encouragement and suggestions. Finally, discussions with Dr Giuseppe Pellicane during the final stage of this work are gratefully acknowledged.
Weinberg’s formalism {#app:weinberg}
====================
Consider a quantum system in a state described by the wave fields $|\Psi\rangle$ and $\langle\Psi|$, where Dirac’s bra-ket notation is used to denote $\Psi(r)\equiv \langle r|\Psi\rangle$ and $\Psi^*(r)\equiv \langle \Psi| r\rangle$. Observables are defined by functions of the type $$a=\langle\Psi|\hat{A}|\Psi\rangle\;,$$ where the operators are Hermitian, $\hat{A}=\hat{A}^{\dag}$. Weinberg’s formalism can be introduced by defining Poisson brackets in terms of the wave fields $|\Psi\rangle$ and $\langle\Psi|$. To this end, one considers the wave fields as “phase space” coordinates $\mbox{\boldmath$\zeta$}\equiv(|\Psi\rangle , \langle\Psi|)$, so that $\zeta_1=|\Psi\rangle$ and $\zeta_2=\langle\Psi|$, and then introduce brackets of observables as $$\begin{aligned}
\{a,b\}_{\mbox{\tiny\boldmath$\cal B$}}&=&\sum_{\alpha=1}^2\frac{\partial a}{\partial \zeta_{\alpha}}
{\mathcal B}_{\alpha\beta}\frac{\partial b}{\partial \zeta_{\beta}}\;.
\label{eq:poissonbracket}\end{aligned}$$ The bracket in Eq. (\[eq:poissonbracket\]) defines a Lie algebra and a Hamiltonian systems. Typically, the Jacobi relation is satisfied, *i.e.* $
{\cal J}=\left\{a,\left\{b,c\right\}_{\mbox{\tiny\boldmath$\cal B$}}
\right\}_{\mbox{\tiny\boldmath$\cal B$}}
+\left\{c\left\{a,b\right\}_{\mbox{\tiny\boldmath$\cal B$}}
\right\}_{\mbox{\tiny\boldmath$\cal B$}}
+\left\{b,\left\{c,a\right\}_{\mbox{\tiny\boldmath$\cal B$}}
\right\}_{\mbox{\tiny\boldmath$\cal B$}}=0$. In order to obtain the usual quantum formalism, one can introduce the Hamiltonian functional in the form $${\cal H}[|\psi\rangle , \langle\psi|]\equiv {\cal H}[\mbox{\boldmath$\zeta$}]
= \langle\psi|\hat{H}|\psi\rangle \;,
\label{eq:h_qm}$$ where $\hat{H}$ is the Hamiltonian operator of the system. Equations of
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|
y}{l l}
\begin{pmatrix} s_i&\pi y_i\\ \pi v_i&1+\pi z_i \end{pmatrix} & \quad \textit{if $i$ is even and $L_i$ is \textit{of type $I^o$}};\\
\begin{pmatrix} s_i&r_i&\pi t_i\\ \pi y_i&1+\pi x_i&\pi z_i\\ v_i&u_i&1+\pi w_i \end{pmatrix} & \quad \textit{if $i$ is even and $L_i$ is \textit{of type $I^e$}};\\
\begin{pmatrix} s_i&\pi r_i&t_i\\ y_i&1+\pi x_i& u_i\\\pi v_i&\pi z_i&1+\pi w_i \end{pmatrix}
& \quad \textit{if $i$ is odd and $L_i$ is \textit{free of type $I$}};\\
m_{i,i} & \quad \textit{otherwise}.
\end{array} \right.$$ Here, $s_i$ is an $(n_i-1 \times n_i-1)$-matrix (resp. $(n_i-2 \times n_i-2)$-matrix) if $i$ is even and $L_i$ is *of type $I^o$* (resp. if $i$ is even and $L_i$ is *of type $I^e$*, or if $i$ is odd and $L_i$ is *free of type $I$*) and $y_i, v_i, z_i, r_i, t_i, y_i, x_i, u_i, w_i$ are matrices of suitable sizes.
3. Assume that $i$ is even and that $L_i$ is *of type I*. Then $$z_i+\delta_{i-2}k_{i-2, i}+\delta_{i+2}k_{i+2, i}=\pi z_i^{\ast}$$ such that $z_i^{\ast}\in B\otimes_AR$. Here,
- $z_i$ is an entry of $m_{i,i}$ as described in the above step (b).
- $k_{i-2, i}$ (resp. $k_{i+2, i}$) is the $(n_{i-2}, n_i)^{th}$-entry (resp. $(n_{i+2}, n_i)^{th}$-entry) of the matrix $m_{i-2, i}$ (resp. $m_{i+2, i}$) if $L_{i-2}$ (resp. $L_{i+2}$) is *of type* $\textit{I}^o$.
- $k_{i-2, i}$ (resp. $k_{i+2, i}$) is the $(n_{i-2}-1, n_i)^{th}$-entry (resp. $(n_{i+2}-1, n_i)^{th}$-entry) of the matrix $m_{i-2, i}$ (resp. $m_{i+2, i}$) if $L_{i-2}$ (resp. $L_{i+2}$) is *of type* $\textit{I}^e$.
4. Assume that $i$ is odd and that $L_i$ is *bound of type I*. Then $$\delta_{i-1}v_{i-1}\cdot m_{i-1, i}+\delta_{i+1}v_{i+1}\cdot m_{i+1, i}=\pi m_{i,i}^{\ast}$$ such that $m_{i,i}^{\ast} \in M_{1\times n_i}(B\otimes_AR)$. Here,
- $v_{i-1}=(0,\cdots, 0, 1)$ (resp. $v_{i-1}=(0,\cdots, 0, 1, 0)$) of size $1\times n_{i-1}$ if $L_{i-1}$ is *of type* $\textit{I}^o$ (resp. *of type* $\textit{I}^e$).
- $v_{i+1}=(0,\cdots, 0, 1)$ (resp.
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| 0.78043
|
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|
small &<br /> large business<br /> for<span> all sectors</span></p>
<a href="http://motors06.denison-automotive.co.uk/denison/denison-2/web-sites/"><span class="viewMorePsGreen">GO</span></a>
</div>
</div>
</div>
<div class="wrapPortalItem col-md-8">
<div class="insideWrapItem">
<span class="iconI-iconDA_yourbrand"></span>
<div class="portalItem">
<h1>BRANDING</h1>
<p><span>branding<br /> </span> and<br /> design</p>
<a href="http://motors06.denison-automotive.co.uk/denison/denison-2/branding/"><span class="viewMorePsGreen">GO</span></a>
</div>
</div>
</div>
<div class="clearfix"></div>
</div>
</div>
A:
It's difficult to say exactly without seeing some code, but I'd guess your problem is the the left edge of your is sitting at 50% but you want the center of the to sit in the center of it's parent?
Try something like this on the span (in addition to any other styles):
span {
position: absolute;
left: 50%;
transform: translateX(-50%);
}
This should move (trasnlate) the half of it's own width to it's left.
Q:
how to integrate vue.js with django?
This is the single page application with vue.js and it does some simple calculation and i am trying to implement this calculation in django but it is not giving me the result I want.
Here I made the array in the vue.js dynamic and this is displaying me only the image of the product perfectly but not product.name and product.sell_price and also @click.prevent="addToCart(product)"this function is not working ?? How can i solve it ?
vue.js
<script src="{% static 'js/vue.js' %}"></script>
<script type="text/javascript" src="{% static '/js/vue-resource.js' %}"></script>
<script>
new Vue({
el: '#posApp',
data: {
total: 0,
discount: 0,
products: [
{% for product in products %}
{
"id": {{product.id}},
"name": "{{pro
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| 0.825073
|
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|
ron.com [mailto:Cooper.Richey@enron.com]
Sent: Thursday, December 06, 2001 8:25 AM
To: JHawker@petersco.com
Subject: RE:
i'll just need a receipt and you're done
-----Original Message-----
From: Jai Hawker <JHawker@petersco.com>@ENRON
Sent: Thursday, December 06, 2001 8:24 AM
To: Richey, Cooper
Subject: RE:
Sure. The original cost was $100.
-----Original Message-----
From: Cooper.Richey@enron.com [mailto:Cooper.Richey@enron.com]
Sent: Thursday, December 06, 2001 8:23 AM
To: JHawker@petersco.com
Subject: RE:
you're done on the 85% discount ?
-----Original Message-----
From: Jai Hawker <JHawker@petersco.com>@ENRON
Sent: Thursday, December 06, 2001 8:21 AM
To: Richey, Cooper
Subject: RE:
We should be done then.
-----Original Message-----
From: Cooper.Richey@enron.com [mailto:Cooper.Richey@enron.com]
Sent: Thursday, December 06, 2001 7:51 AM
To: JHawker@petersco.com
Subject: RE:
9
-----Original Message-----
From: Jai Hawker <JHawker@petersco.com>@ENRON
Sent: Thursday, December 06, 2001 7:44 AM
To: Richey, Cooper
Subject: RE:
What size are your shoes?
-----Original Message-----
From: Cooper.Richey@enron.com
[mailto:Cooper.Richey@enron.com]
Sent: Thursday, December 06, 2001 7:44 AM
To: JHawker@petersco.com
Subject: RE:
i'd have to see them and they'd have to fit my shoes, but as
long
as
the
discount is in the 85-90% range,
i'm cool with it.
-----Original Message-----
From: Jai Hawker <JHawker@petersco.com>@ENRON
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|
_Z$ are both reduced, $Z/R|_Z$ is the seminormalization of $W$ and $Z/R|_Z\to W$ is not an isomorphism.
\[bb.count.exmp\] The following counter example to (\[quot.X/S.finite.lem\]) is proposed in [@bial 6.2]. Consider the diagram $$\begin{array}{ccc}
{\operatorname{Spec}}k[x,y] & \stackrel{p_1}{\longrightarrow} & {\operatorname{Spec}}k[x,y^2,y^3]\\
p_2\downarrow\hphantom{p_2} && \hphantom{q_2}\downarrow q_2\\
{\operatorname{Spec}}k[x+y,x+x^2, y^2,y^3]& \stackrel{q_1}{\longrightarrow} &
{\operatorname{Spec}}k[x+x^2, xy^2, xy^3, y^2,y^3]
\end{array}
\eqno{(\ref{bb.count.exmp}.1)}$$ It is easy to see that the $p_i$ are homeomorphisms but $q_2p_1=q_1p_2$ maps $(0,0)$ and $(-1,0)$ to the same point. If (\[bb.count.exmp\].1) were a universal push-out, one would get a counter example to (\[quot.X/S.finite.lem\]). However, it is not a universal push-out. Indeed, $$\begin{array}{rcl}
\tfrac13(x+y)^3+\tfrac12(x+y)^2&=&\ \
\bigl(\tfrac13 x^3+\tfrac12x^2\bigr)+ (x^2+x)y\ \ \ \ \ \ \ \
+xy^2+\tfrac12y^2+\tfrac13 y^3\\[1ex]
&=&
-\bigl(\tfrac23 x^3+\tfrac12x^2\bigr)+ (x^2+x)(x+y)+xy^2+\tfrac12
y^2+\tfrac13 y^3
\end{array}$$ shows that $\tfrac23 x^3+\tfrac12x^2$ is also in the intersection $k[x,y^2,y^3]\cap k[x+y,x+x^2, y^2,y^3]$.
Another case where $X/R$ is easy to obtain is the following.
\[quot.pure.dim.lem\] Let $p_1,p_2:R\rightrightarrows X$ be a finite, set theoretic equivalence relation where $X$ is normal, Noetherian and $X,R$ are both pure dimensional. Assume that one of the following holds:
1. $X$ is defined over a field of characteristic 0,
2. $X$ is essentially of finite type over $S$, or
3. $X$ is defined over a field of characteristic $p>0$ and the Frobenius map $F^p:X\to X^{(p)}$ (\[frob.say\]) is finite.
Then the geometric quotient $X/R$ exists as an algebraic space. $X/R$ is normal, Noetherian and essentially of finite type over $S$ in case (2).
Proof. Let us first deal with the case when $R$ comes from a finite group acting on $X$. This case is a result of Deligne, discussed in [@Knutson71 IV.1.
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|
a_{4}$ $\beta_{5}$ $\beta_{6}$ $\beta_7$
------ ---------------- ------------- ------------- ------------- ------------- ------------- ------------- -----------
1 K=50 0.054 0.064 0.052 0.052 0.038 0.040 0.048
K=100 0.056 0.062 0.044 0.050 0.050 0.038 0.056
K=150 0.070 0.060 0.062 0.050 0.052 0.050 0.048
mVC 0.056 0.076 0.058 0.044 0.038 0.086 0.072
mMSE 0.068 0.046 0.068 0.062 0.074 0.078 0.044
BLB($n^{0.6}$) 0.000 0.000 0.000 0.000 0.000 0.002 0.000
BLB($n^{0.8}$) 0.004 0.002 0.000 0.004 0.000 0.000 0.000
SDB($n^{0.6}$) 0.000 0.000 0.000 0.000 0.000 0.000 0.000
SDB($n^{0.8}$) 0.000 0.000 0.000 0.000 0.000 0.000 0.000
TB 0.066 0.068 0.058 0.056 0.042 0.042 0.072
2 K=50 0.044 0.050 0.054 0.058 0.066 0.052 0.060
K=100 0.050 0.046 0.050 0.060 0.054 0.032 0.052
K=150 0.054 0.052 0.060 0.070 0.054 0.040 0.052
mVC 0.076 0.098 0.092 0.086 0.094 0.078 0.070
mMSE 0.076 0.086 0.086 0.074 0.082 0.098 0.060
BLB($n^{0.6}$) 0.000 0.000 0.000 0.000 0.000
| 312
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|
extit{if $l=2m-1$}.
\end{array} \right.$$
Both forms are alternating and bilinear.
- Define $Z(L)$ to be the sublattice of $L$ such that $Z(L)/\pi B(L)$ is the radical of the quadratic form $\frac{1}{2^{m+1}}q$ mod $2$ on $B(L)/\pi B(L)$ if $l=2m$.
(see, e.g., page 813 of [@Sa] for the notion of the radical of a quadratic form on a vector space over a field of characteristic 2.)
\[r26\] As in Remark 2.6 of [@C2],
1. We can associate the 5 lattices $(B(L), W(L), X(L), Y(L), Z(L))$ above with $(A_i, h)$ in place of $L$. Let $B_i,W_i,X_i,Y_i,Z_i$ denote the resulting lattices.
2. As $\kappa$-vector spaces, the dimensions of $A_i/B_i$ and $W_i/X_i$ are at most 1.
Let $L=\bigoplus_i L_i$ be a Jordan splitting. We assign a type to each $L_i$ as follows:
parity of $i$ type of $L_i$ condition
--------------- --------------- -----------------------------------------------------------
even $I$ $L_i$ is of parity type $I$
even $I^o$ $L_i$ is of parity type $I$ and the rank of $L_i$ is odd
even $I^e$ $L_i$ is of parity type $I$ and the rank of $L_i$ is even
even $II$ $L_i$ is of parity type $II$
odd $II$ $A_i=B_i$
odd $I$ $A_i \varsupsetneq B_i$
In addition, we assign a subtype to $L_i$ in the following manner:
parity of $i$ subtype of $L_i$ condition
--------------- -------------------- ------------------------------------------------------------------------
even bound of type $I$ $L_i$ is of type $I$ and either $L_{i-2}$ or $L_{i+2}$ is of type $I$
even bound of type $II$ $L_i$ is of type $II$ and either $L_{i-1}$ or $L_{i+1}$ is of type $I$
odd bound either $L_{i-1}$ or $L_{i+1}$ is of type $I$
In all other cases, $L_i$ is called $free$. If $L_i$ with $i$ odd is *of type II*, then $L_i$ should be *free*. In other words, a lattice $L_i$ with $i$ odd cannot be *bound of type II*.
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|
font-size:25px;
line-height:30px;
font-weight:bold;
font-family:Raleway;
text-align:center;
background-repeat:no-repeat;
}
Q:
How to simplify $\Re\left[\sqrt2 \tan^{-1} {x\over \sqrt i}\right]$?
While solving $$\int \frac{x^2+1}{x^4+1}\,dx,$$ I tried to use partial fractions in the denominator by writing $x^4+1=(x^2+i)(x^2-i)$ And then I got $\Re\left[\sqrt2 \tan^{-1}{x\over \sqrt i}\right]$. In my book they used another method without complex numbers and they got $\frac{1}{\sqrt2} \tan^{-1} \left(\frac{x^2-1}{x\sqrt2}\right)$. How do I prove my answer is equal to theirs? I tried the realtions between log and atan but I couldnt get rid of the $i$. Edit: Please note that this question is not about solving the integral (which I already solved to get $\Re\left[\sqrt2 \tan^{-1}{x\over \sqrt i}\right]$.) but about the simplification of the answer I got using complex partial fractions method to reduce it to the real part only.
A:
$$\Re\left[\sqrt2 \tan^{-1}{x\over \sqrt i}\right]=\Re\left[\sqrt2 \tan^{-1}{x\cdot e^{-i\pi/4}}\right]=\frac{(\sqrt2 \tan^{-1}{x\cdot e^{-i\pi/4}})+(\sqrt2 \tan^{-1}{x\cdot e^{i\pi/4}})}{2}$$
$$=\frac{1}{\sqrt{2}}\left( \tan^{-1}{x\cdot e^{i\pi/4}}+\tan^{-1}{x\cdot e^{-i\pi/4}} \right)=\frac{1}{\sqrt{2}}\tan^{-1}\frac{x\cdot e^{i\pi/4}+x\cdot e^{-i\pi/4}}{1-x\cdot e^{i\pi/4}\cdot x\cdot e^{-i\pi/4}}$$
$$=\frac{1}{\sqrt{2}}\tan^{-1}\frac{2x\cos \frac{\pi}{4}}{1-x^2}=\frac{1}{\sqrt{2}}\tan^{-1}\frac{\sqrt{2}x}{1-x^2}$$
where line $2\to3$ is achieved by using that $\tan(x+y)=\frac{\tan x + \tan y}{1- \tan x \tan y}$.
The differs from the expression you give by a constant, after further noting that $\tan^{-1}x+\tan^{-1}\left(\frac{1}{x}\right)=\frac{\pi}{2}$ for $x>0$.
Q:
Separate the contents of a xml node with xsl
I'm modifying my xml document with xsl and having trouble separating contents of a node. Here's an example:
Input XML Document
<root>
<exampleNode>text 1 <insideNodeA/> text 2 <insideNodeB/> text 3</exampleNode>
<exampleNode>text 4<insideNodeB/></exampleNode>
</r
| 314
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| 853
| 365
| 1,466
| 0.789229
|
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|
- 25.2$ and PSNR values are between $18.1 - 19.9\%$. []{data-label="fig:FBPs"}](Cosine "fig:"){width="6.3cm"}]{} (5,3)[![Filtered backprojection reconstructions using (a) Shepp–Logan filter, (b) Cosine filter (c) Hamming filter, (d) Hann filter. Values of relative error (RE) are between $23.6 - 25.2$ and PSNR values are between $18.1 - 19.9\%$. []{data-label="fig:FBPs"}](Hamming "fig:"){width="6.3cm"}]{} (158,3)[![Filtered backprojection reconstructions using (a) Shepp–Logan filter, (b) Cosine filter (c) Hamming filter, (d) Hann filter. Values of relative error (RE) are between $23.6 - 25.2$ and PSNR values are between $18.1 - 19.9\%$. []{data-label="fig:FBPs"}](Hann "fig:"){width="6.3cm"}]{} (87,137)[(a)]{} (240,137)[(b)]{} (87,0)[(c)]{} (240,0)[(d)]{}
Method RE (%) PSNR
---------------------- -------- ------- --
FBP (Ram–Lak filter) 25.86 18.44
GP-SE 29.41 21.76
GP-Matérn 23.26 22.76
GP-Laplacian 29.18 21.79
GP-Tikhonov 23.39 22.73
Lcurve-Laplacian 23.38 22.62
Lcurve-Tikhonov 23.26 22.63
CV-Laplacian 25.18 22.31
CV-Tikhonov 23.47 22.75
: Figures of merit for chest phantom reconstructions.[]{data-label="Figures of merit"}
We also compared the results to the L-curve method and the CV:
- The L-curve method is applied to the Laplacian and the Tikhonov covariances and the L-curve plots from different values of parameter $10^{-1}\leq\sigma\leq10$ for both covariances are shown in Figure \[L-curve chest data\]. Both plots show that the corner of the L-curve is located in between $0.2\leq \sigma \leq 1$.
(100,250) (-30,50)[![The L-curve for (a) Tikhonov and (b) Laplacian covariance from the chest phantom reconstruction.[]{data-label="L-curve chest data"}](LcurveChestTikhonov "fig:"){width="9cm"}]{} (210,50)[![The L-curve for (a) Tikhonov and (b) Laplacian covariance from the chest phantom reconstruction.[]{data-label
| 315
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| 699
| 0.802147
|
github_plus_top10pct_by_avg
|
hared instances to the next step so I created the following code:
@implementation MyClass
static id sharedInstance;
#pragma mark Initialization
+ (instancetype)sharedInstance {
static dispatch_once_t once;
dispatch_once(&once, ^{
sharedInstance = [[self alloc] init];
});
return sharedInstance;
}
- (instancetype)init {
if (sharedInstance) {
return sharedInstance;
}
@synchronized(self) {
self = [super init];
if (self) {
sharedInstance = self;
}
return self;
}
}
@end
I assume the sharedInstance method seems to be ok but I am unsure about the init method. The reason for creating this is that I don't want people using my SDK, to use the init method, and if they do ... make it bullet proof.
A:
Instead of transparently redirecting calls to init to the singleton implementation which can cause very confusing behaviour for the users of your SDK, I suggest not allowing to call init at all:
+ (instancetype)sharedInstance {
static dispatch_once_t once;
dispatch_once(&once, ^{
sharedInstance = [[self alloc] initPrivate];
});
return sharedInstance;
}
- (instancetype)init {
@throw [NSException exceptionWithName:NSInternalInconsistencyException reason:@"..." userInfo:nil];
}
- (instancetype)initPrivate {
if (self = [super init]) {
...
}
return self;
}
A:
I would like to suggest new ways of solving your problem.
You can use NS_UNAVAILABLE in the header file just like this:
//Header file
@interface MyClass : NSObject
+ (instancetype)sharedInstance
- (instancetype)init NS_UNAVAILABLE;
//...
@end
In this case init function will not be available from outside, will not be suggested for autocompletion, and you'll be able to normally use the init method inside implementation file.
As you are making a singleton class I would suggest you to make new method unavailable too by adding this line to the header file:
+ (instancetype)new NS_UNAVAILABLE;
There is also an old way of making methods
| 316
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| 4
| 0.844656
|
github_plus_top10pct_by_avg
|
orra like Wan where he had no previous past lives to turn to for advice (unlike Aang who could turn to Roku, Kyoshi and those other 2 Avatars he spoke to at the end) and thus can still be reincarnated.
A:
Actual Avatar reincarnation means Raava accepts part of current Avatar soul, leaves its body, and finds new Avatar. Communication with previous Avatar incarnations was exactly communication with parts of their souls inside Raava. Since Raava got itself destroyed, and then resurrected, it is in "clear" state, without souls of previous incarnations.
But while Raava exists in this world, it can find new vessel to become next Avatar incarnation. The only consequence of its temporary destruction is that Korra is now much like Wan.
Q:
sWHERE Datatables query with Codeigniter
I want to get the list of documents that needs to be renewed. The documents expire and needs renewal annually. I want to be alerted 4 months to expiry. I don't know the logic am missing here;
Array for column sorting
$aColumns = array('ps_id', 'ssc_number', 'submission_type', 'seru', 'jootrh', 'kppb', 'cdc','csc', 'status', 'audit_status', 'comments', 'systemtime','username');
$aResultColumns = array('ps_id','ssc_number', 'submission_type', 'seru', 'jootrh', 'kppb', 'cdc',
'csc', 'status', 'audit_status', 'comments', 'systemtime', 'username');
Column for indexing and cardinality
$sIndexColumn = "ps_id";
//Table to query
$sTable = "protocol_submissions";
Here's the query. seru is a date variable returned and I want the documents that will expire in 270 days, that is when todays' date is greater that 'seru date+270days'
$sQuery = "SELECT SQL_CALC_FOUND_ROWS " . str_replace(" , ", " ", implode(", ", $aResultColumns)) . "
FROM $sTable
$sWhere WHERE date('m/d/Y', seru +270days) > date('m/d/Y')
$sOrder
$sLimit
";
A:
Try this to get 270 + days from current date:
date('Y-m-d', strtotime("+270 days"));
Q:
Sql querying by the day displays different results
I want to query records by day in a table count them and group b
| 317
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| 971
| 0.796603
|
github_plus_top10pct_by_avg
|
({\mathcal M}_0)_{\eta\eta}^2 - ({\mathcal M}_0)_{ss}^2
\bigr\}^2
+ 2\, \lambda_{s\Phi\eta}^2\, v^2\, v_s^2 \
}
\right\} ,
\label{eq:mH1}\\
m_{{\mathcal H}_2^0}^2
&=&
\frac{1}{\,2\,}
\left\{
({\mathcal M}_0)_{\eta\eta}^2
+ ({\mathcal M}_0)_{ss}^2
+ \sqrt{
\bigl\{
({\mathcal M}_0)_{\eta\eta}^2 - ({\mathcal M}_0)_{ss}^2
\bigr\}^2
+ 2\, \lambda_{s\Phi\eta}^2\, v^2\, v_s^2 \
}
\right\} ,
\label{eq:mH2}\\
m_{{\mathcal A}^0}^2
&=&
({\mathcal M}_0)_{\eta\eta}^2 ,
\label{eq:mA}\\
m_{{\mathcal H}^\pm}^2
&=&
({\mathcal M}_0)_{\eta\eta}^2
- \frac{1}{\,2\,} \lambda_{1\Phi\eta}\, v^2 .
\label{eq:mHpm}\end{aligned}$$ Notice that $m_{{\mathcal H}_1^0} \leq m_{{\mathcal A}^0} \leq m_{{\mathcal H}_2^0}$. We assume $m_{{\mathcal H}_1^0} < m_{{\mathcal H}^\pm}$ and then ${\mathcal H}_1^0$ becomes the dark matter candidate. Hereafter it is assumed that the mixing $\theta_0^\prime$ is small.
The $\mu$-term is generated by the one-loop diagram. Figure \[fig:1-loop\] is the dominant one in the case of small $\theta_0^\prime$. Then, the parameter $\mu$ is calculated as $$\begin{aligned}
\mu
&=&
\frac{ \lambda_{s\Phi\eta}^2\, \mu_\eta^{} v_s^2 }
{ 64\pi^2
\bigl\{
({\mathcal M}_0)_{ss}^2 - ({\mathcal M}_0)_{\eta\eta}^2
\bigr\}
}
\left\{
1
- \frac{ ({\mathcal M}_0)_{ss}^2 }
{ ({\mathcal M}_0)_{ss}^2 - ({\mathcal M}_0)_{\eta\eta}^2 }
\ln\frac{({\mathcal M}_0)_{ss}^2}{({\mathcal M}_0)_{\eta\eta}^2}
\right\} .
\label{eq:mu-loop}\end{aligned}$$ The one-loop induced $\mu$ parameter can be expected to be much smaller than $\mu_\eta$. The suppression factor $|\mu/\mu_\eta|$ is estimated in Sec. \[subsec:DM\].
![ One-loop diagram for the $\mu$-term. We call it “A. oryzae diagram” [@moyasimon]. []{data-label="fig:1-loop"}](1-loop.eps "fig:") ![ One-loop diagram for the $\mu$-term. We call it “A. oryzae diagram” [@moyasimon]. []{data-label="fig:1-loop"}](a-oryzae.eps "fig:")
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|
1 g versus 2 g ceftriaxone dose, given as N (%) for categorical variables or mean ± SD for continuous variables.
---------------------------------------------------------------------
Ceftriaxone 1 g\ Ceftriaxone 2 g\ p-value
(N=34) (N=57)
--------------------- ------------------ ------------------ ---------
Patient age (years) 59.59 ± 11.24 55.10 ± 13.45 0.105
Female gender 9 (26%) 19 (33%) 0.527
MELD 20.55 ± 8.17 18.16 ± 6.48 0.125
Culture positive\ 6 (18%) 6 (11%) 0.331
SBP
Other infectious\ 5 (14%) 9 (16%) 0.890
source\*
---------------------------------------------------------------------
\[\[i\] *Looking at patients admitted to a floor service, excluding prior transplants and prior episodes of SBP.*\]
\[\[ii\] \*Patients with documented pneumonia or urinary tract infection\]
\[\[iii\] *MELD = Model for End-Stage Liver Disease. SBP = Spontaneous Bacterial Peritonitis.*\]
We next compared the hospital course for patients that received either dose of ceftriaxone ( [Table 2](#T2){ref-type="table"}). While both groups were likely to be treated with at least one additional antibiotic during their hospitalization (74% of those treated with 1 g, and 61% of those treated with 2 g), this difference was not significant. The total course of antibiotics -- ceftriaxone or otherwise -- was also similar between groups. The group receiving 2 g ceftriaxone daily did have a trend towards a shorter hospital stay, although this did not meet statistical significance (13.24 days vs. 10.28, p = 0.44). We did see a statistically significant shorter average length of intensive unit (ICU) stay in patients who received 2 g ceftriaxone a day (0.59 ± 1.78 days), compared to those who received 1 g ceft
| 319
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| null | null |
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|
wo domains: *High* and *Low*. It is generalized to arbitrary multi-domain policies in [@von04] as a new notion *nonleakage*. As pointed out in [@Mantel01] that it is important to combine language-based and state-event based security, and a new notion *noninfluence* which is combination of nonleakage with traditional noninterference [@rushby92] is proposed in [@von04].
A system is nonleaking if and only if for any states $s$ and $t$ and a domain $u$, the final states after executing any action sequence $\alpha$ in $s$ and $t$ are indistinguishable for $u$ if $s$ and $t$ are indistinguishable for all domains ($sources(\alpha,u)$) that may interfere with $u$ directly or indirectly during the execution of $\alpha$. The nonleakage is defined as follows.
$$\label{eq:nonlk}
\begin{aligned}
nonleakage \equiv \forall \alpha \ s \ u \ t . s \stackrel{sources(\alpha,u)}{\approx} t \longrightarrow \\
s \lhd \alpha \stackrel{u}{\bumpeq} t \lhd \alpha
\end{aligned}$$
Combination of noninterference and nonleakage introduces the notion *noninfluence* as follows. $$\label{eq:noninfl}
\begin{aligned}
noninfluence \equiv \forall \alpha \ s \ u \ t . s \stackrel{sources(\alpha,u)}{\approx} t \longrightarrow \\
s \lhd \alpha \stackrel{u}{\bumpeq} t \lhd ipurge(\alpha,u)
\end{aligned}$$
The *nonleakage* and *noninfluence* are applied in formal verification of seL4 separation kernel in [@Murray13].
### Temporal Separation Properties
Temporal separation usually concerns sanitization/period processing. A sanitization property (called Temporal Separation) on ED separation kernel is defined in [@Heitmeyer08] as follows to guarantee that the data areas in a partition are clear when the system is not processing data in that partition.
$$\begin{aligned}
(\forall s \in S, 1 \leq i \leq n) \; c_s = 0 \\
\Rightarrow D_{i,s}^1 = 0 \wedge ... \wedge D_{i,s}^k = 0
\end{aligned}$$
where $c_s$ is the id of a partition that is processing data in state $s$. When $c_s$ is 0, it means that no data processing in any partition is in progress. $D_{
| 320
| 403
| 530
| 415
| 114
| 0.824854
|
github_plus_top10pct_by_avg
|
algorithm to another one. Investigating finer resolution images and statistical records would also be interesting future research to evaluate other image quality parameters. Moreover, the proposed method can be applied to multidetector CT imaging [@mookiah2018multidetector; @flohr2005multi] as well as 3D CT problems using sparse data [@sidky2008image; @purisha2018automatic].
Details on the computation of $\Phi$ {#app:compdet}
====================================
Here we derive the closed-form expression of the entries $\Phi_{ij}$ stated in . We get that $$\begin{split}
\Phi_{ij} &= \int_{-R}^R \phi_i({\mathbf x}^0_j+s\hat{{\mathbf u}}_j)ds \\
&=\frac{1}{\sqrt{L_1L_2}}\int_{-R}^{R} \sin(\varphi_{i_1} r_j\cos\theta_j - \varphi_{i_1} s \sin\theta_j +\varphi_{i_1}L_1)\sin(\varphi_{i_2} r_j\sin\theta_j + \varphi_{i_2} s \cos\theta_j+\varphi_{i_2} L_2) ds
\\
& = \frac{1}{\sqrt{L_1L_2}}\int_{-R}^{R} \sin(\alpha_{ij} s + \beta_{ij})\sin(\gamma_{ij} s + \delta_{ij}) ds \\
& = \frac{1}{2\sqrt{L_1L_1}} \int_{-R}^R \cos((\alpha_{ij}-\gamma_{ij})s+\beta_{ij}-\delta_{ij}) - \cos((\alpha_{ij}+\gamma_{ij})s + \beta_{ij} + \delta_{ij})ds \\
& = \frac{1}{2\sqrt{L_1L_1}} \Big[ \frac{1}{\alpha_{ij}-\gamma_{ij}}\sin((\alpha_{ij}-\gamma_{ij})s+\beta_{ij}-\delta_{ij}) - \frac{1}{\alpha_{ij}+\gamma_{ij}}\sin((\alpha_{ij}+\gamma_{ij})s + \beta_{ij} + \delta_{ij})\Big]_{-R}^R
\\
& = \frac{1}{2\sqrt{L_1L_1}} \Big( \frac{1}{\alpha_{ij}-\gamma_{ij}}\sin((\alpha_{ij}-\gamma_{ij})R+\beta_{ij}-\delta_{ij}) - \frac{1}{\alpha_{ij}+\gamma_{ij}}\sin((\alpha_{ij}+\gamma_{ij})R + \beta_{ij} + \delta_{ij})
\\
& \qquad - \frac{1}{\alpha_{ij}-\gamma_{ij}}\sin(-(\alpha_{ij}-\gamma_{ij})R+\beta_{ij}-\delta_{ij}) + \frac{1}{\alpha_{ij}+\gamma_{ij}}\sin(-(\alpha+\gamma_{ij})R + \beta_{ij} + \delta_{ij})\Big),
\end{split}$$ where
$$\begin{aligned}
\alpha_{ij} &= \varphi_{i_1}\sin\theta_j, \\
\beta_{ij} &= \varphi_{i_1}r_j\cos\theta_j+\varphi_{i_1}L_1, \\
\gamma_{ij} &= \varphi_{i_2}\cos\theta_j, \\
\delta_{ij} &= \varphi_{i_2}r_j\si
| 321
| 1,046
| 615
| 413
| null | null |
github_plus_top10pct_by_avg
|
ect estimate ( $\left. \hat{\theta} \right)$ under different scenarios, for the random treatment effect with normal and beta distributions for the intercept data generating mechanisms. Results shown separately for stratified (1) and random (2) intercept models, under each of the different estimation options considered
Mean Percentage Bias of $\hat{\mathbf{\theta}}$
-------------------------------------------------- -------------------------------------------------- ------- -- ------- ------- -- ------- ------- -- ------- -------
Scenario [\*](#sim7930-note-0002){ref-type="fn"}
**Base case** −0.01 0.00 −0.01 −0.01 0.34 0.31 0.33 0.29
**A1** −0.90 −0.90 −0.90 −0.90 −0.02 0.13 −0.06 0.10
**A2** 0.15 0.18 0.16 0.18 −0.48 −0.41 −0.47 −0.40
**B1** 0.67 0.58 0.68 0.58 −0.57 −0.63 −0.58 −0.63
**B2** −0.47 −0.59 −0.47 −0.56 0.29 0.27 0.33 0.28
**B1‐A1** 0.54 0.53 0.53 0.53 −0.14 −0.27 −0.11 −0.24
**B1‐A2** −0.10 −0.11 −0.10 −0.11 0.08 −0.01 0.10 0.01
**
| 322
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| 202
| null | null |
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|
Notice that the type of each $L_i$ is determined canonically regardless of the choice of a Jordan splitting.
Sharpened Structure Theorem for Integral hermitian Forms {#sstm}
--------------------------------------------------------
\[210\] There exists a suitable choice of a Jordan splitting of the given lattice $L=\bigoplus_i L_i$ such that $L_i=\bigoplus_{\lambda}H_{\lambda}\oplus K$, where each $H_{\lambda}= H(i)$ and $K$ is $\pi^i$-modular of rank 1 or 2 with the following descriptions. Let $i=0$ or $i=1$. Then $$K=\left\{
\begin{array}{l l}
\textit{$(a)$ where $a \equiv 1$ mod 2} & \quad \textit{if $i=0$ and $L_0$ is \textit{of type $I^o$}};\\
\textit{$A(1, 2b, 1)$} & \quad \textit{if $i=0$ and $L_0$ is \textit{of type $I^e$}};\\
\textit{$A(2\delta, 2b, 1)$} & \quad \textit{if $i=0$ and $L_0$ is \textit{of type II}};\\
\textit{$A(4a, 2\delta, \pi)$} & \quad \textit{if $i=1$ and $L_1$ is \textit{free of type I}};\\
\textit{$H(1)$} & \quad \textit{if $i=1$, and $L_1$ is \textit{of type II} or \textit{bound of type I}}.
\end{array} \right.$$ Here, $a, b\in A$ and $\delta, \pi$ are explained in Section 2.1.
\[r211\]
1. As mentioned in Remark 2.3.(a) in [@C2], If $L$ is $\pi^i$-modular, then $\pi^j L$ is $\pi^{i+2j}$-modular for any integer $j$. Thus, the above theorem implies its obvious generalization to the case where $i$ is allowed to be any element of $\mathbb{Z}$.
2. Working with a basis furnished by the above theorem, we can describe our lattices $A_i$ through $Z_i$ more explicitly. We refer to Remark 2.11 in [@C2] for a precise description of these lattices.
From now on, the pair $(L,h)$ is fixed throughout this paper.
The construction of the smooth model {#csm}
====================================
We start with introducing the symbol $\delta_j$ according to the type of $L_j$, for the fixed hermitian lattice $(L, h)$. We keep this symbol from now until the end of this paper.
$$\delta_{j} = \left\{
\begin{array}{l l}
1 & \quad \textit{if $L_j$ is \tex
| 323
| 1,267
| 487
| 396
| 1,442
| 0.78954
|
github_plus_top10pct_by_avg
|
0cm]\draw[thick,densely dotted](0,.13)--++(2*.25,0);\end{tikzpicture}}};\star,;\star;\star),$$ which do not occur in any other ${\psi_{2,1}}\circ\tau_i$ (note these tableaux do occur when we compute ${\psi_{2,1}}\circ{\hat\Theta_{T}}$ for $T$ of type $4$, but each one occurs twice when we sum over tableaux of type $4$, so the contributions cancel). So $\tau_5$ does not appear in $\theta$.
Next we consider ${\psi_{3,1}}\circ\tau_i$ for each $i$. For $i=3,6$ or $8$, we find that ${\psi_{3,1}}\circ\tau_i$ involves semistandard tableaux which do not occur in any other ${\psi_{3,1}}\circ\tau_i$; so $\tau_3,\tau_6,\tau_8$ cannot occur in $\theta$. Moreover, we find that ${\psi_{3,1}}\circ\tau_1={\psi_{3,1}}\circ\tau_7$ and ${\psi_{3,1}}\circ\tau_2={\psi_{3,1}}\circ\tau_4$, and that these two homomorphisms are linearly independent. So $\theta$ must be a linear combination of $\tau_1+\tau_7$ and $\tau_2+\tau_4$.
Finally we return once more to ${\psi_{2,1}}\circ\theta$. We find that ${\psi_{2,1}}\circ\tau_1={\psi_{2,1}}\circ\tau_4\neq0$, while ${\psi_{2,1}}\circ\tau_2={\psi_{2,1}}\circ\tau_7=0$. So $\tau_1$ and $\tau_4$ must appear with the same coefficient in $\theta$; so $\theta$ must be a scalar multiple of $\tau_1+\tau_2+\tau_4+\tau_7$, and so the homomorphism space has dimension at most $1$.
Homomorphisms from $S^\mu$ to $S^\la$
-------------------------------------
Now we consider homomorphisms from $S^\mu$ to $S^\la$. We begin by constructing a non-zero homomorphism. Let $C$ be the $\mu$-tableau $${\text{\footnotesize$\gyoungx(1.2,;1;1_{3.5}{{\begin{tikzpicture}[baseline=0cm]\draw[thick,densely dotted](0,.13)--++(3.5*.25,0);\end{tikzpicture}}};1;2;3_2{{\begin{tikzpicture}[baseline=0cm]\draw[thick,densely dotted](0,.13)--++(2*.25,0);\end{tikzpicture}}};{b\!\!+\!\!2},;1;1_{1.5}{{\begin{tikzpicture}[baseline=0cm]\draw[thick,densely dotted](0,.13)--++(1.5*.25,0);\end{tikzpicture}}};1,;2;2)$}}$$ of type $\la$.
\[cd2chom\] With $C$ as above, we have ${\psi_{d,t}}\circ{\hat\Theta_{C}}=0$ for all $d,t$, and ${\hat\The
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|
have entered may not be saved.
Leave Page and Stay on Page"
Can we invoke this confirmation box through some special function of browser? I want to implement it in AngularJS application
A:
Warlock's answer is partly right, but in doing so, you'd break testability.
In Angular, you'd want to use $window, and you'll want to watch $dirty on your form. You'll need to have a named form, notice name="myForm" below. Then you can $watch $dirty on the form in your $scope:
app.controller('MainCtrl', function($scope, $window) {
$scope.name = 'World';
var win = $window;
$scope.$watch('myForm.$dirty', function(value) {
if(value) {
win.onbeforeunload = function(){
return 'Your message here';
};
}
});
});
HTML
<form name="myForm">
Name: <input type="text" ng-model="name"/>
</form>
Here's a plunk to demonstrate: http://plnkr.co/edit/3NHpU1
A:
You could use the "onbeforeunload" event. The syntax is as follows:
window.onbeforeunload = function () {
return "Your text string you want displayed in the box";
}
This event will popup that confirmation dialog that you described above asking whether or not the user truly wants to leave the page.
Hope this helps.
A:
If you want to cancel the route change when you determine your form is dirty, you can do this:
$rootScope.$on('$locationChangeStart', function(event) {
event.preventDefault();
});
This will cancel the routing and keep you on the current page.
Q:
Java string split with multiple delimeters
What would be the best way to split this string directly after the CN= to store both the first and last name in separate fields as shown below?
String distinguisedName = "CN=Paul M. Sebula,OU=BBB,OU=Users,OU=TIES Project,DC=SPHQTest,DC=na,DC=BBBBBB,DC=com"
String firstName"Paul"
String lastName="Sebula"
A:
Don't re-invent the wheel. Assuming these are well-formed DN's, see the accepted answer on this question for how to parse without directly writing your own regex: Parsing the CN out of a certificate DN
Once you've extracted the C
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|
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|
-4b''(1+4b'')&-\pi(1+4b'')\\0&0&\pi(1+4b'') &0 \end{pmatrix}.$$
Let $$\left\{
\begin{array}{l}
\tilde{M}_0=(\oplus_{\lambda}H_{\lambda})\oplus \left( Be_1'\oplus Be_2' \right)\\
\textit{ } \oplus \left( B(e_3'-e_5)\oplus B(e_4'-e_5) \right);\\
\tilde{M}_1=B(e_5-\frac{2b''\pi}{\delta}e_6)\oplus B(e_6+\pi e_3') \oplus (\oplus H(1)).
\end{array}\right.$$ Then $\tilde{M}_0\oplus\tilde{M}_1\oplus(\oplus_{i\geq 2}M_i)$ is another Jordan splitting of $L^j$, where $\tilde{M}_0$ (resp. $\tilde{M}_1$) is $\pi^0$-modular (resp. $\pi^1$-modular) and $\tilde{M}_1$ is isometric to $\oplus H(1)$.
For this choice of a basis, the block associated to $\tilde{M}_0\oplus M_2$ of the image of a fixed element of $F_j$ in the special fiber of the smooth integral model associated to $L^j$ is $$\begin{pmatrix} id&0 &0\\ 0 &\begin{pmatrix} 1&0&0&0 \\ 0&1&0&0 \\ 0&\frac{1}{1+4b''}(\pi x_j-2z_j^{\ast})
&\frac{1}{1+4b''}(1 +\pi x_j) & \frac{1}{1+4b''}(2 z_j^{\ast})\\0&0& 0 & 1 \end{pmatrix} &0 \\ 0& 0 &id \end{pmatrix}.$$ Here, $id$ in the $(1,1)$-block corresponds to the direct summand $(\oplus_{\lambda}H_{\lambda})$ of $\tilde{M}_0$ and $id$ in the $(3,3)$-block corresponds to $M_2$.
We now apply the argument of Steps (i) and (ii) to the above Jordan splitting $\tilde{M}_0\oplus\tilde{M}_1\oplus(\oplus_{i\geq 2}M_i)$ of $L^j$ since $\tilde{M}_1$ is isometric to $\oplus H(1)$. As explained in Steps (i) and (ii), in order to describe the image of a fixed element of $F_j$ in the orthogonal group associated to $M_0''$, we only need the above block associated to $\tilde{M}_0\oplus M_2$. Note that $\frac{1}{1+4b''}$ is a unit and $(x_j)_1=0$. Then $(z_j^{\ast})_1$ is the image of a fixed element of $F_j$ under the map $\psi_j$. Since $(z_j^{\ast})_1$ can be either $0$ or $1$ by Equation (\[e42\]), $\psi_j|_{F_j}$ is surjective onto $\mathbb{Z}/2\mathbb{Z}$ and thus $\psi_j$ is surjective.\
If $N_0$ is *of type II*, then the proof of the surjectivity of
| 326
| 1,683
| 431
| 381
| 2,730
| 0.777452
|
github_plus_top10pct_by_avg
|
, the image of a fixed element of $F_j$ in the special fiber of the smooth integral model associated to $L^j$ is $$\begin{pmatrix} id&0 &0\\ 0 &
\begin{pmatrix} 1+\frac{2}{a+2b}(b\pi x_j-z_j^{\ast})&\frac{a\pi x_j}{a+2b} &\frac{-2}{a+2b}z_j^{\ast}\\
\frac{2}{a+2b}(b\pi x_j-z_j^{\ast}) &1+\frac{a\pi x_j}{a+2b} &\frac{-2}{a+2b}z_j^{\ast} \\
\frac{-2}{a+2b}(b\pi x_j-z_j^{\ast})& \frac{-a\pi x_j}{a+2b} &1+\frac{2}{a+2b}z_j^{\ast} \end{pmatrix}
&0 \\ 0& 0 &id \end{pmatrix}.$$ Here, the $(2,2)$-block corresponds to $A(2b(2b-1), a(a+1), a(2b-1))\oplus (a+2b)$.
As in Case (3), the above formal matrix can be simplified by observing a formal matrix description of an element of $\underline{M}(R)$ for a $\kappa$-algebra $R$, explained in Section \[m\]. Since $A(2b(2b-1), a(a+1), a(2b-1))\oplus (a+2b)$ is *of type $I^o$* and $(x_j)_1=0$ (by Equation (\[e42\])), the $(2,2)$-block of the above formal matrix turns to be $$\begin{pmatrix} 1&0 &\frac{-2}{a+2b}z_j^{\ast}\\
0&1 &\frac{-2}{a+2b}z_j^{\ast} \\
\frac{2}{a+2b}z_j^{\ast}& \frac{-a\pi x_j}{a+2b} &1+\frac{2}{a+2b}z_j^{\ast} \end{pmatrix}.$$
We now follow Step (3) with $L^j$ such that the above formal matrix corresponds to the formal matrix (\[e4.4\]). If we switch the order of the first two vectors in the basis of $A(2b(2b-1), a(a+1), a(2b-1))$, then the only difference between the above formal matrix and the formal matrix (\[e4.4\]) of Step (3) is the appearance of $\frac{-2}{a+2b}z_j^{\ast}$ in the $(2, 3)$-entry and $\frac{-a\pi x_j}{a+2b}$ in the $(3, 2)$-entry of the above formal matrix. However, these entries will be zero after reduction to the orthogonal group associated to $M_0''$, where $M_0''$ is the $\pi^0$-modular Jordan component of $Y(C(M_0'\oplus C(L^j)))$, since $M_0''$ is *free of type II* so that the diagonal block associated to $M_0''$ has no congruence condition. Thus in the corresponding orthogonal group, all entries having $\pi$ as a factor become zero.
Then by using the result of Step (3), $(z_j^{\ast})_1$ i
| 327
| 1,815
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| null | null |
github_plus_top10pct_by_avg
|
with respect to the previous infections (Table [5](#ccr32374-tbl-0005){ref-type="table"}).
######
Information about six previous case reports regarding the *S pluranimalium* infections
Sex Age Infection Previous disease Diagnostic method Ref
--------- --------- --------------- ----------------------------------- ------------------- ------------------------------------------
Male 44 Brain abscess Tuberculosis Vitek 2 [5](#ccr32374-bib-0005){ref-type="ref"}
Male 17 Brain abscess Unknown Vitek 2 [10](#ccr32374-bib-0010){ref-type="ref"}
Male 3 Brain abscess Congenital cyanotic heart disease Vitek 2 [12](#ccr32374-bib-0012){ref-type="ref"}
Male 37 Endocarditis Sinusitis Vitek 2 [13](#ccr32374-bib-0013){ref-type="ref"}
Female 53 Septicemia Health Vitek 2 [14](#ccr32374-bib-0014){ref-type="ref"}
Unknown Unknown Septicemia Unknown PCR [15](#ccr32374-bib-0015){ref-type="ref"}
John Wiley & Sons, Ltd
The studies show that a combination therapy with vancomycin, tetracycline, and the third‐generation cephalosporins is a reliable therapeutic regimen for endocarditis and septicemia infections.[13](#ccr32374-bib-0013){ref-type="ref"} Meanwhile, antibiotics such as vancomycin, the third‐generation cephalosporins, imipenem, meropenem, amikacin are very effective on brain abscesses and CNS infections caused by this bacterium.[5](#ccr32374-bib-0005){ref-type="ref"}, [10](#ccr32374-bib-0010){ref-type="ref"}, [12](#ccr32374-bib-0012){ref-type="ref"}
4. CONCLUSION {#ccr32374-sec-0004}
=============
The current study demonstrates the seventh clinical case report about *S pluranimalium* infection isolated from the neonatal septicemia. Based on the results of present study and the
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| 569
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|
m_{i,i}^{\ast\ast}=0$ *if $i\neq j$*;
- and for $m_{j,j}$, $$\left \{
\begin{array}{l l}
s_j=\mathrm{id~}, y_j=0, v_j=0, z_j=\pi z_j^{\ast} & \quad \textit{if $i$ is even and $L_i$ is \textit{of type} $\textit{I}^o$};\\
s_j=\mathrm{id~}, r_j=t_j=y_j=v_j=u_j=w_j=0, z_j=\pi z_j^{\ast} & \quad \textit{if $i$ is even and $L_i$ is \textit{of type} $\textit{I}^e$};\\
s_j=\mathrm{id~}, r_j=t_j=y_j=v_j=u_j=w_j=0 & \quad \textit{if $i$ is odd and $L_i$ is \textit{free of type I}}.\\
\end{array} \right.$$
We will prove in Lemma \[la9\] below that each element of $F_j(R)$ for a $\kappa$-algebra $R$ satisfies $(z_j^{\ast})_1+(z_j^{\ast})_1^2=0$ (if $j$ is even) or $(z_j)_1+(z_j)_1^2=0$ (if $j$ is odd), where $z_j^{\ast}=(z_j^{\ast})_1+\pi (z_j^{\ast})_2$ and $z_j=(z_j)_1+\pi (z_j)_2$, and that $F_j$ is isomorphic to $ \mathbb{A}^{1} \times \mathbb{Z}/2\mathbb{Z}$ as a $\kappa$-variety, where $\mathbb{A}^{1}$ is an affine space of dimension $1$.
Notice that $F_j$ and $F_{j^{\prime}}$ commute with each other for all integers $j\neq j^{\prime}$, where $j, j^{\prime}\in \mathcal{B}$, in the sense that $f_j\cdot f_{j^{\prime}}=f_{j^{\prime}}\cdot f_j$, where $f_j\in F_j $ and $ f_{j^{\prime}}\in F_{j^{\prime}}$. Let $F=\prod_{j}F_j$. Then $F$ is smooth and is a closed subgroup scheme of $\mathrm{Ker~}\varphi$ as mentioned in the proof of Theorem \[t411\]. If $F^{\dag}$ is the image of $F$ in $G^{\dag}$, then it is smooth and thus a closed subscheme of $(G^{\dag})_{\mathrm{red}}$. By observing Equation (\[32’\]) and $(z_j^{\ast})_1+(z_j^{\ast})_1^2=0$ (if $j$ is even) or $(z_j)_1+(z_j)_1^2=0$ (if $j$ is odd) above, we can easily see that $F^{\dag}$ contains at least one (closed) point of each connected component of $G^{\ddag}$ and this proves our claim.\
Combining this fact with dim $G^{\dag}$ = dim $G^{\ddag}$, we conclude that $(G^{\dag})_{\mathrm{red}}\simeq G^{\ddag}$, and hence, $G^{\dag}=G^{\ddag}$ because $G^{\dag}$ is a subfunctor of $G^{\ddag}$. This completes the proof.
\[la8\
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| 3,684
| 0.770716
|
github_plus_top10pct_by_avg
|
Mother 304 5 (4.0) 299 (78.1)
Other 203 119 (96.0) 84 (21.9)
Dietary supplementation
Yes 135 1 (20.0) 134 (45.3)
No 166 4 (80.0) 162 (54.7)
Numbers vary due to missing data.
*p*\<0.05
*p*\<0.01.
Relationship between maternal vitamin and oxidative stress levels and infant growth {#S0003-S20002}
-----------------------------------------------------------------------------------
Because gestational age and infant sex were thought to be the primary confounding variables for the association between maternal vitamin levels and infant growth, these two variables were adjusted first ([Table 4](#T0004){ref-type="table"}). A high maternal concentration of vitamin C was significantly associated with increased infant weight (*p*=0.02) and head circumference (*p*=0.03) during the first 3 years of life. Conversely, a high maternal MDA was associated with decreased infant weight (*p*=0.01) and height (*p*=0.01). Similarly, infants with a high maternal concentration of vitamin E showed a lower weight and height, but only the association with height was statistically significant (*p*=0.02). Next, other potential confounders including gestational age, infant sex, breastfeeding, period of breastfeeding, household income, and dietary supplementation were adjusted in the final model. After adjustment for these variables, the group with low maternal vitamin A presented a lower head circumference percentile than the group with high maternal vitamin A (*p*\<0.01). Likewise, the vitamin C group showed a similar pattern in head circumference percentiles, but there was no statistical significance (*p*=0.34); they also weighed less than subjects in
| 330
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| null | null |
github_plus_top10pct_by_avg
|
/2}\left( half-hypermultiplet in ${\bf 12}$ of $so(12)$
\lambda^{1-6}_{-1/2}, \overline{\lambda}^{1-6}_{-1/2}
\right) \otimes \left(
\psi^3_{-1/2}, \overline{\psi}^4_{-1/2} \right)$
$\left( \overline{\partial} X^3, \overline{\partial} \overline{X}^4 \right) 1 singlet hypermultiplet
\otimes \left( \overline{\psi}^3_{-1/2}, \psi^4_{-1/2} \right)$
$\left( \overline{\partial} \overline{X}^3, \overline{\partial} X^4 \right) 1 singlet hypermultiplet
\otimes \left( \psi^3_{-1/2}, \overline{\psi}^4_{-1/2} \right)$
$\lambda^7_{-1/2} \overline{\lambda}^8_{-1/2} \otimes \left( 1/2 singlet hypermultiplet
\psi^3_{-1/2}, \overline{\psi}^4_{-1/2} \right)$
$\overline{\lambda}^7_{-1/2} \lambda^8_{-1/2} \otimes \left( 1/2 singlet hypermultiplet
\overline{\psi}^3_{-1/2}, \psi^4_{-1/2} \right)$
--------------------------------------------------------------------------------------------------------------------------------
There are no massless states in the untwisted (R,NS) sector, and no massless states in $k=1$, $k=2$ sectors. The $k=3$, $4$, $5$ sectors are copies of the $k=0$, $1$, $2$ sectors, respectively. Thus, altogether, the spectrum is two copies of the states above.
Note that since there are no (R,NS) states, the nonabelian gauge symmetry is only $so(12)$; it is not enhanced to $e_7$. Also, since the spectrum is two copies of the states above, the spectrum contains two gravitons, and hence would be a likely candidate for decomposition.
Unfortunately, the spectrum is also anomalous. The gauge symmetry is $so(12)
\times e_8 \times u(1)^4$ (including the second $E_8$, which until now has been suppressed), so the total number of vector multiplets is 318, and the nu
| 331
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| null | null |
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|
}_n\}, k)}{{\sync}(\{{\mathit{s}}_n\}, k)} =
\lim_{\;k \to \infty} \frac{N_Z(\{{\mathit{s}}'_n\}, k)}{{\sync}(\{{\mathit{s}}'_n\}, k))}$$ for a reference set of steps $\varnothing \neq Z \subseteq {\mathbb{S}}$.
The synchronization function allows expression of the absolute operational profile as an intensity (rate or quasi-frequency).
The *counting norm* is written using the double bar notation ${\Vert{\cdot}\Vert}$: $${\Vert{Z}\Vert} = \lim_{\;k \to \infty} \frac{N_Z(\{{\mathit{s}}_n\}, k)}{\sync(\{{\mathit{s}}_n\}, k)}.$$
The absolute operational profile is properly a subadditive seminorm on sets of steps. As the limiting ratio of two counts in the natural numbers, the norm is positive. The norm is a seminorm because for some nonempty set $Z$ it may be true that ${\Vert{Z}\Vert} = 0$ (if the usage pattern does not activate any member of the reference set). This norm is subadditive because for any other set $S$, $N_{Z \cup S}(\{{\mathit{s}}_n\}, k) \leq N_Z(\{{\mathit{s}}_n\}, k) + N_S(\{{\mathit{s}}_n\}, k)$. It follows that ${\Vert{Z \cup S}\Vert} \leq {\Vert{Z}\Vert} + {\Vert{S}\Vert}$.
Application
===========
The safety demonstration furnishes data for the indemnification statistic, which originates in the compound Poisson random process.
Reliability demonstration
-------------------------
A reliability demonstration is a structured random experiment carrying controlled statistical uncertainty and providing [hard]{} evidence against potential liability.
### Safety demonstration {#S:SAFETY_DEMONSRATION}
In software safety analysis, a hazard is a region of code bearing potential harmful side effects if incorrectly implemented. A safety demonstration is a special type of reliability demonstration posed to exercise a hazard. Here the region is presumed to be an acyclic cone, with the hazard located at its crux. The crux is a point of software/hardware transduction, illustrating the principle of emergence[^6] (see §\[S:PRINCIPLE\_OF\_EMERGENCE\]).
To oversimplify, a safety demonstration is a random s
| 332
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| 1,259
| 0.791961
|
github_plus_top10pct_by_avg
|
that for each binding $V_i \setminus t_i$, $1\leq i \leq n$, either:
- $V_i \in Var(B_1)$ and $V_i$ is labeled as integer and $t_i$ is an integer expression, or
- $V_i \in Var(B_1)$ and $V_i$ is labeled as input but not as integer variable, or
- $V_i \in Var(A_1)$, $V_i$ is not labeled as input, no variable of $Var(t_i)$ is labeled as input and $t_i$ does not contain integers. $\hfill \square$
Since the selected atoms of nodes $N_5$ and $N_9$ in Figure \[fig:count\_to\] are variants, Proposition \[prop:mmg\_int\_ins\] holds. $\hfill \square$
Generating the constraints on the integers of the query
-------------------------------------------------------
In this subsection, we introduce the constraints on the integer variables of the moded query, identifying values for which all integer conditions in the considered derivations succeed. These constraints consist of reachability constraints, identifying queries for which the derivation up till the last node is applicable, and an implication proving that the integer conditions will also succeed in the following iterations.
\[example:count\_to\_int\_cons\] As a first example, we introduce the constraints for the path between $N_5$ and $N_9$ in the moded SLD-tree of $count\_to$ in Figure \[fig:count\_to\]. For this path, Theorem \[th:analysis1\] holds and thus every query denoted by $\leftarrow count\_to(\underline{N},L)$ is either non-terminating or terminates due to an integer condition.
To restrict the class of considered queries to those for which the derivation to $N_9$ is applicable, all integer conditions in the derivation are expressed in terms of the integers of the query, yielding $0 > \underline{N}$ and $0 + 1 > \underline{N}$. For this program and considered class of queries, the condition $0 > \underline{N}$ implies that the derivation is applicable until node $N_9$. The following implication states that if the condition of node $N_7$ holds for any two values $M$ and $N$, then it also holds for the values of the next iteration. $$\forall M,N \
| 333
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| 1,073
| 0.794782
|
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|
a situation in which there is no thermal disorder in the quantum degrees of freedom so that $\iota=1$: *viz.*, the density matrix becomes that of a pure state $\rho_{\alpha\alpha^{\prime}}(X,t)\to C_{\alpha}(X,t)C_{\alpha^{\prime}}^{*}(X,t)$. Then, equations (\[eq:c\]) and (\[eq:cstar\]) remain unaltered and one has just to remove the index $\iota$ from the coefficients. Therefore, it can be realized that no classical trajectory propagation, and no state switching are involved by Eqs. (\[eq:c\]) and (\[eq:cstar\]). Instead, in order to calculate averages according to Eq. (\[eq:qc-ave-ad\]), one has to sample phase space points and integrate the matrix equations.
In the next section, an equilibrium approximation of Eqs. (\[eq:c\]) and (\[eq:cstar\]), along the lines followed by the method of *Wigner trajectories* [@wignertraj], is given and applied, with good numerical results, to the adiabatic and nonadiabatic dynamics of the spin-boson model.
Wave dynamics of the spin-boson model {#sec:sb}
=====================================
The theory developed in the previous sections can be applied to simulate the relaxation dynamics of the spin-boson system [@sb]. This system has already been studied within the framework of quantum-classical dynamics of operators in Ref. [@qc-sb] and “exact” numerical results were obtained at short-time by means of an iterative path integral procedure developed by Nancy Makri and co-worker [@makri]. The short-time results of Ref. [@sb] numerically coincide with those obtained by the path integral calculation of Ref. [@makri]. However, as it is shown later by Fig. \[fig:fig2\], the quantum-classical results of Ref. [@sb] have some limitations concerning the numerical stability of the algorithm beyong a certain time length. Using the dimensionless variables of Ref. [@qc-sb], the quantum-classical Hamiltonian operator of the spin-boson system reads $$\begin{aligned}
\hat{H}(X)&=&-\Omega\hat{\sigma}_x
+\sum_{j=1}^N\left(\frac{P_j^2}{2}+
\frac{1}{2}\omega_j^2R_j^2-c_j\ha
| 334
| 31
| 772
| 437
| null | null |
github_plus_top10pct_by_avg
|
960 (11.99)
\ Other^c^ 1441 (18.00)
\ Do not know 240 (3.00)
--------------------------------------------------------------------------------
^a^Average of the percentage for all four countries.
^b^Other education corresponds to vocational education, matriculation, or other types of education.
^c^Other occupation corresponds to other types of jobs or status such as at-home mother/father.
Research Question Results
-------------------------
The majority of respondents were willing to share their PHD under specific conditions as shown in [Table 2](#table2){ref-type="table"}. The results differed according to the country the respondents were from. [Figure 1](#figure1){ref-type="fig"} shows the country-wise distribution of the participant responses. Gender of the participants did not impact the results, although men (2234/3922, 56.96%) were slightly more willing to share their health data compared with women (2239/4002, 55.95%). Regarding age, young people were more willing to share their data than older people, as shown in [Figure 2](#figure2){ref-type="fig"}. [Figure 3](#figure3){ref-type="fig"} shows that participants living in cities and urban areas were more willing to share their PHD compared with those living in the countryside. [Figure 4](#figure4){ref-type="fig"} presents the results per education level of participants. [Figure 5](#figure5){ref-type="fig"} presents the results according to the respondent occupation type.
######
Participant responses about the conditions of sharing their personal health data (N=8004).
Responses Value^a^, n (%)
--------------------------------------------------------- -----------------
No 2384 (29.78)
Information is used for scientific research 1811 (22.63)
I would be paid for it 1139 (1
| 335
| 774
| 1,263
| 497
| null | null |
github_plus_top10pct_by_avg
|
{\nu}{W}>0\\
-1&\frac{\nu}{W}<0\;,
\end{array}\right.$$ so that $E_0$ falls either above (for $\nu/W > 0$) or below (for $\nu/W < 0$) the energy band (\[eq:band\]). The probability to find the particle at the $\ell$-th site, when it is bound by the defect, is given by $$\label{eq:loc}
{p}_{\ell}
= \frac{2\left|\nu\right|}{\sqrt{4\nu^2+W^2}}
\left(\sqrt{\frac{4\nu^2}{W^2}+1}
-2\left|\frac{\nu}W\right|\right)^{2\left|\ell-\gamma\right|}\;,$$ as can be derived with the help of resolvent operator techniques (see, [*e.g.*]{}, Ref. ). In the following, knowledge of the amplitudes $a_\ell$ themselves will be required: As shown in the Appendix \[sec:eigen\], the eigenstate corresponding to the defect energy (\[eq:E\_0\]) reads $${{\left|\psi_0\right.\rangle}}=\sum_{\ell=-\infty}^{\infty}a_{\ell}{{\left|\ell\right.\rangle}}
\label{eq:psi0}$$ with $$a_{\ell}={\cal N}(-p)^{\ell-\gamma}\left(x_-\right)^{\left|\ell-\gamma\right|}\;,
\label{eq:al}$$ where $\cal N$ is the normalization constant, and the auxiliary quantities $$\label{eq:x_pm}
x_{\pm} = \sqrt{\frac{4\nu^2}{W^2}+1}\pm 2\left|\frac{\nu}W\right|$$ have been introduced. They obey $x_-x_+=1$, and $x_-<x_+$. The fact that the wave function (\[eq:psi0\]) with the amplitudes (\[eq:al\]) indeed is normalizable for $\frac{\nu}W\ne0$, and hence describes a localized state, follows immediately from $0<\left|x_-\right|<1$.
Localization control by forcing {#sec:force}
===============================
If an oscillating electric field is applied to the system, linearly polarized along the direction of the lattice and with amplitude $F$, the interaction is modeled by $$\label{eq:force}
\hat{H}_{\rm int}(t)
=
e F d \cos(\omega t)
\sum_{\ell}\left|\ell\right>\ell\left<\ell\right|\;,$$ where $e$ is the particle’s charge. Since the total Hamiltonian $\hat{H}_0 + \hat{V}_{\rm r} + \hat{H}_{\rm int}(t)$ then is periodic in time, with period $T = 2\pi/\omega$, the Floquet theorem [@Shirley65; @Zeldovich67; @Ritus67] asserts that there is a complete sy
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|
- \psi^{1-2}(\sigma), \\
\psi^{3-4}(\sigma + 2 \pi) & = & - \psi^{3-4}(\sigma), \\
\lambda^{1-6}(\sigma + 2 \pi) & = & + \lambda^{1-6}(\sigma), \\
\lambda^{7-14}(\sigma + 2 \pi) & = & + \exp\left( 2 \pi i
\frac{2}{4} \right) \lambda^{7-14}(\sigma) \: = \:
- \lambda^{7-14}(\sigma), \\
\lambda^{15-16}(\sigma + 2 \pi) & = & + \lambda^{15-16}(\sigma).\end{aligned}$$ It is straightforward to compute that $E_{\rm left} = 0$, $E_{\rm right} = -1/2$. There is a multiplicity of left vacua, as $\lambda^{1-6}$ and $\lambda^{15-16}$ are periodic. In particular, $|\pm \mp \rangle_{15-16}$ are invariant under ${\mathbb Z}_4$, whereas $|\pm \pm \rangle_{15-16}$ get a sign flip. Therefore, the ${\mathbb Z}_4$-invariant massless states are of the form
-------------------------------------------------------------------------------------------------------------
State Count
--------------------------------------------------------- ---------------------------------------------------
$| \pm \cdots \pm \rangle_{1-6} spacetime vector
| \pm \mp \rangle_{15-16}
\otimes
\left( \psi^{1-2}_{-1/2}, \overline{\psi}^{1-2}_{-1/2}
\right)$
in $({\bf 32},{\bf 2})$ of $so(12)\times so(4)$
$| \pm \cdots \pm\rangle_{1-6} |\pm \pm \rangle_{15-16} 4 sets of scalars
\otimes
\left( \psi^{3-4}_{-1/2}, \overline{\psi}^{3-4}_{-1/2}
\right)$
in $({\bf 32}',{\bf 2}')$ of $so(12)\times so(4)$
-------------------------------------------------------------------------------------------------------------
We can rearrange the spacetime vecto
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|
times I)}={\mathop{\mathrm{ess\hspace{1mm}sup}}}_{(x,\omega,E)\in G\times S\times I}
\int_S\tilde\sigma(x,\omega',\omega,E)d\omega' \\
&{\left\Vert \int_S\tilde\sigma(\cdot,\cdot,\omega',\cdot)d\omega'\right\Vert}_{L^\infty(G\times S\times I)}={\mathop{\mathrm{ess\hspace{1mm}sup}}}_{(x,\omega,E)\in G\times S\times I}
\int_S\tilde\sigma(x,\omega,\omega',E)d\omega'$$
We begin with a lemma.
\[csdale0\] For all $\psi\in C^1(\ol G\times S\times I)$, $$\begin{gathered}
\label{se4}
{\left\langle}{{\frac{\partial (S_0\psi)}{\partial E}}},\psi{\right\rangle}_{L^2(G\times S\times I)}\leq q{\left\Vert \psi\right\Vert}^2_{L^2(G\times S\times I)} \\
+\frac{1}{2}\int_{G\times S} \big(S_0(x,E_m)\psi^2(x,\omega,E_m)-
S_0(x,0)\psi^2(x,\omega,0)\big)dx d\omega,\end{gathered}$$ where \[q\] q:=[12]{}\_[(x,E)GI]{}[E]{}(x,E).
Integrating by parts, we have \[se5\] &,\_[L\^2(GSI)]{} = ,\_[L\^2(GSI)]{} +,S\_0\_[L\^2(GSI)]{}\
=& ,\_[L\^2(GSI)]{} -, [E]{}\_[L\^2(GSI)]{}\
&+\_[GS]{} (S\_0(x,E\_m)(x,,E\_m)\^2 - S\_0(x,0)(x,,0)\^2)dx d, and therefore &2,\_[L\^2(GSI)]{}\
=& ,\_[L\^2(GSI)]{} +\_[GS]{} (S\_0(x,E\_m)(x,,E\_m)\^2 - S\_0(x,0)(x,,0)\^2) dx d\
& 2q\^2\_[L\^2(GSI)]{} +\_[GS]{} (S\_0(x,E\_m)(x,,E\_m)\^2-S\_0(x,0)(x,,0)\^2) dx d. This finishes the proof.
Note that if $E\mapsto S_0(x,E)$ is decreasing for every $x\in G$ then $q\leq 0$ (and therefore $C$ below vanishes).
Let $$\begin{aligned}
\label{eq:def_C}
C:=\frac{\max\{q,0\}}{\kappa}.\end{aligned}$$ We make the following change of the unknown function. We replace $\psi$ by $$\begin{aligned}
\label{eq:exp_trick}
\phi(x,\omega,E):=e^{CE}\psi(x,\omega,E).\end{aligned}$$ This substitution changes the equation (\[se1\]) to (here and below by writing $e^{CE}$ we mean a function $(x,\omega,E)\mapsto e^{CE}$) \[csda3A\] -[E]{}+\_x+C S\_0+-K\_C=e\^[CE]{}f, where $K_C$ is given by \[collc\] (K\_C)(x,,E)=\_[SI]{}(x,’,,E’,E) e\^[C(E-E’)]{}(x,’,E’)d’ dE’ . The inflow boundary and the initial conditions are \_[|\_-]{}=&e\^[CE]{}g, \[finalbc\]\
(x,,E\_m)=&0, \[finalic\] the latt
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|
Sigma_{8,3,\{0,4\}}$ and $T_{3,7}$](t_and_sigma "fig:"){height="2.2in"}
\[subbicyclic\][@ruskuc] Let $S$ be a subsemigroup of the bicyclic monoid. Then one of the following conditions holds:\
1. $S$ is a subset of the diagonal, $S \subseteq D$.\
2. $S$ is a union of a subset of a triangle, a subset of the diagonal above the triangle, a square below the triangle and some lines belonging to a strip determined by the square and the triangle, or the reflection of this union with respect to the diagonal. Formally there exist $q, p \in \mathbb{N}^0$ with $q \leq p, d \in \mathbb{N}, I \subseteq \{q, . . . , p-1\}$ with $q \in I, P \subseteq \{0, . . . , d - 1\}$ with $0 \in P, \ F_{D} \subseteq D \cap L_{q}, \ F \subseteq T_{q,p}$ such that $S$ is of one of the following forms:
\(i) $S = F_{D} \cup F \cup \Lambda_{I,p,d}\cup \Sigma_{p,d,P}$;\
(ii) $S = F_{D} \cup \widehat{F} \cup \widehat{\Lambda}_{I,p,d}\cup \Sigma_{p,d,P}$.\
3\. There exist $d \in \mathbb{N},\ I \subseteq \mathbb{N}^0,\ F_{D} \subseteq D \cap L_{min(I)}$ and sets $S_{i} \subseteq \Lambda_{i,i,d}\ (i \in I)$ such that $S$ is of one of the following forms:
(i) $S = F_{D}\cup\bigcup_{i\in I} S_{i}$;\
(ii) $S = F_{D}\cup\bigcup_{i\in I} \widehat{S_{i}}$;
where each $S_{i}$ has the form $$S_{i} = F_{i} \cup \Lambda_{i,m_i,d}$$ for some $m_{i} \in \mathbb{N}^0$ and some finite set $F_{i}$, and $$I = I_{0} \cup \{r + ud : r \in R, u \in \mathbb{N}^0, r + ud \geq N\}$$ for some (possibly empty) $R \subseteq \{0, . . . , d - 1\}$, some $N \in \mathbb{N}^0$ and some finite set $I_{0} \subseteq \{0, . . . ,N - 1\}.$\
\
We call diagonal subsemigroups those defined by 1., two-sided subsemigroups those defined by 2., upper subsemigroups those defined by 3.(i) and lower subsemigroups those defined by 3.(ii).
We begin with the following example which plays a significant role in studying left I-orders in $\mathcal{B}$.
\[exRclass\] Let $R_1=\{a^0b^j: j\geq 0\}$ be the $\mathcal{R}$-class of the identity element 1 of $\mathcal{B}$ and $q=a^mb^n\in \ma
| 339
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|
hat{H} & \hat{\chi} \end{array}\right]
\cdot\mbox{\boldmath$\Omega$}\cdot
\left[\begin{array}{c} \hat{H} \\ \hat{\chi}\end{array}\right]
\nonumber\\
&=&\frac{i}{\hbar}
[\hat{H} , \hat{\chi}]_{\mbox{\tiny\boldmath$\Omega$}}
\;.
\label{eq:gen-qlm}\end{aligned}$$ The non-Hamiltonian commutator of Eq. (\[eq:gen-quantum-algebra\]) defines a generalized form of quantum mechanics where, nevertheless, the Hamiltonian operator $\hat{H}$ is still a constant of motion because of the antisymmetry of $\mbox{\boldmath$\Omega$}$.
Quantum-classical wave dynamics {#sec:qcwd}
===============================
In Refs. [@qc-bracket; @kcmqc], quantum-classical evolution has been formulated in terms of phase space dependent operators. In this scheme of motion operators evolve according to $$\begin{aligned}
\hat{\chi}(X,t)&=&\exp\left\{t
\left[\hat{H},\ldots\right]_{\mbox{\tiny\boldmath$\cal D$}}\right\}
\hat{\chi}(X)\nonumber\\
&=&\exp\left\{it{\mathcal L}\right\}\hat{\chi}(X)\;,
\label{eq:qc-heisenberg}\end{aligned}$$ where the last equality defines the quantum-classical Liouville propagator. Quantum-classical averages are calculated as $$\begin{aligned}
\langle\hat{\chi}\rangle(t)
&=&{\rm Tr}'\int dX\hat{\rho}(X)\hat{\chi}(X,t)
\nonumber\\
&=&{\rm Tr}'\int dX\hat{\rho}(X,t)\hat{\chi}(X)\;,
\label{eq:qc-average}\end{aligned}$$ where $\hat{\rho}(X)$ is the quantum-classical density matrix and $\hat{\rho}(X,t)=\exp\left\{-it{\mathcal L}\right\}\hat{\rho}(X)$. Either evolving the dynamical variables or the density matrix, one is still dealing with phase space dependent operators: *viz.*, one deals with a form of generalized quantum-classical matrix mechanics. As it has been discussed in the Introduction, this theory has interesting formal features and a certain number of numerical schemes have been proposed to integrate the dynamics and calculate correlation functions [@kapral; @qc-sb; @num-qc]. However, these algorithms have been applied with success only to short-time dynamics because of statistical uncertainties that grow with ti
| 340
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|
re, if we denote $F^{(i)}_{m,n} =\phi^{(i)}_{m-1,n} \phi^{(i)}_{m,n} \phi^{(i)}_{m+1,n} $, $$\begin{gathered}
A^{(0)}_{m,n} = F^{(0)}_{m,n} F^{(1)}_{m,n} F^{(2)}_{m,n} \phi^{(1)}_{m,n}\phi^{(2)}_{m,n}\phi^{(3)}_{m,n} ,\qquad
A^{(1)}_{m,n} = F^{(0)}_{m,n} F^{(1)}_{m,n} F^{(2)}_{m,n} F^{(3)}_{m,n} \frac{\phi^{(2)}_{m,n}}{\phi^{(0)}_{n,m}},\\
A^{(2)}_{m,n} = \phi^{(2)}_{m,n} \phi^{(3)}_{m,n},\qquad A^{(3)}_{m,n} = \phi^{(0)}_{m-1,n} \phi^{(0)}_{m+1,n},\\
B_{m,n} = \sum_{j=0}^{3} A^{(j)}_{m,n} + F^{(0)}_{m,n} F^{(1)}_{m,n}\phi^{(2)}_{m,n}.\end{gathered}$$ The corresponding master symmetry is $$\begin{gathered}
\partial_\tau \phi^{(i)}_{m,n} = m \partial_{t_1} \phi^{(i)}_{m,n}, \qquad i= 0,\ldots,3,\end{gathered}$$ along =-1 with $\partial_\tau \alpha = 1$. This is used to construct a hierarchy of symmetries for the system (\[eq:N5-sys\]). We omit here the second symmetry as the expressions become cumbersome for the unreduced case.
### The reduced system {#the-reduced-system-1 .unnumbered}
The reduction (\[self-dual-equn\]) now has components $\phi^{(0)}_{m,n}$, $\phi^{(1)}_{m,n}$, with $\phi^{(2)}_{m,n}=\frac{1}{\phi^{(1)}_{m,n}}$, $\phi^{(3)}_{m,n}=\frac{1}{\phi^{(0)}_{m,n}}$, $\phi^{(4)}_{m,n}= 1$, and the $2$-component system takes the form
\[eq:sys-5-red\] $$\begin{gathered}
\phi^{(0)}_{m+1,n+1} \phi^{(0)}_{m,n} = \frac{1}{\phi^{(0)}_{m+1,n}\phi^{(0)}_{m,n+1}} \left(\frac{\phi^{(0)}_{m+1,n}+\phi^{(0)}_{m,n+1}}{\phi^{(1)}_{m+1,n}+\phi^{(1)}_{m,n+1}}\right),\\[3mm]
\phi^{(1)}_{m+1,n+1} \phi^{(1)}_{m,n} (\phi^{(0)}_{m+1,n}+\phi^{(0)}_{m,n+1}) = 2.\end{gathered}$$
Only the even indexed generalised symmetries of the system (\[eq:N5-sys\]) are consistent with this reduction. This means that the lowest order generalised symmetry is
\[eq:sym-self-dual-5a\] $$\begin{gathered}
\partial_{t_2} \phi^{(0)}_{m,n} = \phi^{(0)}_{m,n} \frac{P^{(0)}_{m,n}}{ P^{(2)}_{m,n}} \left( \frac{1}{P^{(2)}_{m+1,n}} - \frac{1}{P^{(2)}_{m-1,n}}\right),\\
\partial_{t_2} \phi^{(1)}_{m,n} = \phi^{(1)}_{m,n} \frac{1}{ P^{(2)}_{m,n}} \lef
| 341
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|
fix}(c)={\it True}$;]{} (15,232)[begin]{} (0,220)[$1.$for $i:=1$ to $h$ do $A_{c}(i,i):=0$;]{} (0,198)[2. $E:= \left(
\begin{array}{cccc}
\sigma_{2} & \sigma_{3} & \ldots & \sigma_{h} \\
0 & 0 & \ldots & 0
\end{array}
\right)
$;]{} (0,176)[3.$X:=$**Huffman**$(E,h-1)$;]{} (0,164)[4.for $i:=2$ to $h$ do]{} (0,152)[ begin]{} (0,140)[5. $A_{c}(1,i):=1\cdot X(1,i-1)$;]{} (0,128)[6.$X(1,i-1):=1\cdot X(1,i-1)$;]{} (0,116)[7. $A_{c}(i,1):=X(1,i-1)$;]{} (0,104)[ end]{} (0,92)[8.for $j:=2$ to $h$ do]{} (0,80)[ begin]{} (0,68)[9.for $i:=2$ to $j-1$ do $A_{c}(i,j):=X(1,i-1)$;]{} (-5,56)[10.for $i:=j+1$ to $h$ do $A_{c}(i,j):=X(1,i-1)$;]{} (0,44)[ end]{} (-5,32)[11.for $i:=1$ to $h$ do $A_{c}(i,h+1):=A_{c}(1,i)$;]{} (-5,20)[12.return $A_{c}$;]{} (15,8)[end]{} (-8,282)[(1,0)[330]{}]{} (-8,2)[(1,0)[330]{}]{} (-8,282)[(0,-1)[280]{}]{} (322,282)[(0,-1)[280]{}]{}
Let $c:\{{\texttt{\textup{a}}},{\texttt{\textup{b}}},{\texttt{\textup{c}}}\}\times\{{\texttt{\textup{a}}},{\texttt{\textup{b}}},{\texttt{\textup{c}}}\}^{\leq{1}}\rightarrow\{0,1\}^{+}$ be a function. One can verify that $A_{c}$ is the matrix given below.
$A_{c}=\left(
\begin{array}{cccc}
0 & 10 & 11 & 0 \\
11 & 0 & 10 & 10 \\
10 & 11 & 0 & 11
\end{array}
\right)
$.
Let $w={\texttt{\textup{abbbcabccaabccabbcba}}}$ be an input data string. It is easy to verify that ${\it Pairs}(w)=\{2,3,8,10,13,16\}$, ${\it NRpairs}(w)=6$, and ${\it Prate}(w)=0.3$. Encoding the string $w$ by $c$ requires the computation of $\overline{c}(w)$. Using Definition 2.1, we get that $|\overline{c}(w)|=33$. Let us apply Huffman’s algorithm to the data string $w$ in order to make a comparison between the results. If we denote by ${\it Huffman}(w)$ the codeword associated to $w$ by Huffman’s algorithm, we get that $|Huffman(w)|=32$. An even better result can be obtained when the input data
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|
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|
label="fig:failure_mode"}](figures/failure_mode.pdf){width="0.8\linewidth"}
Triplet Network Visualization {#triplet-network-visualization .unnumbered}
-----------------------------
Here we illustrate how a triplet network is trained. An anchor, positive example, and negative example are all passed through the same embedding network. The triplet loss is then computed which encourages the distance between the anchor and positive example to be some margin $\alpha$ closer together than the anchor and negative example.
![Illustration of how a triplet network works on the MNIST dataset.[]{data-label="triplet_net"}](figures/triplet_net.pdf){width="\textwidth"}
The triplet loss function is shown here for convenience:
$$L(x, x_{-}, x_{+}) = \mathrm{max}(0, \alpha + \mathrm{d}(x, x_{+}) - \mathrm{d}(x, x_{-}))$$
Agreement Between LeNet and Triplet Network {#agreement-between-lenet-and-triplet-network .unnumbered}
-------------------------------------------
We investigated the agreement between LeNet and triplet network we trained in order to confirm that a concordance based detector is a viable option, and does not result in false positives on normal images. Importantly, the models agree 90% (Table \[table:concordance\]) of the time on normal images, so false positives are not a major concern.
Overall Concordance Correct Concordance Incorrect Concordance
--------------------- --------------------- -----------------------
0.911 0.908 0.003
: Concordance between LeNet and triplet network on predictions on normal images.[]{data-label="table:concordance"}
---
abstract: 'I present the results of first principles calculations of the electronic structure and magnetic interactions for the recently discovered superconductor YFe$_2$Ge$_2$ and use them to identify the nature of superconductivity and quantum criticality in this compound. I find that the Fe $3d$ derived states near the Fermi level show a rich structure with the presence of both linearly dispersive and h
| 343
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bounce the projection off the mirror on one side of the room and then read it off the wall on the other side of the room. This should get you up to 14 inches.
However, the image will be reversed. If you have two mirrors the image could be corrected and you could have a final size of 21 inches.
CAUTION: The larger the projection, the dimmer it will be. I don't know if it will still be readable after enlarging it with the mirrors.
Q:
Pure CSS3 slideshow repeats the last 4 slides?
I found a script, namely: "Pure CSS / CSS3 Slideshow with Image Panning and zooming Effect".
The problem with this it that it repeats the last 4 slides. Could someone tell me why and how to resolve this problem?
My first fiddle, demonstrating the issue.
My second one, proving the issue.
The HTML:
<div class="pic-wrapper lejatszokep">
<figure class="pic-1"></figure>
<figure class="pic-2"></figure>
<figure class="pic-3"></figure>
<figure class="pic-4"></figure>
<figure class="pic-5"></figure>
<figure class="pic-6"></figure>
<figure class="pic-7"></figure>
<figure class="pic-8"></figure>
<figure class="pic-9"></figure>
<figure class="pic-10"></figure>
<figure class="pic-11"></figure>
<figure class="pic-12"></figure>
<figure class="pic-13"></figure>
<figure class="pic-14"></figure>
<figure class="pic-15"></figure>
<figure class="pic-16"></figure>
<figure class="pic-17"></figure>
<figure class="pic-18"></figure>
<figure class="pic-19"></figure>
</div>
The CSS3:
.pic-wrapper {
margin: 0px 0px 0px 0px;
padding: 0px;
position: absolute;
width: 259px;
height: 200px;
overflow: hidden;
}
figure {
margin: 0;
padding: 0;
position: absolute;
top: 0;
left: 0;
width: 258px;
height: 200px;
opacity: 0;
/*animation*/
animation: slideShow 24s linear infinite;
-o-animation: slideShow 24s linear infinite;
-moz-animation: slideShow 24s linear inf
| 344
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| 0.818019
|
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|
or }2$. We also have to incorporate Equations (\[ea25\]) and (\[ea27\]) together with the two formal equations about $(\tilde{z_i^{\ast}})_1$ and $(\tilde{z_i^{\ast}})_2$ given just before Equation (\[ea31\]), and Conditions (e), (f) of the description of an element of $\tilde{M}(R)$ given at the paragraph following Lemma \[la1\].\
Since $\sum_{l=0}^{m_j}\mathcal{F}_{j-2l}(\tilde{m})$ does not include any factor of type $(\tilde{x}_i)_2$, we finally obtain $\sum_{l=0}^{m_j}\mathcal{F}_{j-2l}(m)$ as follows: $$\begin{gathered}
\label{ea32}
0=\sum_{0\leq l \leq m_j}c_{j-2l}=\sum_{l=0}^{m_j}\mathcal{F}_{j-2l}(m)=\sum_{l=0}^{m_j}\left(z_{j-2l}^{\ast}+(z_{j-2l}^{\ast})^2 \right)+\\
\sum_{\textit{$L_{j-2l}$ : of type $I^e$, $l=0$}}^{m_j}\bar{\gamma}_{j-2l}\left(x_i^2+1/2\cdot{}^tr_i\bar{a}_ir_i+\left(\delta_{i-2}(m_{i-2, i}^{\natural})^2+\delta_{i+2}(m_{i+2, i}^{\natural})^2\right)\right)+\\
\frac{1}{2}\left({}^t(m_{j-2m_j-2, j-2m_j})'\cdot a_{j-2m_j-2}\cdot (m_{j-2m_j-2, j-2m_j})'+{}^t(m_{j+2, j})'\cdot a_{j+2}\cdot (m_{j+2, j})'\right)+\\
\left(\delta_{j-2m_j-3}'(k_{j-2m_j-3, j-2m_j})^2+ \delta_{j+3}'(k_{j+3, j})^2\right)+
\left(\delta_{j-2m_j-4}(k_{j-2m_j-4, j-2m_j})^2+ \delta_{j+4}(k_{j+4, j})^2\right).\end{gathered}$$ Here, notations as as explained in Equations (\[ea30\]) and (\[ea31\]). Thus we get polynomials $\sum_{l=0}^{m_j}\mathcal{F}_{j-2l}$ on $\mathrm{Ker~}\tilde{\varphi}/\tilde{M}^1$, vanishing on the subscheme $\mathrm{Ker~}\varphi/\tilde{G}^1$.\
7. This step is similar to Step (5) in the proof of Theorem A.6 of [@C2]. Recall that $\mathcal{B}$ is the set of integers $j$ such that $L_j$ is *of type I* and $L_{j+2}, L_{j+3}, L_{j+4}$ (resp. $L_{j-1}, L_{j+1},$ $L_{j+2}, L_{j+3}$) are *of type II* if $j$ is even (resp. odd). We choose $j\in \mathcal{B}$.
For $j\in \mathcal{B}$, there is a nonnegative integer $k_j$ such that $L_{j-k_j}$ is *of type I*, $j-l\notin\mathcal{B}$ for all $l$ with $0 < l \leq k_j$, and $L_{j-k_j-2}, L_{j-k_j-3}, L_{j-k_j-4}$ (resp. $L_{
| 345
| 1,182
| 406
| 397
| 2,870
| 0.776426
|
github_plus_top10pct_by_avg
|
$\begin{aligned}
\frac{\exp\lrp{-\frac{7\aq\Rq^2}{3}}}{2}\leq \psi(r)\nu(r)\leq 1
\end{aligned}$$ Where we use Lemma \[l:tau\] and the fact that $\nu(r) \in [1/2,1]$
**Proof of \[f:q”(r)\_bounds\]** Recall that $$\begin{aligned}
q''(r) = \psi'(r) \nu(r) + \psi(r) \nu'(r)
\end{aligned}$$
That $q''\leq 0$ can immediately be verified from the definitions of $\psi$ and $\nu$.
Thus $$\begin{aligned}
\lrabs{q''(r)}
\leq& \lrabs{\psi'(r) \nu(r)} + \lrabs{\psi(r) \nu'(r)}\\
\leq& \aq \tau'(r) + \lrabs{\psi(r) \nu'(r)}
\end{aligned}$$ From Lemma \[l:tau\], we can upperbound $\tau'(r) \leq \frac{5\Rq}{4}$. In addition, $\Psi(r) = \int_0^r \psi(s) \geq r \psi(r)$, so that $$\begin{aligned}
\numberthis \label{e:l:psi(r)/psi(r)}
\frac{\Psi(r)}{\psi(r)} \geq r
\end{aligned}$$ (Recall again that $\psi(s)$ is monotonically decreasing). Thus $\Psi(r)/r \geq r$ for all $r$. In addition, using the fact that $\psi(r) \leq 1$, $$\begin{aligned}
\numberthis \label{e:l:psi(r)_upperbound}
\Psi(r) = \int_0^r \psi(s)ds \leq r
\end{aligned}$$
Combining the previous expressions, $$\begin{aligned}
\lrabs{\psi(r) \nu'(r)}
=& \lrabs{ \frac{1}{2}\frac{\mu(r)\Psi(r)}{\int_0^{4\Rq}\frac{\mu(s)\Psi(s)}{\psi(s)} ds}}\\
\leq& \lrabs{\frac{1}{2}\frac{\mu(r) r}{\int_0^{\Rq}\frac{\Psi(s)}{\psi(s)} ds}}\\
\leq& \lrabs{\frac{1}{2} \frac{4\Rq}{\int_0^{\Rq} s ds}}\\
\leq& \frac{4}{\Rq}
\end{aligned}$$ Where the first inequality are by definition of $\mu(r)$ and , and the second inequality is by and the fact that $\mu(r) = 0$ for $r\geq 4\Rq$. Combining with our bound on $\psi'(r) \nu(r)$ gives the desired bound.
**Proof of \[f:q”’(r)\_bounds\]** $$\begin{aligned}
q'''(r) = \psi''(r) \nu(r) + 2\psi'(r) \nu'(r) + \psi(r) \nu''(r)
\end{aligned}$$ We first bound the middle term: $$\begin{al
| 346
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| null | null |
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|
\]
3. The base change profunctor $(\id\times u)_!\lI_{A\op}\in \cProf({\sV})(A\op,B\op)$ has a left adjoint in $\cProf({\sV})$.\[item:sd1op\]
4. The morphism $u_!\colon{\sV}^A\to{\sV}^B$ has a left adjoint that is a weighted colimit functor.\[item:sd2\]
5. The right Kan extension $(u\op)_\ast\colon {\sV}^{A\op} \to {\sV}^{B\op}$ exists and is a -weighted *colimit* functor.\[item:sd2op\]
We first show that \[item:sd1\] and \[item:sd1op\] are equivalent. The right adjoint in \[item:sd1\] would be an object $Z\in {\sV}(A\times B\op)$, whereas the left adjoint in \[item:sd1op\] would be an object $Z'\in {\sV}(B\op\times (A\op)\op)$; but of course these are equivalent categories. The unit and counit in \[item:sd1\] would be morphisms $$\begin{aligned}
\eta &: \lI_B \to (u\times\id)_!\lI_A \otimes_{[A]} Z \cong (u\times\id)_! Z\\
\ep &: (\id\times u\op)^\ast Z \cong Z \otimes_{[B]} (u\times\id)_!\lI_A \to \lI_A
\end{aligned}$$ whereas the unit and counit in \[item:sd1op\] would be morphisms $$\begin{aligned}
\eta' &: \lI_{B\op} \to Z'\otimes_{[A\op]} (\id\times u)_!\lI_{A\op} \cong (\id\times u)_! Z'\\
\ep' &: (u\op\times \id)^\ast Z' \cong (\id\times u)_!\lI_{A\op} \otimes_{[B\op]} Z' \to \lI_{A\op}.
\end{aligned}$$ Thus, to give $\eta$ is the same as to give $\eta'$, since $\lI_{B\op}$ corresponds to $\lI_B$ under the equivalence ${\sV}(B\times B\op) \simeq {\sV}(B\op \times (B\op)\op)$, and so on. We leave it to the reader to check that the triangle identities likewise correspond.
Now we show that \[item:sd0\] implies \[item:sd1\]. We take the right adjoint to be $(\id\times u\op)_\ast \lI_A \in \cProf({\sV})(A,B)$. Then morphisms $Y\to (\id\times u\op)_\ast \lI_A$ are equivalent to morphisms $(\id\times u\op)^\ast Y \to \lI_A$, i.e. morphisms $Y\otimes_{[B]} (u\times\id)_!\lI_A \to \lI_A$. In bicategorical language, $(\id\times u\op)_\ast \lI_A$ is a *right lifting* of $\lI_A$ along $(u\times\id)_!\lI_A$. In general, a right lifting of the identity along a 1-cell $X$ is a righ
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github_plus_top10pct_by_avg
|
ing.html
My initial code was like this:
<?php
namespace ApplicationTest\Controller;
use Zend\Http\Request;
use Zend\Http\Response;
use Zend\Test\PHPUnit\Controller\AbstractHttpControllerTestCase;
class IndexControllerTest extends AbstractHttpControllerTestCase {
protected $controller;
protected $request;
protected $response;
protected $routeMatch;
protected $event;
protected $traceError = true;
public function setUp() {
$this->setApplicationConfig(
include '../../../config/application.config.php'
);
parent::setUp();
}
public function testIndexActionCanBeAccessed() {
$this->dispatch('/');
$this->assertResponseStatusCode(200);
}
}
And when I ran phpunit, I got the following error message:
PHPUnit 3.7.21 by Sebastian Bergmann.
Configuration read from /usr/share/php/tool/module/Application/test/phpunit.xml
onDispatch called.
E
Time: 1 second, Memory: 14.50Mb
There was 1 error:
1) ApplicationTest\Controller\IndexControllerTest::testIndexActionCanBeAccessed
Zend\ServiceManager\Exception\ServiceNotFoundException: Zend\ServiceManager\ServiceManager::get was unable to fetch or create an instance for Zend\Db\Adapter\Adapter
Then I followed the second set of instructions to configure the service manager.
public function testIndexActionCanBeAccessed() {
$albumTableMock = $this->getMockBuilder('User\Model\UserData')
->disableOriginalConstructor()
->getMock();
$albumTableMock->expects($this->once())
->method('getUserSessionArray')
->will($this->returnValue(array()));
$serviceManager = $this->getApplicationServiceLocator();
$serviceManager->setAllowOverride(true);
$serviceManager->setService('User\Model\UserData', $albumTableMock);
$this->dispatch('/');
$this->assertResponseStatusCode(200);
}
And this time, I got the following error:
PHPUnit 3.7.21 by Sebastian Bergmann.
Configuration read from /usr/share/php/tool/module/Application/test/phpunit.xml
onDispatch ca
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| 126
| 160
| 23
| 0.837358
|
github_plus_top10pct_by_avg
|
- Yury Kochetkov
title: 'On enumeration of tree-rooted planar cubic maps'
---
Introduction
============
Plane triangulation is a planar map, where the perimeter of each face is three. The corresponding dual graph is *cubic*, i.e. the degree of each vertex is three. A plane triangulation will be called *proper*, if each edge is incident to exactly *two* faces. Otherwise it will be called *improper*.
$$\begin{picture}(265,70) \put(15,5){\small proper triangulation}
\put(165,5){\small improper triangulation} \put(25,20){\line(1,0){60}}
\put(25,20){\circle*{2}} \put(85,20){\circle*{2}} \put(55,65){\circle*{2}}
\put(25,20){\line(2,3){30}} \put(85,20){\line(-2,3){30}}
\put(215,45){\oval(40,40)} \put(180,45){\circle*{2}} \put(195,45){\circle*{2}}
\put(210,45){\circle*{2}} \put(180,45){\line(1,0){30}}
\end{picture}$$ The corresponding dual graphs are presented below: $$\begin{picture}(160,50) \put(20,25){\oval(40,40)} \put(20,5){\circle*{2}}
\put(20,45){\circle*{2}} \put(20,5){\line(0,1){40}} \put(60,22){¨}
\put(100,25){\oval(30,30)} \put(160,25){\oval(30,30)} \put(115,25){\circle*{2}}
\put(145,25){\circle*{2}} \put(115,25){\line(1,0){30}}
\end{picture}$$
A connected graph with marked directed edge will be called *edge-rooted*. Proper edge-rooted triangulations where enumerated by Tutte in the work [@Tu]: the number $T_n$ of proper planar triangulations with $2n$ faces and marked directed edge is $$T_n=\frac{2\,(4n-3)!}{n!\,(3n-1)!}.$$
A combinatorial proof of Tutte formula see in [@PS] (see also [@AP]).
Let $F_n$ be the number of planar edge-rooted cubic graphs with $2n$ vertices, i.e. the number of planar edge-rooted triangulations (proper and improper) with $2n$ faces. Let us define numbers $f_n$, $n\geqslant -1$, in the following way:
- $f_{-1}=1/2$;
- $f_0=2$;
- $f_n=(3n+2)F_n$, $n>0$.
In [@GJ] a recurrent relation for numbers $f_n$ was proposed: $$f_n=\frac{4(3n+2)}{n+1}\sum_{\scriptsize \begin{array}{c} i\geqslant -1,\, j\geqslant
-1\\ i+j=n-2\end{array}} f(i)f(j).\eqno(1)$$
From (1) it follows
| 349
| 2,780
| 775
| 374
| 1,120
| 0.79409
|
github_plus_top10pct_by_avg
|
1
, B. P., [Findlay]{}, J. R., [Sutherland]{}, W. J., [et al.]{} 2013, , 779, 24
, M. 2012, Science, 337, 544
, M., & [Rees]{}, M. J. 2005, , 633, 624
, M., [Silk]{}, J., & [Dubus]{}, G. 2015, , 804, 148
, K.-y., [Fukue]{}, J., [Takeuchi]{}, M., & [Mineshige]{}, S. 2000, , 52, 133
, D., & [Norman]{}, M. L. 2008, , 673, 664
, D. J., & [Norman]{}, M. L. 2008, , 672, 287
, C. J., [Delorme]{}, P., [Reyl[é]{}]{}, C., [et al.]{} 2010, , 139, 906
, J. H., & [Abel]{}, T. 2007, , 665, 899
, X.-B., [Wang]{}, F., [Fan]{}, X., [et al.]{} 2015, , 518, 512
, H., & [Khochfar]{}, S. 2016, , 457, 2423
, M., [Sadeghpour]{}, H. R., & [Dalgarno]{}, A. 1998, , 496, 1044
, N., [Omukai]{}, K., & [Hernquist]{}, L. 2008, Science, 321, 669
, F., [Gan]{}, Z., [Narayan]{}, R., [et al.]{} 2015, , 804, 101
, F., [Abbassi]{}, S., & [Mosallanezhad]{}, A. 2016, , 823, 92
, B., [Dalgarno]{}, A., [Kimura]{}, M., & [Lane]{}, N. F. 1989, , 40, 2340
details of chemical and thermal modelling {#sec:chem_detail}
=========================================
Reaction rates {#sec:reaction_rates}
--------------
No. Reaction Rate coeff. ${\mathrm{[cm^3\,s^{-1}]}}$ Ref.
--------- ------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------- ------
1 ${\mathrm{H}}+{\mathrm{e}} \rightarrow {\mathrm{H^+}} + 2{\mathrm{e}}$ $k_1=$ 1
2 ${\mathrm{He}}+{\mathrm{e}} \rightarrow {\mathrm{He^+}} + 2{\mathrm{e}}$ $k_2=$ 1
3 ${\mathrm{He^+}}+{\
| 350
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| 1,822
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| null | null |
github_plus_top10pct_by_avg
|
r\Delta_B-\bar\Delta_C} E(w)\end{aligned}$$ with numerical coefficient: $$\begin{aligned}
\label{A:BC:step4coef}\# &= (-1)^{-\Delta_E + \Delta_D + \Delta_C}(-1)^{-\bar \Delta_E + \bar \Delta_D + \bar \Delta_C} \cr
& \times \frac{(\Delta_D - \Delta_A - \Delta_B)(\Delta_D - \Delta_A - \Delta_B-1)...(\Delta_E - \Delta_A - \Delta_B-\Delta_C+1)}{(-\Delta_E + \Delta_D + \Delta_C)!} \cr
& \times \frac{(\bar\Delta_D - \bar\Delta_A - \bar\Delta_B)(\bar\Delta_D - \bar\Delta_A - \bar\Delta_B-1)...(\bar\Delta_E - \bar\Delta_A - \bar\Delta_B-\bar\Delta_C+1)}{(-\bar\Delta_E + \bar\Delta_D + \bar\Delta_C)!} .\end{aligned}$$ Let us stress that a given term in the result of the OPE may receive contributions from an $infinite$ number of terms in the OPE between $A$ and $B$. This makes the computation of OPEs involving composite operators rather involved. One may need to resort to perturbation theory in a small parameter to render the calculation manageable. The perturbation theory that we use in the bulk of the paper is explained in section \[bootstrap\] and in the appendices \[XXOPEs\] and \[consistentPertOPEs\].
- Let us turn to the OPE between $A(z)$ and $C(w)$, which we evaluate at the point $w$. This second step is simpler than the first. Again, we concentrate on one term in this OPE: A(z) C(w) = ... + (z-w)\^[\_F - \_A - \_B]{}(|z-|w)\^[|\_F - |\_A - |\_B]{} F(w) + ...We then have to perform the OPE between the right-hand side and the operator $B(x)$. We evaluate the result at the point $w$. Let us write down one term in the result: $$\begin{aligned}
&(z-w)^{\Delta_F - \Delta_A - \Delta_B}(\bar z-\bar w)^{\bar\Delta_F - \bar\Delta_A - \bar \Delta_B} B(x) F(w)
=\cr
&...+ (z-w)^{\Delta_F - \Delta_A - \Delta_B}(\bar z-\bar w)^{\bar\Delta_F - \bar\Delta_A - \bar \Delta_B}(x-w)^{\Delta_G - \Delta_B - \Delta_F}(\bar x-\bar w)^{\bar\Delta_G - \bar\Delta_B - \bar \Delta_F} G(w) +...
\nonumber\end{aligned}$$ Finally we take the straightforward normal ordered limit $:x\to w:$, that discards all the t
| 351
| 1,568
| 826
| 439
| 2,624
| 0.778323
|
github_plus_top10pct_by_avg
|
in the process. Instead of $\overline{e}^{1/2}$, if we utilize $\sigma_w$ in the definitions of $L_b$ and $\mathcal{L}$, we get: $\overline{\varepsilon} = \sigma_w^2 N$. This equation is identical to Eq. \[W81\] which was derived by Weinstock [@weinstock81]. His derivation, based on inertial-range scaling, is summarized in Appendix 2.
In the right panel of Fig. \[fig3\], we plot $L_H/\mathcal{L}$ versus $L_{C}/\mathcal{L}$. Both these normalized length scales have limited ranges; nonetheless, they are proportional to one another. Like Eq. \[Lb\_vs\_LOZ\], we can write in this case: $$\frac{L_H}{\mathcal{L}} \equiv \left(\frac{L_{C}}{\mathcal{L}}\right)^n,
\label{LH_vs_LC}$$ where, $n$ is an unknown power-law exponent. The expansion of this equation leads to either $\overline{\varepsilon} = \overline{e} S$ or $\overline{\varepsilon} = \sigma_w^2 S$, depending on the definition of $L_H$ and $\mathcal{L}$.
Parameterizing the Energy Dissipation Rate
==========================================
Earlier in Fig. \[fig3\], we have plotted normalized OLS values against one another. It is plausible that the apparent data collapse is simply due to self-correlation as same variables (i.e., $\mathcal{L}$, $N$, and $S$) appear in both abscissa and ordinate. To further probe into this problematic issue, we produce Fig. \[fig4\]. Here, we basically plot normalized $\overline{\varepsilon}$ as functions of normalized $\overline{e} N$, $\overline{e} S$, $\sigma_w^2 N$, and $\sigma_w^2 S$, respectively. These plots have completely independent abscissa and ordinate terms and do not suffer from self-correlation. Please note that the appearance of $Re_b$ and $Ri_b$ in these figures are due to the normalization of variables in DNS; Appendix 3 provides further details. Throughout the paper, the subscript “$n$” is used to denote a normalized variable.
{width="49.00000%"} {width="49.00000%"}\
{width="49.00000%"} {width="49.00000%"}
It
| 352
| 736
| 1,318
| 491
| 431
| 0.809951
|
github_plus_top10pct_by_avg
|
**Mean ± SEM\*** **Before weight loss** **After weight loss** **P value**
-------------------------------- ------------------ ------------------------ ----------------------- -------------
*Choline (umol/L)* \- 68.8 (34.1-287.8) 57.5 (22.9-129.9) 0.046
*Betaine (umol/L)* \- 94.8 (54.2-251.6) 83.0 (44.1-153.4) 0.79
*Urinary selenium (umol/L)* \- 1886 (51--7317) 2633 (430--4634) 0.31
*Urinary Selenium:creatinine* \- 0.10 (0.03-0.20) 0.14 (0.07-0.24) 0.006
*Taurine (nmol/ml)* 77 ± 2.1 99.7 (63.5-232.1) 109.9 (71.0-345.6) 0.19
*Aspartic Acid (nmol/ml)* 7 ± 0.2 14.0 (0.9-27.7) 12.5 (3.6-90.6) 0.73
*Threonine (nmol/ml)* 178 ± 5.0 211.4 (89.6-359.2) 184.5 (85.5-324.6) 0.02
*Serine (nmol/ml)* 107 ± 2.6 110.0 (72.8-168.1) 111.6 (71.0-151.7) 0.64
*Asparagine (nmol/ml)* 40 ± 1.1 37.3 (0.0-63.9) 39.0 (17.6-111.9) 0.68
*Glutamic Acid (nmol/ml)* 23 ± 1.2 154.2 (75.9-303.5) 117.4 (25.2-219.8) 0.07
*Glutimine (nmol/ml)* \- 485.4 (43.7-855.2) 452.3 (170.8-650.7) 0.27
*Glycine (nmol/ml)* 268 ± 8.4 188.6 (101.3-304.9) 204.7 (125.6-290.7) 0.045
*Alanine (nmol/ml)* 388 ± 9.6 373.3 (144.2-783.3) 384.8 (225.8-743.2) 0.99
*Citrulline (nmol/ml)* 41 ± 1.9 47.2 (0.0-159.3) 40.6 (0.0-99.9) 0.08
*Amino-Butyric Acid (nmol/ml)* \- 21.9 (0.0-64.6) 21.7 (5.0-53.3) 0.53
*Valine (nmol/ml)* 157 ± 4.1 186.0 (130.2-275.3) 188.2 (122.9-261.8) 0.52
| 353
| 2,105
| 668
| 425
| null | null |
github_plus_top10pct_by_avg
|
=w^{-1}({\alpha }_p),\,\gamma _j=w^{-1}({\alpha }_j)\big)
\end{aligned}
\label{eq:J'}
\end{aligned}$$ and $$\begin{aligned}
J=J'+\big(
f_{\beta ,\beta }^{{b^{\chi}} (\beta )}-1\,|\,
\beta \in R^\chi _{+{\mathrm{fin}}} \big).
\label{eq:J}
\end{aligned}$$ Then, by Lemma \[le:equalrs\], Def. \[de:Cartan\], and Eq. , $V^\chi _{\underline{n}}$ is the set of points $\chi ''\in \maxspec
{\bar{{\Bbbk }}}[{\overline{{\mathcal{X}}}}]/J$ such that
- $f_{\beta ,\beta }^n(\chi '')\not=1$ for all $\beta \in R^\chi _{+\infty }$, $1\le n\le n_\beta $ and
- $(f_{\gamma _p,\gamma _p}^m f_{\gamma _p,\gamma _j}
f_{\gamma _j,\gamma _p}-1)(\chi '')\,
(f_{\gamma _p,\gamma _p}^{m+1} -1)(\chi
'')\not=0$ for all $j,p\in I$, $w\in {\mathrm{Hom}}(\chi ,\underline{\,\,})$, and $m\in \{0,1,\dots ,-c^{w^*\chi }_{pj}-1\}$, where $j\not=p$ and $\gamma _p=w^{-1}({\alpha }_p)$, $\gamma _j=w^{-1}({\alpha }_j)$.
This is clearly an open subset, which proves the proposition.
\[pr:X5dense\] Let $\chi \in {\overline{{\mathcal{X}}}}_3$. Assume that $\chi (\beta ,\beta )\not=1$ for all $\beta \in R^\chi _+$. Let $\underline{n}=(n_\beta )_{\beta \in
R^\chi _{+\infty }}$, where $n_\beta \in {\mathbb{N}}$ for all $\beta \in
R^\chi _{+\infty }$. Let $V^\chi _{\underline{n}}$ be as in Prop. \[pr:Vchi\]. Then ${\overline{{\mathcal{X}}}}_5\cap V^\chi _{\underline{n}}$ is Zariski dense in $V^\chi _{\underline{n}}$.
Prop. \[pr:Vchi\] gives that $V^\chi _{\underline{n}}\subset {\overline{{\mathcal{X}}}}_3$ satisfies the conditions on $V$ in Lemma \[le:gendensity\], where $k=|I|^2$ and $\{x_i\,|\,i=1,2,\dots,k\}=\{f_{{\alpha }_i,{\alpha }_j}\,|\,i,j\in
I\}$. Since ${\overline{{\mathcal{X}}}}_4$ contains all finite sets $V_{n_1,\dots ,n_k}$ in Lemma \[le:gendensity\], and ${\overline{{\mathcal{X}}}}_5\cap V^\chi _{\underline{n}}=
{\overline{{\mathcal{X}}}}_4\cap V^\chi _{\underline{n}}$ by definition of $V^\chi _{\underline{n}}$, the proof is completed.
Similarly to Eq. define ${P}
| 354
| 1,285
| 424
| 419
| null | null |
github_plus_top10pct_by_avg
|
le distribution in the daily scale. Manipulation on those data (e.g. Fig. \[fig:example-ecdf\]) results in a drift or distortion of the distribution, which can be captured to trigger an alarm.
Statistical Divergence Detection with Reference(SDD-R) {#sec:alg-opt-reference}
------------------------------------------------------
From Section \[sec:preliminaries\] we know that statistical divergence only provides a distance between two or more distributions. In a set of data collections, we can only draw a complete graph where nodes denote data collections and edges refer to the symmetric divergence between two connected nodes. From the graph we can find some points that have apparently larger distances with most of other points and return them as anomalies. This may work if anomalous nodes do not compose a large proportion. However the procedure will be too complicated to work out with large amounts of data. If it is assured that data collections form only one cluster, some optimizations can be applied to reduce complexity.
Alternatively we can provide a frame of reference that generates absolute coordinates rather than the relative ones. This optimization is feasible if data collections form one single cluster in distribution space. This is true in most reality scenarios given that distribution is adopted to depict a macro property which comes out as one universal conclusion. In other words , if multiple distributions are used to describe subgroups of entire sample space, then a conclusive one can be obtained by averaging all these sub-distributions. Therefore, we can use an estimate cluster center as reference and test distances between the reference and each other data collections(Algorithm \[alg:sdd-r\]), yielding absolute distances.
Data Collections $\mathbb{D} = \{D_1, \dots, D_n\}$ Estimated anomalous probability $\alpha$ Anomalous Data Collections $P_i \gets$ the distribution of $D_i$ $P_R \gets \frac{1}{n}\sum_{i = 1}^n P_i$ $d_i \gets D(P_i||P_R)$ $\mathcal{N}(\mu, \sigma) \gets$ Gaussian distributi
| 355
| 2,132
| 918
| 442
| 4,111
| 0.768032
|
github_plus_top10pct_by_avg
|
journal.pone.0165605.t003
###### Proportion of discontinued trials.
{#pone.0165605.t003g}
REC Freiburg Other RECs[^1^](#t003fn001){ref-type="table-fn"}
----------------------------------------------------------- -------------- ----- -------------------------------------------------- ----- ----- --------- -----
**All studies**
Unclear/missing = excluded 8% 16% 13% 14% 27% \<0.001 27%
Unclear/missing = completed 7% 15% 11% 13% 25% \<0.001 25%
Unclear/missing = discontinued 15% 22% 25% 22% 31% 0.014 33%
Unclear/missing = 50% completed, 50% discontinued 11% 18% 18% 17% 28% 0.004 29%
**Excluding studies stopped for harm, benefit, futility**
Unclear/missing = excluded 4% 13% 13% 12% 19% 0.057 22%
Unclear/missing = completed 4% 12% 11% 11% 18% 0.047 20%
Unclear/missing = discontinued 12% 19% 25% 20% 24% 0.251 29%
Unclear/missing = 50% completed, 50% discontinued 8% 16% 18% 15% 21% 0.128 25%
^1^ approved by 5 r
| 356
| 4,590
| 297
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| null | null |
github_plus_top10pct_by_avg
|
$}};\\
\xi^{i/2}a_i & \quad \textit{if $L_i$ is \textit{of type $II$}}.
\end{array} \right.$$ Here, $a_i$ is a formal $(n_i-1 \times n_i-1)$-matrix (resp. $(n_i-2 \times n_i-2)$-matrix or $(n_i \times n_i)$-matrix) when $L_i$ is *of type $I^o$* (resp. *of type $I^e$* or *of type $II$*). Non-diagonal entries of $a_i$ are in $B\otimes_AR$ and the $j$-th diagonal entry of $a_i$ is of the form $2x_i^j$ with $x_i^j \in R$. In addition, for non-digonal entries of $a_i$, we have the relation $\sigma({}^ta_i)=a_i$. And $b_i, d_i, e_i$ are matrices of suitable sizes with entries in $B\otimes_AR$ and $c_i, f_i$ are elements in $R$.
3. Assume that $i=j$ is odd. Then $$\pi^i f_{i,i}=\left\{
\begin{array}{l l}
\xi^{(i-1)/2}\cdot \pi\begin{pmatrix} a_i&\pi b_i& e_i\\ -\sigma(\pi \cdot {}^tb_i) &\pi^3f_i&1+\pi d_i \\
-\sigma({}^te_i) &-\sigma(1+\pi d_i) &\pi+\pi^3c_i \end{pmatrix} & \quad \textit{if $L_i$ is \textit{free of type $I$}};\\
\xi^{(i-1)/2}\cdot \pi a_i & \quad \textit{otherwise}.
\end{array} \right.$$ Here, $a_i$ is a formal $(n_i-2 \times n_i-2)$-matrix (resp. $(n_i \times n_i)$-matrix) if $L_i$ is *free of type I* (resp. otherwise). Non-diagonal entries of $a_i$ are in $B\otimes_AR$ and the $j$-th diagonal entry of $a_i$ is of the form $\pi^3 x_i^j$ with $x_i^j \in R$. In addition, for non-digonal entries of $a_i$, we have the relation $\sigma({}^ta_i)=-a_i$. And $b_i, d_i, e_i$ are matrices of suitable sizes with entries in $B\otimes_AR$ and $c_i, f_i$ are elements in $R$.
4. Assume that $i$ is odd and that $L_i$ is *bound of type I*. Then $$\delta_{i-1}(0,\cdots, 0, 1)\cdot f_{i-1,i}+\delta_{i+1}(0,\cdots, 0, 1)\cdot f_{i+1,i} = \pi f_{i, i}^{\ast}$$ for a matrix $f_{i, i}^{\ast}$ of size $(1 \times n_i)$ with entries in $B\otimes_AR$.
**
To simplify notation, each element $$((f_{i,j})_{i< j}, (a_i, x_i^j)_{\textit{$L_i$ of type II}}, (a_i, x_i^j, b_i, c_i)_{\textit{$L_i$ of type $I^o$}},
(a_i, x_i^j, b_i, c_i, d_i, e_i, f_i)_{\textit{$L_i$ of type
| 357
| 1,835
| 467
| 421
| 2,696
| 0.77776
|
github_plus_top10pct_by_avg
|
img = cam.get_image()
pygame.image.save(img,"current.jpeg")
cam.stop()
host = ftputil.FTPHost(**)
host.upload("./current.jpeg", "/domains/*/public_html/webcam.jpg", mode='b')
host.close()
if not count:
host = ftputil.FTPHost(**)
filename = str(time.time()) + ".jpg"
host.upload("./current.jpeg", "/webcamarchive/"+filename, mode='b')
host.close()
count = 10
logging.info(str(time.time())+": Still running")
count -= 1
time.sleep(3)
I run the script from ssh. But I would like to make it start when the computer starts up, as well, how would I do this?
A:
Let's not worry about getting it to run every time your computer starts up until you can get it to run continuously in a normal login session.
If you're sshing into the computer and starting it, just leave the ssh session open, and watch what it prints out. If you can't do that for whatever reason, capture the output by doing, e.g., python foo.py >foo.out 2>foo.err instead of just python.py. Either way, you'll be able to see why it's stopped, instead of just knowing that it's stopped.
You should also look at the log.log file that you explicitly create in your code, and at the syslogs (/var/log/syslog by default on most linux distros), to see if there's anything relevant there.
Also, please tell us exactly how you're "run[ning] the script from ssh". If you're backgrounding it with &, sending it as the ssh command, etc., the instructions above need to be modified. (But you don't have to wait for the modified version—just this once, ssh into a normal login script, run it without backgrounding, and leave it running.)
With only the information that you've given us so far, it's impossible to know exactly what's going on. But my first guess is that you're getting an unhandled exception, which you'd see as an exception traceback, something like this:
Traceback (most recent call last):
File "exc.py", line 7, in <m
| 358
| 1,320
| 492
| 269
| 3,427
| 0.77246
|
github_plus_top10pct_by_avg
|
en and $L_i$ is *of type $I^o$* (resp. if $i$ is even and $L_i$ is *of type $I^e$*, or if $i$ is odd and $L_i$ is *free of type $I$*) and $y_i, v_i, z_i, r_i, t_i, y_i, x_i, u_i, w_i$ are matrices of suitable sizes with entries in $B\otimes_AR$. Similarly, in other cases, i.e. if $i$ is even and $L_i$ is of type $II$, or if $i$ is odd and $L_i$ is of type $II$ or *bound of type $I$*, then $m_{i,i}$ is an $(n_i \times n_i)$-matrix with entries in $B\otimes_AR$.
3. Assume that $i$ is even and that $L_i$ is *of type I*. Then $$z_i+\delta_{i-2}k_{i-2, i}+\delta_{i+2}k_{i+2, i}=\pi z_i^{\ast}$$ such that $z_i^{\ast}\in B\otimes_AR$. This equation is considered in $B\otimes_AR$ and $\pi$ stands for $\pi\otimes 1\in B\otimes_AR$. Here,
- $z_i$ is an entry of $m_{i,i}$ as described in the above step (b).
- $k_{i-2, i}$ (resp. $k_{i+2, i}$) is the $(n_{i-2}, n_i)^{th}$-entry (resp. $(n_{i+2}, n_i)^{th}$-entry) of the matrix $m_{i-2, i}$ (resp. $m_{i+2, i}$) if $L_{i-2}$ (resp. $L_{i+2}$) is *of type* $\textit{I}^o$.
- $k_{i-2, i}$ (resp. $k_{i+2, i}$) is the $(n_{i-2}-1, n_i)^{th}$-entry (resp. $(n_{i+2}-1, n_i)^{th}$-entry) of the matrix $m_{i-2, i}$ (resp. $m_{i+2, i}$) if $L_{i-2}$ (resp. $L_{i+2}$) is *of type* $\textit{I}^e$.
4. Assume that $i$ is odd and that $L_i$ is *bound of type I*. Then $$\delta_{i-1}v_{i-1}\cdot m_{i-1, i}+\delta_{i+1}v_{i+1}\cdot m_{i+1, i}=\pi m_{i,i}^{\ast}$$ such that $m_{i,i}^{\ast} \in M_{1\times n_i}(B\otimes_AR)$. This equation is considered in $B\otimes_AR$ and $\pi$ stands for $\pi\otimes 1\in B\otimes_AR$. Here,
- $v_{i-1}=(0,\cdots, 0, 1)$ (resp. $v_{i-1}=(0,\cdots, 0, 1, 0)$) of size $1\times n_{i-1}$ if $L_{i-1}$ is *of type* $\textit{I}^o$ (resp. *of type* $\textit{I}^e$).
- $v_{i+1}=(0,\cdots, 0, 1)$ (resp. $v_{i+1}=(0,\cdots, 0, 1, 0)$) of size $1\times n_{i+1}$ if $L_{i+1}$ is *of type* $\textit{I}^o$ (resp. *of type* $\textit{I}^e$).
5. Assume that $i$ is odd and that $L_i$ is *bound of type I*. Then $$\delta_{i-1}v_{i-1}\cdot {}^tm_{
| 359
| 1,379
| 619
| 408
| 1,468
| 0.789177
|
github_plus_top10pct_by_avg
|
cruited in our research. The average age of included patients was 56.9 years old. Of the patients, 46 exhibited complete response (CR) or partial response (PR), showing an overall response rate of 44.2%. [Table 2](#T2){ref-type="table"} described clinical profiles for all enrolled subjects.
###### The association between *CLU* expression and clinical features in HCC
Characteristics Total number (*n*) *CLU* expression χ^2^ *P*
----------------------- -------------------- ------------------ ------ ------- -------
Gender 0.122 0.727
Male 58 27 31
Female 46 23 23
Age 0.732 0.392
≥55 60 31 29
\<55 44 19 25
Tumor size 0.555 0.456
≥5 46 24 22
\<5 58 26 32
Tumor stage 7.550 0.006
I+II 52 18 34
III+IV 52 32 20
Lymph node Metastasis 9.861 0.002
Yes 52 33 19
No 52 17 35
Serum AFP 0.594 0.441
≥200 ng/dl 50 26 24
\<200 ng/dl 54 24 30
| 360
| 5,158
| 117
| 130
| null | null |
github_plus_top10pct_by_avg
|
rst isomorphism theorem, $\ker{f}$ has index $2$ in $G$.
Q:
Python: solving unicode hell with unidecode
I have been working on ways to flatten text into ascii. So ā -> a and ñ -> n, etc.
unidecode has been fantastic for this.
# -*- coding: utf-8 -*-
from unidecode import unidecode
print(unidecode(u"ā, ī, ū, ś, ñ"))
print(unidecode(u"Estado de São Paulo"))
Produces:
a, i, u, s, n
Estado de Sao Paulo
However, I can't duplicate this result with data from an input file.
Content of test.txt file:
ā, ī, ū, ś, ñ
Estado de São Paulo
# -*- coding: utf-8 -*-
from unidecode import unidecode
with open("test.txt", 'r') as inf:
for line in inf:
print unidecode(line.strip())
Produces:
A, A<<, A<<, A, A+-
Estado de SAPSo Paulo
And:
RuntimeWarning: Argument is not an unicode object.
Passing an encoded string will likely have unexpected results.
Question: How can I read these lines in as unicode so that I can pass them to unidecode?
A:
Use codecs.open
with codecs.open("test.txt", 'r', 'utf-8') as inf:
A:
import codecs
with codecs.open('test.txt', encoding='whicheveronethefilewasencodedwith') as f:
...
The codecs module provides a function to open files with automatic Unicode encoding/decoding, among other things.
Q:
Laravel DB Schema when referencing to two tables
There a able, called 'interests' which hold the id(s) of 'categories' and/or 'brands' that each user has interest in.
To prevent creating two separate tables for user_category_interests and user_brand_interest I added an enum column called type.
Now I can't figure out how should I create a migration in Schema Builder, How to set relations and foreign keys,... to take advantage of using Eloquent methods.
Schema::create('user_interests', function (Blueprint $table) {
$table->increments('id');
$table->enum('type', ['categories', 'brands']);
$table->integer('reference_id')->unsigned();
$table->timestamps();
});
Is there any better way instead of creating two separate tables and mo
| 361
| 1,943
| 119
| 237
| 569
| 0.805417
|
github_plus_top10pct_by_avg
|
ions on $\mathcal{L}_{Q}^{P}$.
A$_{1}$. *The propositional letters* $p$*,* $q$*, ... are substituted by the symbols* $E(x)$*,* $F(x)$*, ..., with* $E$*,* $F$*, ...* $\in \mathcal{E}$*.*
A$_{2}$. *The set* $\psi _{R}^{Q}$* of all rfs of* $\mathcal{L}_{Q}^{P}$* reduces to the set of all atomic rfs of* $\mathcal{L}_{Q}^{P}$* (in different words, if* $\alpha $* is a rf of* $\mathcal{L}_{Q}^{P}$*, then* $\alpha =E(x)$*, with* $E\in
\mathcal{E}$*).*
A$_{3}$. *Only the logical-pragmatic signs* $\vdash $*,* $N$*,* $K$* and* $A$* appear in the afs of* $\mathcal{L}_{Q}^{P}$*.*
The substitution in A$_{1}$ aims to suggest the *intended interpretation* that we adopt in the following. To be precise, the rfs $E(x)$, $F(x)$, ... are interpreted as sentences stating that the physical object $x$ has the properties $E$, $F$, ..., respectively (Sec. 2.4).
The restriction in A$_{2}$ aims to select rfs that are interpreted as *testable* sentences, i.e., sentences stating testable physical properties (Sec. 2.1), so that physical procedures exist for testing their truth values (which may not occur in the case of a rf of the form, say, $E(x)\vee F(x)$; note that a similar restriction has been introduced in Ref. 27 when recovering intuitionistic propositional logic within $\mathcal{L}^{P} $).
The restriction in A$_{3}$ is introduced for the sake of simplicity, since only the pragmatic connectives $N$, $K$ and $A$ are relevant for our goals in this paper.
Because of A$_{1}$, A$_{2}$ and A$_{3}$, the set $\psi _{A}^{Q}$ of afs of $\mathcal{L}_{Q}^{P}$ is made up by all formulas constructed by means of the following recursive rules.
\(i) *Let* $E(x)$* be a rf. Then* $\vdash E(x)$* is an af.*
\(ii) *Let* $\delta $* be an af. Then,* $N\delta $* is an af.*
\(iii) *Let* $\delta _{1}$* and* $\delta _{2}$* be afs. Then,* $\delta _{1}K\delta _{2}$* and* $\delta _{1}A\delta _{2}$* are afs.*
Let us come now to the semantics of $\mathcal{L}_{Q}^{P}$. We introduce the following assumption on $\mathcal{L}_{Q}^{P}$.
A$_{4}$. *E
| 362
| 3,708
| 847
| 398
| 2,410
| 0.780018
|
github_plus_top10pct_by_avg
|
r experiment 0, we invited a group of participants consisting of 28 tunnel technology professionals, while for the second part (experiments 1--4) we invited a group of 50 students.
10.1371/journal.pone.0201732.t001
###### Short characteristics of all performed experiments including estimated visibility, group familiarity with tunnel and tasks for participants.
{#pone.0201732.t001g}
--------------------------------------------------------------------------------------------------------
Number Level of smokiness Tunnel familiarity Task for pedestrians
-------------- -------------------- -------------------------------- -----------------------------------
Experiment 0 No smoke Yes To evacuate
Experiment 1 Light smoke\ No No direct, expressed task
∼ 0.1 − 0.2*m*^−1^
Experiment 2 Moderate smoke\ Yes To evacuate
∼ 0.4 − 0.5*m*^−1^
Experiment 3 Heavy smoke\ Yes To achieve possibly the best time
∼ 0.8 − 0.9*m*^−1^
Experiment 4 Heavy smoke\ Yes (different starting point) To evacuate
∼ 1.0 − 1.1*m*^−1^
--------------------------------------------------------------------------------------------------------
Participants of experiments 1-4 were asked about their familiarity with the conditions that occur during experiments. Only 2 of them have ever participated in a real or trial tunnel evacuation, and only 5 have ever tried to move/evacuate in smoke conditions. On the other hand, 41 participants took part in a real or trial evacuation in the past.
3.2 Experiments assumptions and scenario {#sec005}
----------------------------------------
The main assump
| 363
| 4,898
| 335
| 210
| null | null |
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|
r = 0.62, p\<0.001 in men; r = 0.73, p\<0.001 in women). Among males, the number of subjects categorized as having dismobility syndrome (gait speed \<0.6 m/s) was 6 (9%) according to 4-MM, and 19 (28%) according to 4-MA. Among females, 22 subjects (21%) had dismobility syndrome according to 4-MM and 30 (29%) according to 4-MA. [Table 3](#pone.0153583.t003){ref-type="table"} shows the categorization of participants according to the different measurement techniques and using 0.6 m/s as gait speed cut-off in men and women, respectively. In 13/69 males (19%) and 24/103 females (23%) the two methods of gait speed assessment disagreed for the presence of dismobility syndrome.
10.1371/journal.pone.0153583.t002
###### Unadjusted coefficient correlation investigating the relationship between 4-MM, 4-MA and objectives measures of physical performance and functional capacity.
{#pone.0153583.t002g}
Men(N = 69) Women(N = 103)
----------------------- ------------- ---------------- ------ ---------- ------ ---------- ------ ----------
**Handgrip strength** 0.51 \< .0001 0.40 0.005 0.38 0.0001 0.29 0.001
**4-MM** \- \- 0.62 \< .0001 \- \- 0.73 \< .0001
**6-MWT** 0.59 \< .0001 0.50 0.0004 0.49 \< .0001 0.22 0.048
**4-MA** 0.62 \< .0001 \- \- 0.73 \< .0001 \- \-
4-MM: 4-meter walking speed measured manually by stopwatch; 4-MA: 4-meter walking speed measured instrumentally by accelerometer; 6MWT: 6-minute walking test.
10.1371/journal.pone.0153583.t003
###### Categorization of male (n = 69) and female participants (n = 103) by using gait speed cut-off 0.6 m/s according to the two different methods of gait speed assessment (4-MM, manual assessment; 4-MA accelerometer assessment).
4-MM showed a poor sensitivity to detect dismobility syndr
| 364
| 23
| 1,106
| 462
| null | null |
github_plus_top10pct_by_avg
|
of a Markov chain of order $k$, we separate single paths by prepending a sequence of $k$ generic *RESET* states to each path, and also by appending one *RESET* state at the end of each path. This enables us to connect independent paths and – through the addition of the *RESET* state – to forget the history between different paths. Hence, we end up with an ergodic Markov chain (see [@chierichetti]). With this artificial *RESET* state, the final number of states is $|S|+1$.
Results {#sec:results .unnumbered}
=======
In this section we present the results obtained from analyzing human navigation patterns based on our datasets at hand introduced in Section “”. We begin by presenting the results of our investigations of memory – i.e., appropriate Markov chain order using the Markov chain methods thoroughly explained in the section called “” – of user navigation patterns in the section entitled “”. Based on these calculations and observations we dig deeper into the structure of human navigation and try to find consistent patterns – i.e., specific sequences of navigated states – in the section named “”.
Memory {#subsec:memory .unnumbered}
------
We start by analyzing human navigation over Wikipedia pages on the Wikigame page dataset. Afterwards, we will focus on our topic datasets for getting insights on a topical level.
### Page navigation {#subsubsec:pagenavi .unnumbered}
#### Wikigame page dataset
[[ The initial Markov chain model selection results (see Figure \[fig:paths\_all\]) obtained from experiments on the Wikigame page dataset confirm our theoretical considerations. We observe that the likelihoods are rising with higher Markov chain orders (confirming what [@chierichetti] found) which intuitively would indicate a better fit to the data using higher order models. However, the likelihood grows per definition with increasing order and number of model parameters and therefore, the likelihood based methods for model selection fail to penalize the increasing model complexity (c.
| 365
| 24
| 942
| 409
| null | null |
github_plus_top10pct_by_avg
|
ion for the final step of the James’s method.
To summarize, the James algorithm consists of the following four steps: (1) Solve the Poisson equation with the zero boundary condition to obtain $\Psi$; (2) Evaluate the screening charge $\sigma$ by applying the discrete Laplace operator to the ghost cells ($\sigma = \Delta^2\Psi/4\pi G$); (3) Use the DGF to calculate the gravitational potential $\Theta^{\rm B}$ at the domain boundary due to $\sigma$; (4) Solve the Poisson equation with the Dirichlet boundary condition $\Phi^{\rm B} = - \Theta^{\rm B}$. In section \[s:interior\_solver\] we have presented the method we adopt for the interior Poisson solver, which is employed in Steps (1) and (4) and also is used to pre-compute the DGF (see Appendix \[s:calc\_dgf\]), which enters in Step 3. In what follows, we describe Steps (2) and (3) in more detail.
Computation of the Screening Charges {#s:James_boundary_charges}
------------------------------------
Once the preliminary gravitational potential $\Psi$ with the zero boundary condition is obtained (using the method of Section \[s:interior\_solver\] and the original density distribution), one can readily apply the discrete Laplace operators at the ghost cells in each boundary to calculate the screening charges.
### Cartesian Grid
A Cartesian grid has six boundary surfaces consisting of the loci of ghost zones immediately outside the problem domain: bottom (bot; $k=0$), top (top; $k=N_z+1$), south (sth; $j=0$), north (nth; $j=N_y+1$), west (wst; $i=0$), and east (est; $i=N_x+1$). With $\Psi=0$ in both the first and second layer of ghost zones outside the domain, the screening charges on these boundary surfaces are given by $$\begin{aligned}
\sigma_{i,j}({\rm bot}) &= \frac{1}{4\pi G (\delta z)^2} \Psi|_{k=1}, & \sigma_{i,j}({\rm top}) &= \frac{1}{4\pi G (\delta z)^2} \Psi|_{k=N_z},\nonumber\\
\sigma_{j,k}({\rm wst}) &= \frac{1}{4\pi G (\delta x)^2} \Psi|_{i=1}, & \sigma_{j,k}({\rm est}) &= \frac{1}{4\pi G (\delta x)^2} \Psi|_{i=N_x},\nonumber\\
\sigma_{i,k}(
| 366
| 2,967
| 1,535
| 444
| 1,902
| 0.784584
|
github_plus_top10pct_by_avg
|
NA, respectively. (B) SWV responses of the DNA biosensor for (a) PBS, (b) 1% BSA, (c) 1000 fM ncDNA, (d) 10 fM ctDNA and (e) 1000 fM ctDNA.](ntnov02p0012g003){#F2}
{#F3}
{#F4}
{#F5}
######
Comparison of DNA biosensor values with known concentrations of ctDNA spiked in human plasma
Sample No. 1 2 3 4 5
-------------------- ------------ ------------- ----------- --------------- ----------------
Known (fM) 50 200 1000 5000 10000
DNA biosensor (fM) 52.11±1.09 203.69±3.41 991±10.81 5087.72±99.78 9899.09±129.06
Recovery (%) 104.2% 101.8% 99.1% 101.8% 99.0%
######
The patient informations and ctDNA levels (fM) before and after treatment
Patient No. 1 2 3 4
-------------------- ---------------- --------------- -------------- ----------------
Cancer type Breast Lung Ovary Rectum
Age 49 55 51 36
Gender Female Male Female Female
Treatment approach Radiotherapy Chemotherapy Chemotherapy Chemotherapy
Before therapy 3890.09±172.32 839.9±47.72 939.01±49.99 4502.02±214.38
After therapy
| 367
| 1,946
| 1,021
| 482
| null | null |
github_plus_top10pct_by_avg
|
AR, h\otimes_AR)$. Here we consider $\mathrm{Aut}_{B\otimes_AR}(L\otimes_AR, h\otimes_AR)$ as a subgroup of $ \mathrm{Res}_{E/F}\mathrm{GL}_E(V)(F\otimes_AR)$. To ease the notation, we say $g\in \mathrm{Aut}_{B\otimes_AR}(L\otimes_AR, h\otimes_AR)$ stabilizes a lattice $M\subseteq V$ if $g(M\otimes_AR)=M\otimes_AR$.
Main construction {#mc}
-----------------
Let $R$ be an étale $A$-algebra. In this subsection, as mentioned above, we observe properties of elements of $\mathrm{Aut}_{B\otimes_AR}(L\otimes_AR, h\otimes_AR)$ and their matrix interpretations. We choose a Jordan splitting $L=\bigoplus_iL_i$ and a basis of $L$ as explained in Theorem 2.4 and Remark 2.5.(a). Let $n_i=\mathrm{rank}_{B}L_i$, and $n=\mathrm{rank}_{B}L=\sum n_i$. Assume that $n_i=0$ unless $0\leq i < N$. Let $g$ be an element of $\mathrm{Aut}_{B\otimes_AR}(L\otimes_AR, h\otimes_AR)$. We always divide a matrix $g$ of size $n \times n$ into $N^2$ blocks such that the block in position $(i, j)$ is of size $n_i\times n_j$. For simplicity, the row and column numbering starts at $0$ rather than $1$.
1. First of all, $g$ stabilizes $A_i$ for every integer $i$. In terms of matrices, this fact means that the $(i,j)$-block has entries in $\pi^{max\{0,j-i\}}B\otimes_AR$. From now on, we write $$g= \begin{pmatrix} \pi^{max\{0,j-i\}}g_{i,j} \end{pmatrix}.$$
2. Let $i$ be even. Then $g$ stabilizes $A_i, B_i, W_i, X_i$ and induces the identity on $A_i/B_i$ and $W_i/X_i$. We also interpret these facts in terms of matrices as described below:
- If $L_i$ is *of type II*, then $A_i=B_i$ and $W_i=X_i$ and so there is no contribution.
- If $L_i$ is *of type* $\textit{I}^o$, the diagonal $(i,i)$-block $g_{i,i}$ is of the form $$\begin{pmatrix} s_i&\pi y_i\\ \pi v_i&1+\pi z_i \end{pmatrix}\in \mathrm{GL}_{n_i}(B\otimes_AR),$$ where $s_i$ is an $(n_i-1) \times (n_i-1)-$matrix, etc.
- If $L_i$ is *of type* $\textit{I}^e$, the diagonal $(i,i)$-block $g_{i,i}$ is of the form $$\begin{pmatrix} s_i&r_i&\pi t_i\\ \pi y_i&1+\pi x_i&\pi z_i\\ v_i&
| 368
| 1,077
| 772
| 417
| 2,311
| 0.780936
|
github_plus_top10pct_by_avg
|
wo vectors is $\pi^1$-modular with the norm $(4)$ (so that it is isometric to $H(1)$ by Theorem \[210\]) and the lattice spanned by the former two vectors is $A(1+4(b+b'), 2a+4(b+b'), 1+4(b+b'))$, which is $\pi^0$-modular and *of type $I^e$*. Let $$\left\{
\begin{array}{l}
\tilde{M}_0=\left(\oplus H(0)\right)\oplus \left( B(e_5-e_1')\oplus B(e_6-e_1') \right);\\
\tilde{M}_1=\left(\oplus H(1)\right)\oplus \left( Be_3'\oplus Be_4' \right)
\oplus \left( B(e_1'-\frac{2\pi(b+b') }{\delta(1+4b')}e_2')\oplus B(\pi e_5+\frac{1}{1+4b'}e_2') \right).
\end{array}\right.$$ Then $\tilde{M}_0\oplus\tilde{M}_1\oplus(\oplus_{i\geq 2}M_i)$ is another Jordan splitting of $L^{j-1}$, where $\tilde{M}_0$ is $\pi^0$-modular and *of type $I^e$* and $\tilde{M}_1$ is isometric to $\oplus H(1)$.
For $\tilde{M}_0\oplus M_2$, the associated diagonal block of the image of a fixed element of $F_j$ in the special fiber of the smooth integral model associated to $L^{j-1}$ is
$$\begin{pmatrix}id&0&0 \\ 0&\begin{pmatrix}1+2z_j&2z_j\\ 0&1 \end{pmatrix}&0
\\ 0&0&id \end{pmatrix}.$$ Here, the $(2,2)$-block corresponds to $\left( B(e_5-e_1')\oplus B(e_6-e_1') \right)$.
We now follow the argument used in Steps (i) and (ii) of Step (1) in even case. Namely, the lattice $M_0''$ can be constructed by using $\tilde{M}_0$ and $M_2$. Then we can easily check that the Dickson invariant of the image of a fixed element of $F_j$ in the orthogonal group associated to $M_0''$ is $(z_j)_1$.
In conclusion, $(z_j)_1$ is the image of a fixed element of $F_j$ under the map $\psi_j$. Since $(z_j)_1$ can be either $0$ or $1$ by Equation (\[e42\]), $\psi_j|_{F_j}$ is surjective onto $\mathbb{Z}/2\mathbb{Z}$ and thus $\psi_j$ is surjective.\
3. Assume that $M_0$ is *of type $I^o$*. Let $M_0=\left(\oplus H(0)\right)\oplus (a)$ with $a\equiv 1$ mod $2$ and let $(e_5)$ be a basis for $(a)$. We consider the lattice spanned by $(e_5, e_1', e_2')$ with the Gram matrix $(a)\oplus A(4(b+b'), -2\delta(1+4b'), \pi(1+4b'))$. Then b
| 369
| 2,173
| 512
| 379
| 3,531
| 0.771715
|
github_plus_top10pct_by_avg
|
ical self-concept show values of just 60 out of a maximum 99.
######
Satisfaction of basic psychological needs in unstructured and organized activities, physical self-concept, and weekly PA.
*M* *SD* As *K*
----------------------- ------- ------- ------- -------
Autonomy (U) 4.13 0.77 −1.10 1.99
Competence (U) 3.80 0.82 −0.74 −0.81
Relatedness (U) 4.38 0.85 −1.86 3.29
Autonomy (O) 3.62 0.71 −0.36 −0.08
Competence (O) 4.04 0.76 −0.63 −0.42
Relatedness (O) 4.40 0.78 −1.38 1.05
Physical self-concept 60.27 20.06 −0.49 −0.28
U, unstructured PA; O, organized PA; M, mean; SD, standard deviation; As, asymmetry; K, kurtosis.
As expected, satisfaction of the need for autonomy is significantly higher in unstructured activities than in organized ones ([Table 4](#T4){ref-type="table"}), and effect size is high ([@B23]). Differences are also observed in relation to satisfaction of the need for competence, with organized activities appearing to satisfy the need for competence more than unstructured activities. The significance of this difference should be interpreted with caution, however, as effect size in this case is small.
######
Satisfaction of basic psychological needs for unstructured and organized PA.
PA *N* *M (SD)* *T* *d* *P*
------------- -------------- ----- ------------- ------------ ------ ------
Autonomy Unstructured 83 4.16 (0.72) 6.15\*\*\* 0.68 0.99
Organized 3.61 (0.71)
Competence Unstructured 83 3.85 (0.81) −2.50\* 0.27 0.68
Organized 4.04 (0.76)
Relatedness Unstructured 81 4.38 (0.82) 0.30 0.03 0.05
Organized 4.36 (0.81)
\*p \< 0.05, \*\*\*p \< 0.001; M, me
| 370
| 4,178
| 203
| 161
| null | null |
github_plus_top10pct_by_avg
|
d}$$ The WMTF in is the sum of independent Gaussian contributions, firstly, from a baseline effect of $N({\bar{\mu}},{\bar{\nu}}^{-1})$ and, secondly, from each MU that fires. If the $j$th MU fires then it makes a $N(\mu_j,\nu^{-1})$ contribution to the WMTF. The parameters ${\boldsymbol{\mu}}=
(\mu_1, \ldots, \mu_u)^\top$, $\nu$, ${\bar{\mu}}$, ${\bar{\nu}}$ are collectively referred to as the *observation parameters*. Each firing event in , $X_{j,t}$, is a Bernoulli random variable with success probability given by a sigmoidal function $F$ of the stimulus, called the *excitability curve* [@Bro76]. The *excitability parameters* for the $t$th MU, $\eta_j$ and $\lambda_j$, characterise its excitation features; conditional on these values, firing events are independent. The acyclic graph in Figure \[fig:MUNEdag\] depicts the dependencies within the neuromuscular model. Key to the strategy in this paper is that the observational and excitability parameters are conditionally independent given the unobserved firing events ${\mathbf{x}}_{1:T}$.
![Directed acyclic graph of the neuromuscular model for a fixed number of motor units, $u$. Arrows denote direct dependencies between known data (square nodes) and unknown parameters and states (circle nodes). Pallets indicate repeated cases according to the stated index.[]{data-label="fig:MUNEdag"}](figures/MUNEdag.pdf){width="80.00000%"}
The excitability curve is a non-decreasing sigmoid function of the stimulus, parameterised by its median, $\eta$ and the reciprocal gradient at the median: $F(s=\eta;\eta,\lambda) = 1/2$, and $F'(s=\eta;\eta,\lambda) = 1/\lambda$. Under assumption A1, @Rid06 specifies the excitability curve as the Gaussian cumulative distribution function (CDF): $F(s) =
\Phi[\delta(s-\eta)]$ where $\Phi(x)$ denotes the standard Gaussian CDF with $\delta = \sqrt{2\pi}/\lambda$. Evidence for this definition [@Hal04] focused on the central structure of the excitability curve by applying a binned chi-squared goodness-of-fit test. However, evidence to distinguis
| 371
| 1,313
| 1,102
| 422
| 1,547
| 0.788381
|
github_plus_top10pct_by_avg
|
l to $B_{2n}$, the Bell number.
For $w\in\Sigma_n^1$ consider a rectangle with $n$ marked points on the bottom and the same $n$ on the top as in Figure \[fig:plan\].
![A seat-plan of $\Sigma_5$[]{data-label="fig:plan"}](1.eps)
The $n$ marked points on the top are labeled by $1, 2, \ldots n$ from left to right. Similarly, the $n$ marked points on the bottom are labeled by $1', 2', \ldots, n'$. If $w$ consists of $s$ parts, then put $s$ shaded circles in the middle of the rectangle so that they have no intersections. Then we join the $2n$ marked points and the $s$ circles with $2n$ shaded bands so that each shaded circle represent a part of $w$.
Using these diagrams, for $w_1,w_2\in\Sigma_n^1$, an arbitrary pair of seat-plans, we can define a product $w_1 w_2$. The product is obtained by placing $w_1$ on $w_2$, gluing the corresponding boundaries and shrinking half along the vertical axis. We then have a new diagram possibly containing some shaded regions which are not connected to the boundaries. If the resulting diagram has $p$ such regions, then the product is defined by the diagram with such region removed and multiplied by $Q^p$. Here $Q$ is an indeterminate. (It is easily checked that the product defined above is closed in the linear span of the set of seat-plans $\Sigma_n^1$ over $\mathbb{Z}[Q]$.) For example, if $$w_1 = \{\{1,1',4'\}, \{2,5\},\{3,4\}, \{2'\},\{3',5'\}\}\in\Sigma_5^1$$ and $$w_2 = \{\{1,1',3',4'\}, \{2\}, \{3,5\}, \{4\}, \{2',5'\}\}\in\Sigma_5^1,$$ then we have $$w_1w_2 =
Q^2\{\{ 1,1',3',4'\}, \{2,5\}, \{3,4\}, \{2',5'\}\}
\in \mathbb{Z}[Q]\Sigma_5^1$$ as in Figure \[fig:prod\].
![The product of seat-plans[]{data-label="fig:prod"}](2.eps)
By this product, the set of linear combinations of the elements of $\Sigma_n^1$ over $\mathbb{Z}[Q]$ makes an algebra $A_{n}(Q)$ called the [*partition algebra*]{}. The identity of $A_{n}(Q)$ is a diagram which corresponds to the partition $$1 = \{\{1, 1'\}, \{2, 2'\}, \ldots, \{n, n'\}\}.$$ We put $A_{0}(Q) = A_{1}(Q)= \mathbb{Z}[Q]$. We ca
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|
\[theorem\][Предложение]{} \[theorem\][Следствие]{} \[theorem\][Гипотеза]{} \[theorem\][Проблема]{}
\[theorem\][Определение]{} \[theorem\][Замечание]{} Ø[[**O**]{}]{}
Self-intersection of immersions and Kervaire Invariant
======================================================
The Kervaire Invariant One Problem is an open problem in Algebraic topology, for algebraic approach see \[B-J-M\], \[C-J-M\]. We will consider a geometrical approach; this approach is based on results by P.J.Eccles, see \[E1\]. For a geometrical approach see also \[C1\],\[C2\].
Let $f: M^{n-1} \looparrowright \R^n$, $n= 2^l -2$, $l>1$, be a smooth (generic) immersion of codimension 1. Let us denote by $g:
N^{n-2} \looparrowright \R^n$ the immersion of self-intersection manifold.
### Definition 1 {#definition-1 .unnumbered}
The Kervaire invariant of $f$ is defined as $$\Theta(f) = <w_2^{\frac{n-2}{2}}; [N^{n-2}] >,$$ where $w_2 = w_2(N^{n-2})$ is the normal Stiefel-Whitney of $N^{n-2}$.
$$$$ The Kervaire invariant is an invariant of the regular cobordism class of the immersion $f$. Moreover, the Kervaire invariant is a well-defined homomorphism $$\Theta: Imm^{sf}(n-1,1) \to \Z/2. \eqno(1)$$
The normal bundle $\nu(g)$ of the immersion $g: N^{n-2}
\looparrowright \R^n$ is a 2-dimensional bundle over $N^{n-2}$ equipped with a $\D_4$–framing. The classifying mapping $\eta:
N^{n-2} \to K(\D_4,1)$ of this bundle is well-defined. The $\D_4$-structure of the normal bundle or the $\D_4$–framing is the prescribed reduction of the structure group of the normal bundle of the immersion $g$ to the group $\D_4$ corresponding to the mapping $\eta$. The pair $(g,\eta)$ represents an element in the cobordism group $Imm^{\D_4}(n-2,2)$. The homomorphism $$\delta: Imm^{sf}(n-1,1) \to Imm^{\D_4}(n-2,2) \eqno(2)$$ is well-defined.
Let us recall that the cobordism group $Imm^{sf}(n-k,k)$ generalizes the group $Imm^{sf}(n-1,1)$. This group is defined as the cobordism group of triples $(f,\Xi,\kapp
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nonumber \\
&\times&
\left\{ (UX)^{\dagger} A W \right\}_{i K}
\left\{ W ^{\dagger} A (UX) \right\}_{K k}
\left\{ (UX)^{\dagger} A W \right\}_{k L}
\left\{ W ^{\dagger} A (UX) \right\}_{L i}.
\label{hatS-4th-order-ii-4th}\end{aligned}$$
Structure of $S$ matrix elements {#sec:structure-S-matrix}
================================
Here we present details in computation of the $S$ matrix elements.
The $S$ matrix elements $S_{\alpha \beta}^{(4)}$
------------------------------------------------
We decompose $S_{\alpha \beta}^{(4)}$ into the following three pieces (include both $\alpha \neq \beta$ and $\alpha = \beta$) $$\begin{aligned}
S_{\alpha \beta}^{(4)} &=& S_{\alpha \beta}^{(4)} [3+4] + S_{\alpha \beta}^{(4)} [3] + S_{\alpha \beta}^{(4)} [2]
\label{Sab-4th}\end{aligned}$$ where $[n]$ implies that the term comes from $n$-th order perturbation of $H_{1}$. To prevent too long expression, we decompose the first term in (\[Sab-4th\]) as $$\begin{aligned}
S_{\alpha \beta}^{(4)} [3+4]
&=&
S_{\alpha \beta}^{(4)} [3]_{ \text{ diag } } + S_{\alpha \beta}^{(4)} [4]_{ \text{ diag } } +
S_{\alpha \beta}^{(4)} [3]_{ \text{ offdiag } } + S_{\alpha \beta}^{(4)} [4]_{ \text{ offdiag } }
\label{Sab-4th-3+4}\end{aligned}$$ where ($n = 3, 4$) “diag” and “offdiag”, respectively, implies $$\begin{aligned}
S_{\alpha \beta}^{(4)} [n]_{ \text{ diag } }
&=&
\sum_{k} (UX)_{ik}
\left( \hat{S}_{kk}^{(4)} [n] \right)
\left\{ (UX)^{\dagger} \right\}_{kj},
\nonumber \\
S_{\alpha \beta}^{(4)} [n]_{ \text{ offdiag } }
&=&
\sum_{k \neq l} (UX)_{ik}
\left( \hat{S}_{kl}^{(4)} [n] \right)
\left\{ (UX)^{\dagger} \right\}_{lj}. \end{aligned}$$ The latter two terms in (\[Sab-4th\]) are given, respectively, by $$\begin{aligned}
S_{\alpha \beta}^{(4)} [3]
&=&
\sum_{k L} (UX)_{ik} \hat{S}_{kL}^{(3)} \left\{ (W^{\dagger}) \right\}_{L j}
+ \sum_{K l} W_{iK} \hat{S}_{Kl}^{(3)} \left\{ (UX)^{\dagger} \right\}_{lj},
\nonumber \\
S_{\alpha \beta}^{(4)} [2] &=&
\sum_{K} W_{iK} \hat{S}_{KK}^{(2)} \left\{ (W^{\dagger}) \right\}_{K j
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|
force ${\boldsymbol{F}}^{(0)}$. For ${\boldsymbol{F}}^{(1)}$, we obtain analytical expressions in the simple case where the impurity is moving with a constant velocity in an otherwise uniform BEC.
The desired relationships between $\nabla \delta\rho_0$ and $\nabla \delta\rho_1$ in Eqs. (\[eq:fp\_unperturb\])-(\[eq:fp\_perturb\]), and $\delta{\boldsymbol{v}}^{(0)}$ and ${\boldsymbol{V}}_p$ will be obtained from the linearization of the dGPE Eq. (\[eq:GPe\_dimless\]) around the uniform steady state $\psi_h=1$: $$\begin{aligned}
\partial_t \delta\psi_0 &=& (i+\gamma)\left(\frac{1}{2}\nabla^2 -1\right)\delta\psi_0 \nonumber \\
&-& (i+\gamma)\delta\psi^*_0,
\label{eq:psi0lin} \\
\partial_t \delta\psi_1 &=&
(i+\gamma)\left(\frac{1}{2}\nabla^2-1\right)\delta\psi_1 \nonumber \\
&-&(i+\gamma)\delta\psi_1^* - (i+\gamma) \mathcal U_p({\boldsymbol{r}}-{\boldsymbol{r}}_p) \ .
\label{eq:psi1lin}\end{aligned}$$ Terms containing $V_{ext}$ are not included in Eq. (\[eq:psi0lin\]) because of our assumption of sufficient distance between possible stirring sources and the neighborhood of the particle position, the only region that–as we will see– will enter into the calculation of the forces. In the next sections we solve these linearized equations to relate density perturbations to undisturbed velocity field and particle velocity.
Inertial force {#sec:inertial}
--------------
To convert Eq. (\[eq:fp\_unperturb\]) for the inertial force into an expression suitable for comparison for the corresponding term in classical fluids, we need to express $\nabla\delta\rho_0$ in terms of the undisturbed velocity field ${\boldsymbol{v}}^{(0)}({\boldsymbol{r}},t)=\delta{\boldsymbol{v}}^{(0)}({\boldsymbol{r}},t)$. To this end, we substract Eq. (\[eq:psi0lin\]) from its complex conjugate, obtaining: $$\begin{aligned}
\left(\nabla^2-4\right)\nabla\delta\rho_0=
4 \left(\partial_t-\frac{\gamma}{2}\nabla^2\right)\delta{\boldsymbol{v}}^{(0)},
\label{eq:drhodv0}\end{aligned}$$ where we have used Eqs. (\[eq:density\_linear\]) and (\[eq:velocity
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|
5 25 200 33 100
------- ---------------- --------------------------- ---------------- ---------------------------
: Parameters of the VXD layers for the standard and CMOS configuration. 50 $\mu$m and 15 $\mu$m sensitive thickness, 3 and 5 hit pixels in average for straight impact respectively.[]{data-label="Tab::sC"}
The results for the occupancy in each layer are shown for the two configurations in Tab. \[Tab::occupancy\].
------- -------- ---------------- ---------------- -------- ---------------- ----------------
layer
total large hit time short hit time total large hit time short hit time
1 0.0790 0.0347 0.0443 0.0183 0.0080 0.0103
2 0.0381 0.0164 0.0217 0.0062 0.0026 0.0035
3 0.0105 0.0049 0.0056 0.0054 0.0025 0.0029
4 0.0041 0.0020 0.0021 0.0021 0.0010 0.0011
5 0.0016 0.0006 0.0010 0.0008 0.0003 0.0005
------- -------- ---------------- ---------------- -------- ---------------- ----------------
: Occupancy for each layer in absence of an anti-DID for the standard and CMOS configurations. The large and small hit time components are shown, as well as their sum.[]{data-label="Tab::occupancy"}
The values are averaged over $\phi$. In fact, due to the $\phi$ dependence shown in Figure \[Fig::occl1\], the local occupancy in a $\phi$ sector can be twice as high as the mean. In average, one can conclude that the large hit time contribution to the occupancy is more than $40\%$ of the total rate.
Anti-DID magnetic field {#aD}
-----------------------
A Detector Integrated Dipole (anti-DID), aligning the outgoing beam with the experimental magnetic field, can be used to reduce the beam size growth due to sy
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|
d from the moded SLD-tree.
Let $C$ be an integer condition or expression and $N_i$ and $N_j$ two nodes in a moded SLD-tree $D$. Let $Cons$ be the set of all integer constructors occurring as selected atom in a node $N_p~(i \leq p \leq j)$ in $D$.
The function *$apply\_cons(C,N_i,N_j)$* returns the integer condition or expression obtained by exhaustively applying $\underline{I}\setminus Expr$ to $C$, for any $\underline{I} ~is~ Expr \in Cons$. $\hfill \square$
The constraints guaranteeing a derivation to $N_j$ to be applicable, can be obtained using $apply\_cons(Cond,N_0,N_i)$ for any integer condition $Cond$ in a node $N_i$ in the considered derivation. For a path from $N_b$ to $N_e$, the precondition of the implication is obtained using $apply\_cons(Cond,N_b,N_i)$, for each condition $Cond$ in a node $N_i$ between nodes $N_b$ to $N_e$ and universally quantifying the integer variables of $N_b$.
\[example:apply\_cons\] The derivation to $N_9$ in Figure \[fig:count\_to\], contains integer conditions in nodes $N_3$ and $N_7$. These are expressed on the integer variable of the query, $\underline{N}$, using $apply\_cons$.
- $apply\_cons(0>\underline{N},N_0,N_3) = 0 > \underline{N}$
- $apply\_cons(\underline{M1}>\underline{N},N_0,N_7) = 0 + 1 > \underline{N}$
To obtain the precondition of the implication, the integer condition in $N_7$ is expressed in terms of the integer variables of $N_5$.
- $apply\_cons(\underline{M1}>\underline{N},N_5,N_7) = \underline{M1} > \underline{N}$
Universally quantifying these variables yields the precondition. $\hfill \square$
To obtain the consequence of the implication for a path from $N_b$ to $N_e$, one first replaces the integer variables of $N_b$ in the precondition by the corresponding integer variables of $N_e$. Then, $apply\_cons$ is used to express the consequence in terms of the values in the previous iteration.
Let $LHS$ be the precondition of an implication, consisting of integer conditions and constraints of the form $I \in Dom_I$. Let $N_i$ and $N_j$ be two
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c(\sigma_{h},\sigma_{1}) & c(\sigma_{h},\sigma_{2}) & \ldots & c(\sigma_{h},\sigma_{h}) & c(\sigma_{h},\lambda)
\end{array} \right)
$.
Let us denote by **Huffman**$({\it EF}(w),n)$ the well-known Huffman’s algorithm [@ds1], where $n\geq{1}$, and ${\it EF}(w)$ is the matrix given below.
$
{\it EF}(w) =
\left(\begin{array}{ccccc}
\sigma_{1} & \sigma_{2} & \ldots & \sigma_{n} \\
f(\sigma_{1},w) & f(\sigma_{2},w) & \ldots & f(\sigma_{n},w)
\end{array} \right)
$.
We assume that the first row of the matrix ${\it EF}(w)$ contains the symbols which are being encoded, while the second row contains their frequencies, that is, $f(\sigma_{i})$ is the frequency of the symbol $\sigma_{i}$ in $w$. Also, we assume that **Huffman**$({\it EF}(w),n)$ is the matrix given by
$
\textbf{Huffman}({\it EF}(w),n) =
\left(\begin{array}{ccccc}
H(\sigma_{1},w) & H(\sigma_{2},w) & \ldots & H(\sigma_{n},w)
\end{array} \right)
$
where $H(\sigma_{i},w)$ is the codeword associated to the symbol $\sigma_{i}$ by Huffman’s algorithm. The algorithm **Builder** described further on takes linear time, and constructs an adaptive code of order one satisfying ${\it Prefix}(c)={\it True}$.
Let $c:\Sigma\times\Sigma^{\leq{1}}\rightarrow\{0,1\}^{+}$ be a function given by the matrix **Builder**$(c)$. Then, $c\in{{\it AC}(\Sigma,\{0,1\},1)}$ and ${\it Prefix}(c)={\it True}$.
**Proof** Applying the algorithm **Builder** to the function $c$, one can easily verify that ${\it Prefix}(c)={\it True}$. Therefore, according to **Theorem 2.1**, $c$ is an adaptive code of order one, that is, $c\in{{\it AC}(\Sigma,\{0,1\},1)}$. $\diamondsuit$
(340,282) (15,268)[**Builder**(c)]{} (15,256)[input:$c:\Sigma\times\Sigma^{\leq{1}}\rightarrow\{0,1\}^{+}$, $\Sigma=\{\sigma_{1},\sigma_{2},\ldots,\sigma_{h}\}$;]{} (15,244)[output:$A_{c}$ *such that* $c\in{{\it AC}(\Sigma,\{0,1\},1)}$ *and* ${\it Pre
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ainly be done once, manually, it's even more powerful to bake the commands into a script that can be called from the Vagrantfile during provisioning. Such a script might look like this:
./scripts/create-nat-hyperv-switch.ps1:
# See: https://www.petri.com/using-nat-virtual-switch-hyper-v
If ("NATSwitch" -in (Get-VMSwitch | Select-Object -ExpandProperty Name) -eq $FALSE) {
'Creating Internal-only switch named "NATSwitch" on Windows Hyper-V host...'
New-VMSwitch -SwitchName "NATSwitch" -SwitchType Internal
New-NetIPAddress -IPAddress 192.168.0.1 -PrefixLength 24 -InterfaceAlias "vEthernet (NATSwitch)"
New-NetNAT -Name "NATNetwork" -InternalIPInterfaceAddressPrefix 192.168.0.0/24
}
else {
'"NATSwitch" for static IP configuration already exists; skipping'
}
If ("192.168.0.1" -in (Get-NetIPAddress | Select-Object -ExpandProperty IPAddress) -eq $FALSE) {
'Registering new IP address 192.168.0.1 on Windows Hyper-V host...'
New-NetIPAddress -IPAddress 192.168.0.1 -PrefixLength 24 -InterfaceAlias "vEthernet (NATSwitch)"
}
else {
'"192.168.0.1" for static IP configuration already registered; skipping'
}
If ("192.168.0.0/24" -in (Get-NetNAT | Select-Object -ExpandProperty InternalIPInterfaceAddressPrefix) -eq $FALSE) {
'Registering new NAT adapter for 192.168.0.0/24 on Windows Hyper-V host...'
New-NetNAT -Name "NATNetwork" -InternalIPInterfaceAddressPrefix 192.168.0.0/24
}
else {
'"192.168.0.0/24" for static IP configuration already registered; skipping'
}
Then, add an appropriate trigger to the top of the Vagrantfile config section, which will ensure that the configuration is always correct upon vagrant up:
config.trigger.before :up do |trigger|
trigger.info = "Creating 'NATSwitch' Hyper-V switch if it does not exist..."
trigger.run = {privileged: "true", powershell_elevated_interactive: "true", path: "./scripts/create-nat-hyperv-switch.ps1"}
end
2. Configure Vagrant Reload Trigger
Rebooting (reloading) the VM in the middle of provisioning, in order to change ove
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| 0.82622
|
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|
0.036\*
C53 0.8965 (3) −0.1062 (4) 0.5675 (2) 0.0377 (15)
H53 0.8744 −0.1643 0.5638 0.045\*
C54 0.9519 (3) −0.1034 (4) 0.5582 (2) 0.0327 (13)
H54 0.9682 −0.1597 0.5483 0.039\*
C55 0.9841 (3) −0.0190 (4) 0.5631 (2) 0.0297 (12)
H55 1.0223 −0.0171 0.5563 0.036\*
C56 0.9603 (2) 0.0633 (4) 0.5781 (2) 0.0246 (11)
H56 0.9826 0.1212 0.5819 0.030\*
C57 0.8633 (2) 0.1414 (3) 0.66613 (17) 0.0137 (9)
C58 0.9155 (2) 0.1100 (3) 0.70346 (17) 0.0182 (10)
H58 0.9518 0.0962 0.6950 0.022\*
C59 0.9142 (2) 0.0992 (4) 0.75240 (18) 0.0200 (10)
H59 0.9496 0.0777 0.7775 0.024\*
C60 0.8614 (2) 0.1197 (4) 0.76500 (18) 0.0209 (10)
H60 0.8610 0.1132 0.7989 0.025\*
C61 0.8097 (2) 0.1492 (3) 0.72898 (19) 0.0188 (10)
H61 0.7737 0.1628 0.7379 0.023\*
C62 0.8100 (2) 0.1593 (3) 0.67889 (18) 0.0170 (9)
H62 0.7739 0.1783 0.6538 0.020\*
C63 0.92682 (19) 0.2589 (3) 0.61403 (16) 0.0116 (8)
H63A 0.9638 0.2360 0.6399 0.014\*
H63B 0.9377 0.2695 0.5826 0.014\*
C64 0.9232 (2) 0.3680 (3) 0.70338 (17) 0.0138 (9)
C65 0.9833 (2) 0.3707 (4) 0.73330 (18) 0.0212 (10)
H65 1.0153 0.3700 0.7181 0.025\*
C66 0.9974 (2) 0.37
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|
ed topological spaces [@heller:stable]. and make precise various additional slogans saying, for instance, that spectra are obtained from spaces or pointed spaces by forcing certain colimit and limit type constructions to commute. We illustrate this by two examples.
1. If one forces homotopy finite colimits and homotopy finite limits to commute in the derivator of spaces, then one obtains the derivator of spectra.
2. If one forces partial cones and partial fibers of squares to commute in the derivator of pointed spaces, then this yields the derivator of spectra.
\[rmk:stable-rep-triv\] The phenomenon that certain colimits and limits commute is well-known from ordinary category theory. To mention an instance, let us recall that filtered colimits are exact in Grothendieck abelian categories, i.e., filtered colimits and finite limits commute in such categories. Additional such statements hold in locally presentable categories, Grothendieck topoi, and algebraic categories.
Now, the phenomenon of stability is invisible to ordinary category theory; in fact, a represented derivator is stable if and only if the representing category is trivial (this follows from since the suspension morphism is trivial in pointed represented derivators). As a consequence the commutativity statements in have no counterparts in ordinary category theory.
Stability versus absoluteness {#sec:galois}
=============================
The close family resemblance between \[prop:ptd-comm,thm:stable-lim-III\] suggests the following definition.
Let $\Phi$ be a class of functors between small categories. A derivator is **left $\Phi$-stable** if for every $(u\colon A\to B)\in\Phi$, left Kan extensions along $u$ in ${\sD}$ commute with arbitrary right Kan extensions. Dually, ${\sD}$ is **right $\Phi$-stable** if ${\sD}\op$ is left $\Phi$-stable, i.e. right Kan extensions along each $u\in \Phi$ in ${\sD}$ commute with arbitrary left Kan extensions. If ${\sD}$ is left (resp. right) $\Phi$-stable, we say that $\Phi$ is left (resp. right) **-absol
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the PMNS matrix in order to add two new CP-violating phases, called Majorana phases, $$U_{PMNS}\rightarrow U_{PMNS}\cdot diag(1,e^{i\alpha_{M}},e^{i\beta_{M}}).$$ Let us consider the PMNS-induced quark and lepton EDMs in this scenario. The dominant diagrams are:
![PMNS-induced quark (on the left) and lepton (on the right) EDMs[]{data-label="fig:MajoEDMs"}](figures/FigMajoEDMs)
The CP-violating flavor structures which tune these EDMs are $J_{\mathcal{CP}}^{\mathrm{Majo}}$ [@Branco] and $Im(\mathbf{X}_{e}^{\mathrm{Majo}})^{11}$, where: $$\begin{aligned}
J_{\mathcal{CP}}^{\mathrm{Majo}}= & \frac{1}{2i}Tr[\mathbf{\Upsilon}_{\nu}^{\dagger}\mathbf{\Upsilon}_{\nu}\cdot\mathbf{Y}_{e}^{\dagger}\mathbf{Y}_{e}\cdot\mathbf{\Upsilon}_{\nu}^{\dagger}(\mathbf{Y}_{e}^{\dagger}\mathbf{Y}_{e})^{T}\mathbf{\Upsilon}_{\nu}-\mathbf{\Upsilon}_{\nu}^{\dagger}(\mathbf{Y}_{e}^{\dagger}\mathbf{Y}_{e})^{T}\mathbf{\Upsilon}_{\nu}\cdot\mathbf{Y}_{e}^{\dagger}\mathbf{Y}_{e}\cdot\mathbf{\Upsilon}_{\nu}^{\dagger}\mathbf{\Upsilon}_{\nu}]\\
\mathbf{X}_{e}^{\mathrm{Majo}}= & [\mathbf{\Upsilon}_{\nu}^{\dagger}\mathbf{\Upsilon}_{\nu},\mathbf{\Upsilon}_{\nu}^{\dagger}(\mathbf{Y}_{e}^{\dagger}\mathbf{Y}_{e})^{T}\mathbf{\Upsilon}_{\nu}].\end{aligned}$$ We find that $Im(\textbf{X}_{e}^{Majo})^{11}$ is 4 orders of magnitude larger than $J_{\mathcal{CP}}^{Majo}$ but in this scenario they are not correlated. In figure \[fig:CorrelationMajo\], we can see the values that can take the PMNS-induced quark and lepton EDMs (tuned respectively by $J_{\mathcal{CP}}^{Majo}$ and $Im(\textbf{X}_{e}^{Majo})^{11}$). The lightest neutrino mass $m_{\nu 1}$ is set to $1eV$ and the CP-violating phases (PMNS phase $\delta_{13}$ and the Majorana phases $\alpha_{M}$ and $\beta_{M}$) are allowed to take on any values.
![Area spanned by $J_{\mathcal{CP}}^{Majo}$ and $Im(\textbf{X}_{e}^{Majo})^{11}$[]{data-label="fig:CorrelationMajo"}](figures/CorrelationMajo)
The lines show the strict correlation occuring when only one phase is non-zero. When the three phases are into action,
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|
0.030 0.022
R2 Between 0.904 0.938 0.877 0.912
R2 Within 0.085 0.143 0.085 0.143
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Note. Unstandardized Coefficients. Standard errors in parentheses. MLR.
\* *p* ≤ 0.05,
\*\* *p* ≤ 0.01,
\*\*\* *p* ≤ 0.001.
Models 6 and 8 account also for mediation of institutional trust at the individual level. Sources: ESS, EUROSTAT, QoG regional data.
In Models 6 and 8, we assess to what extent these correlations are due to institutional trust. Results support H2 and illustrate that the impact of both Corruption and Impartiality are mediated by confidence in institutions, suggesting that widespread unfairness will lead people to trust less each other because of a lower confidence in the institutions (Model 6 and 8). As a matter of fact, Model 8 shows that about 61% of the total effect of the Corruption Pillar on social trust passes through institutional trust. Similar results can be observed for the Impartiality Pillar in Model 6 (about 42% of the total effect is mediated). However, Impartiality maintains a strong and significant direct impact on social trust (p \< 0.001) even in the MSEM accounting for the intervening role of institutional trust (Model 6). This indicates that the mediation mechanism works in a weaker way for this dimension of
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|
and: python app.py
ports:
- "80:5000"
volumes:
- .:/service
container_name: external
networks:
- ws_bridge
networks:
ws_bridge:`
I want to be able to get the Part object by its id
The code that i wrote:
@GetMapping("/parts/{id}")
public PcPart getPartFromOtherService(@PathVariable String id) {
RestTemplate restTemplate = new RestTemplate();
ResponseEntity<PcPart[]> response =
restTemplate.getForEntity(
"http://external:80/api/parts/" + id, // The problem lies here in the url
PcPart[].class);
PcPart[] parts = response.getBody();
return parts[0];
}
What url should i use or how to connect them to be able to retrieve the data (changing external to localhost in the url doesn't help)
A:
Just use your Service-name(computer-parts:5000/api/parts)
You'll find your data.
In docker-compose service name is used as a host for that container.
Q:
Firebase SMS Invites
I am Using Firebase for integrating App Invitation for Android. I am using SMS only invites. I have been through the firebase docs, and haven't find any method to get mobile nos. of the people whom I have Invited and the invitation has been successfully sent to them. I can only see this:
public static String[] getInvitationIds (int resultCode, Intent result)
method only in the docs.How can I get the numbers of people who have recieved the invite.
A:
You can't. This is intentional, as the user hasn't necessarily agreed to share their contacts' phone numbers with you.
Q:
Validate Captcha in JSP Page using AJAX
Trying to Use Captcha in my JSP page as below
<%@ page import="net.tanesha.recaptcha.ReCaptcha" %>
<%@ page import="net.tanesha.recaptcha.ReCaptchaFactory" %>
<html>
<head>
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an; SD, standard deviation; T, T-values (Paired Samples t-test); d, Cohen's d; P, observed power.
No significant differences are observed in relation to the effect of activity type on satisfaction of the need for relatedness.
[Table 5](#T5){ref-type="table"} summarizes the results of the comparison of male and female subjects in relation to all the psychological variables discussed above. Values for satisfaction of the need for autonomy and relatedness through unstructured activities are similar for both groups of subjects. For all the other parameters, the results show higher levels of satisfaction of psychological needs for male subjects than for their female counterparts. Results for physical self-concept also show significant variation between male and female participants, with values for the former scoring close to 70 points out of a possible 99, and the latter averaging just over 50. This is the only case in which a large effect size is observed.
######
Satisfaction of basic psychological needs and self-concept for male and female students.
Sex *N* *M (SD)* *T* *d* *P*
----------------------- -------- ----- --------------- ------------- ------ ------
Autonomy (U) Female 61 4.02 (0.86) −1.42 0.26 0.41
Male 59 4.22 (0.65)
Competence (U) Female 61 3.60 (0.84) −2.62\*\* 0.49 0.85
Male 59 3.99 (0.74)
Relatedness (U) Female 57 4.23 (1.02) −1.89 0.35 0.59
Male 58 4.53 (0.62)
Autonomy (O) Female 38 3.39 (0.85) −2.50\*\* 0.55 0.81
Male 51 3.78 (0.53)
Competence (O) Female 38 3.84 (0.88) −2.02\* 0.44 0.66
Male 51 4.18 (0.61)
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| 488
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github_plus_top10pct_by_avg
|
om the duality proposal.
We use $X^{3-4}$ to denote the bosons in the $T^4$, and $\psi^{3-4}$ their right-moving superpartners. We shall use $\lambda^{1-8}$ to denote the free left-moving fermions and $\lambda^{9-16}$ to denote the left-moving fermions in the bundle above.
Let us begin the spectrum computation in the untwisted sector.
First, consider (NS,NS) states. Here, the left- and right-moving vacuum energies are given by $E_{\rm left} = -1$, $E_{\rm right} =
-1/2$. The ${\mathbb Z}_4$-invariant states have the form
-------------------------------------------------------------------------------------------------------------------------------------
State Count
------------------------------------------------------------------------- -----------------------------------------------------------
$\left( \lambda^{1-8}_{-1/2}, \overline{\lambda}^{1-8}_{-1/2} \right)^2 spacetime vector, valued in adjoint of $so(16)$
\otimes \left( \psi^{1-2}_{-1/2}, \overline{\psi}^{1-2}_{-1/2} \right)$
$\overline{\partial} X^{1-2}_{-1} \otimes gravity, tensor multiplet contribution
\left( \psi^{1-2}_{-1/2}, \overline{\psi}^{1-2}_{-1/2} \right)$
$\left( \lambda^{9-16}_{-1/2} \overline{\lambda}^{9-16}_{-1/2} \right) spacetime vector, valued in adjoint, ${\bf 1}$ of $su(8)$
\otimes \left( \psi^{1-2}_{-1/2}, \overline{\psi}^{1-2}_{-1/2} \right)$
(${\bf 1}$ from the trace)
$\overline{\partial} X^{3-4}_{-1} 16 spacetime scalars (toroidal moduli),
\otimes \left( \psi^{3-4}_{-1/2}, \overline{\psi}^{3-4}_{-1/2} \right)$
forming 4 hypermultiplets
$\left( \left( \lambda^{9-16}_{-1/2} \right)^2,
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github_plus_top10pct_by_avg
|
----------------------
In this experiment, we tested all seven algorithms on totally synthetic data sets. Results are shown in TABLE \[tab:performance-synthetic\]. It shows that our technique can be applied towards any kind of distributions. And these techniques worked better under irregular distributions since difference were clearer among these. Comparison between SDD-R and static SDD-E shows that adaptive thresholds provided more flexible classifiers. Results under random-shape drifting proves the efficiency of sliding windows toward drifting context.
-------------------- ------------ ------------ ----------- ------------ ------------ ------------ ----------- ------------ ------------ ------------ ----------- ------------ ------------ ------------ ----------- ------------
**Pre(%)** **Rec(%)** **F1(%)** **T(ms)** **Pre(%)** **Rec(%)** **F1(%)** **T(ms)** **Pre(%)** **Rec(%)** **F1(%)** **T(ms)** **Pre(%)** **Rec(%)** **F1(%)** **T(ms)**
**SDD-R** 10.00 **100.00** 18.18 349.42 24.78 69.20 36.49 401.82 10.00 **100.00** 18.18 351.65 9.97 **99.00** 18.11 353.65
**SDD-R+** 22.40 22.40 22.40 348.49 34.40 34.40 34.40 **398.02** 58.40 58.40 58.40 **350.87** 1.20 1.20 1.20 **346.67**
**SDD-E Static** 43.71 82.60 57.17 372.74 33.34 66.60 44.44 410.72 69.24 93.20 79.45 372.77 12.34 97.20 21.91 369.63
**SDD-E Static+** **75.10** 60.20 **66.83** 371.72 **45.93** 45.80 **45.86** 412.95 **89.52** 85
| 387
| 4,611
| 223
| 236
| null | null |
github_plus_top10pct_by_avg
|
_{-(m-1)+i} = {\mathit{v}}_{-(n-1)+i}$, then ${\mathfrak{A}}({\mathit{u}}_{-(m-1)+i}) = {\mathfrak{A}}({\mathit{v}}_{-(n-1)+i}) = {\mathfrak{A}}({\mathit{s}})$. By transitivity of equality, ${\mathit{u}}_{-(m-1)+(i+1)} = {\mathfrak{A}}({\mathit{s}}) = {\mathit{v}}_{-(n-1)+(i+1)}$.
Without loss of generality suppose $m \leq n$. Then ${\mathit{u}}_{-(m-1)+i} = {\mathit{v}}_{-(n-1)+i}$ is true for $i = 0, 1, \;...\; m-1$. At $i = m - 1$ we have ${\mathit{s}}_{\text{crux}} = {\mathit{u}}_0 = {\mathit{v}}_{-(n-1)+(m-1)} = {\mathit{v}}_{-(n-m)}$. Since ${\mathit{v}}$ is a localized predecessor walk of a cone, then ${\mathit{v}}_0 = {\mathit{s}}_{\text{crux}}$. But ${\mathit{v}}_0 = {\mathit{s}}_{\text{crux}} = {\mathit{v}}_{-(n-m)}$. Because the cone is assumed acyclic, ${\mathit{v}}_0$ and ${\mathit{v}}_{-(n-m)}$ must then be the same identical step – that is, $m = n$.
Here the assumption of two different local predecessor walks with the same edge step leads to the contradiction that both are indeed the same identical walk. This means local predecessor walks within an acyclic cone ${\mathcal{C}}$ are in one-to-one correspondence with ${{\operatorname{edge}{{\mathcal{C}}}}}$ via the edge step relation.
Operational profile {#S:OPERATIONAL_PROFILE_SECTION}
-------------------
An operational profile is a limit of the cumulative history of software execution ratios under normal operations (which is troublesome to define).
This section frequently uses the compound idiom that $\{x_n\}$ represents an anonymous sequence of objects of the same type as $x$. That is, if $X$ is the set of all $x_i$, then $\{x_n\} \colon {\mathbb{N}}\to X$.
### Musa’s operational profile {#S:MUSA_OP_PROFILE}
Musa et al intended operational profiles as a tool for analysis of software reliability. A notion of the operational profile appeared in their pioneering exposition [@jM87]. This reference gives a definition in terms of the program’s higher purpose, as reflected in run types. Consequently an operational profile is the set of run ty
| 388
| 2,575
| 1,539
| 472
| 1,200
| 0.792836
|
github_plus_top10pct_by_avg
|
ha({\mathbf{d}}(s))(x)]$ showing that $s*\widetilde{\alpha}([{\mathbf{d}}(s),x])$ is defined, too. The proof is completed by the following calculation using the fact that components of $\alpha$ commute with the translation maps: $$\widetilde{\alpha}(s\circ ([{\mathbf{d}}(s),x]))=\widetilde{\alpha}([{\mathbf{r}}(s),F({\mathbf{r}}(s),s)(x)])=
[{\mathbf{r}}(s), \alpha({\mathbf{r}}(s))F({\mathbf{r}}(s),s)(x)];$$ $$s*\widetilde{\alpha}([{\mathbf{d}}(s),x])=s*[{\mathbf{d}}(s), \alpha({\mathbf{r}}(s))(x)]=[{\mathbf{r}}(s),F'({\mathbf{r}}(s),s)(\alpha({\mathbf{d}}(s),x))].$$
We set $\Psi(\alpha)=\widetilde{\alpha}$. Let ${\mathsf{Repr}}(S)$ denote the category of all non-strict $S$-sets, ${\mathsf{ConRepr}}(S)$ the category of all connected non-strict $S$-sets and ${\mathsf{TF}}(L(S))$ the category of torsion-free functors on $L(S)$.
It is routine to verify that the assignments $\Phi\colon {\mathsf{Repr}}(S)\to {\mathsf{TF}}(L(S))$ and $\Psi\colon {\mathsf{TF}}(L(S))\to {\mathsf{ConRepr}}(S)$ are functorial. We denote the restriction of the functor $\Phi$ to the category ${\mathsf{ConRepr}}(S)$ by $\Phi'$. We obtain the following result.
\[th:equiv\] There is an equivalence of categories $${\mathsf{ConRepr}}(S) \,\,
{\mathrel{
\settowidth{\@tempdima}{$\scriptstyle\Phi'$}
\settowidth{\@tempdimb}{$\scriptstyle\Psi$}
\ifdim\@tempdimb>\@tempdima \@tempdima=\@tempdimb\fi
\mathop{\vcenter{
\offinterlineskip\ialign{\hbox to\dimexpr\@tempdima+2em{##}\cr
\rightarrowfill\cr\noalign{\kern.3ex}
\leftarrowfill\cr}}}\limits^{\!\Phi'}_{\!\Psi}}} \,\, {\mathsf{TF}}(L(S)).$$
Let $F\colon L(S)\to {\mathsf{Sets}}$ be a torsion-free functor and show that $F$ is naturally isomorphic to the functor $\Phi\Psi(F)$. By construction, for $e\in E$ we have $$\Phi\Psi(F)(e)=\{[e,x]\colon e\cdot x \text{ is defined}\}.$$ Clearly, the maps $\tau_e\colon x\to [e,x]$, $x\in F(e)$, $e\in E$, are bijections. In addition, these maps commute with the translation maps because for any arrow $(f,s)$ in $L(S)$, we have $$[{\mathbf{d}}(s
| 389
| 1,715
| 411
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github_plus_top10pct_by_avg
|
0.972 −0.972 −0.972
(−1.479, −0.465); (−1.482, −0.462); (−1.740, −0.204); (−1.653, −0.291); (−1.481, −0.462); (−1.482, −0.462); (−1.731, −0.212); (−1.646, −0.298);
1.97E−16 2.58E−12 2.58E−12 2.58E−12 9.52E−11 5.94E−16 5.94E−16 5.94E−16
**20** −0.821 −0.820 −0.820 −0.820 −0.830 −0.830 −0.830 −0.830
(−1.102, −0.540); (−1.243, −0.396); (−1.298, −0.342); (−1.286, −0.354); (−1.217, −0.442); (−1.235, −0.426); (−1.290, −0.370); (−1.276, −0.384);
1.11E−14 0.317 0.317 0.317 0.210 0.258 0.258 0.258
CI = confidence interval
Options: ML, maximum likelihood estimation with standard CI derivation; REML, restricted maximum likelihood estimation with standard CI derivation; REML+KR, REML estimation with Kenward‐Roger CI derivation; REML+Satt, REML estimation with Satterthwaite CI derivation.
These results are in agreement with the key findings observed in Section [3.2](#sim7930-sec-0010){ref-type="sec"} and summarized in Figure [3](#sim7930-fig-0003){ref-type="fig"}. Firstly, the magnitude of summary treatment effect estimate was similar throughout, irrespective of model used or estimation method. Secondly, with ML estimation, the stratified intercept model gave narrower 95% CIs and smaller estimates of the between trial variance than the random intercept model, especially with *K*
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| 1,838
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github_plus_top10pct_by_avg
|
array(27) {
[0]=> array(6) {
["frags"]=> string(1) "0"
["ping"]=> string(2) "26"
["nick"]=> string(10) "DIVINEBRAH"
["gq_name"]=> string(10) "DIVINEBRAH"
["gq_score"]=> string(1) "0"
["gq_ping"]=> string(2) "26"
}
[1]=> array(6) {
["frags"]=> string(1) "0"
["ping"]=> string(2) "35"
["nick"]=> string(7) "><> <><"
["gq_name"]=> string(7) "><> <><"
["gq_score"]=> string(1) "0"
["gq_ping"]=> string(2) "35"
}
[2]=> array(6) {
["frags"]=> string(1) "0"
["ping"]=> string(2) "42"
["nick"]=> string(10) "xXthe0neXx"
["gq_name"]=> string(10) "xXthe0neXx"
["gq_score"]=> string(1) "0"
["gq_ping"]=> string(2) "42"
}
$servers['promod'] = array('cod4', '67.202.102.224');
$servers['promod2'] = array('cod4', '67.202.102.224');
$gq = new GameQ();
$gq->addServers($servers);
$results = $gq->requestData();
function print_results($results) {
foreach ($results as $id => $data)
And this is what I am trying to use to list the current players.
$promodplist = $data['promod']['players'];
foreach($promodplist as $k => $v)
I just simply want to echo out the nick (nickname) in each array.
A:
$promodplist = $data['promod']['players'];
foreach($promodplist as $k => $v)
print($v['nick']);
Should do what you want. foreach iterates through the key/value pairs in the array, where $k is the element's key (a 0-based index, in your case) and $v is the value (an array of player data, for you). You can access the rest of the information by using its name as the key in the array accessor.
Q:
How to deploy angular2 cli app on github?
I am front and engineer and have no experience with deploying.
I am developing my pet project using angular-cli.
How can I deploy it on github pages?
There is another simple way to do this?
A:
You should follow the angular-cli Wiki stories which can be found here.
The one you're looking for is Deploy to GitHub Pages.
A simpl
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| 1,232
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| 0.830658
|
github_plus_top10pct_by_avg
|
se $p < 4k$ : linear mixing and hitting times
---------------------------------------------------
![The $p<4k$ case: a plot of $P[0]$ and $P[1]$ versus time, for $k =1$, $n=5$, $p = 0.5$[]{data-label="fig2"}](pless4k){width="3in"}
When $p < 4k$, we recover the perhaps most interesting feature of the non-decohering walk: the instantaneous mixing time is linear in $n$. To exactly determine the mixing times for our decohering walk, we solve $P[0] = P[1] = \frac{1}{2}$; this amounts to determining when $$\gamma
= \frac{1}{2} e^{-\frac{pt}{2n}} \left[\cos\left(\frac{\beta t}{2n}\right)
+ \frac{p}{\beta}~\sin\left(\frac{\beta t}{2n}\right) \right]$$ equals zero. Clearly the exponential decay term results in mixing as $t \to \infty$; our principle concern, however, is with the periodic mixing times analogous to those of the original walk. We thus ignore the exponential term when solving the equality $\gamma = 0$, which yields $$\frac{p^2}{\beta^2} = \frac{1 + \cos(\beta t/n)}{1 - \cos(\beta t/n)}.$$ This equation actually has more solutions than the one we started with, because of the use of half-angle formulas for simplification. The solutions that we want are $$t_{mix} = \frac {n}{\beta} \left[2\pi c - \arccos\left(\frac{p^2}{8k^2}-1\right) \right]$$ where $c$ ranges over the positive integers. Evidently, the mixing times still occur in linear time; an example is shown in Figure \[fig2\]. Note also that if we let $p = 0$, we have $t_{mix} = n\pi(2c - 1)/(4k)$, which are exactly the nice periodic mixing times of the non-decohering walk. In the decohering case, however, these mixing times drift towards infinity, and cease to exist altogether beyond the threshold of $p = 4k$. This proves Theorem 1.
We now wish to determine when our small system is as close as possible to $\vert 1 \rangle$. Since our large-system walk begins at $\vert 0 \rangle^{\otimes
n}$, this will correspond to approximate hitting times to the opposite corner $\vert 1 \rangle^{\otimes n}$. These times correspond to local maxima of $P[1]$; the
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| 4,579
| 450
| 277
| 2,619
| 0.778388
|
github_plus_top10pct_by_avg
|
0.00253 (13) 0.00284 (13)
Ag3 0.01196 (17) 0.01387 (16) 0.01320 (16) −0.00216 (12) 0.00038 (13) 0.00199 (12)
Ag4 0.01172 (16) 0.01111 (15) 0.01114 (15) −0.00089 (12) 0.00175 (12) 0.00073 (12)
S1 0.0119 (5) 0.0230 (6) 0.0107 (5) −0.0008 (4) 0.0009 (4) 0.0018 (4)
S2 0.0118 (5) 0.0124 (5) 0.0151 (5) −0.0015 (4) 0.0049 (4) 0.0014 (4)
S3 0.0149 (5) 0.0121 (5) 0.0154 (5) 0.0014 (4) 0.0069 (4) 0.0030 (4)
S4 0.0166 (6) 0.0149 (5) 0.0165 (5) 0.0016 (4) 0.0077 (4) −0.0022 (4)
S5 0.0178 (6) 0.0134 (5) 0.0100 (5) −0.0002 (4) 0.0047 (4) 0.0002 (4)
S6 0.0313 (7) 0.0250 (6) 0.0236 (6) 0.0131 (5) 0.0168 (6) 0.0079 (5)
S7 0.0139 (6) 0.0241 (6) 0.0093 (5) −0.0017 (4) 0.0043 (4) 0.0032 (4)
S8 0.0199 (7) 0.0608 (10) 0.0151 (6) −0.0208 (6) −0.0006 (5) 0.0056 (6)
P1 0.0146 (6) 0.0116 (5) 0.0102 (5) −0.0019 (4) 0.0036 (4) 0.0007 (4)
P2 0.0103 (5) 0.0127 (5) 0.0118 (5) −0.0002 (4) 0.0019 (4) 0.0012 (4)
P3 0.0126 (6) 0.0123 (5) 0.0105 (5) −0.0008 (4) 0.0012 (4) 0.0014 (4)
P4 0.0119 (5) 0.0107 (5) 0.0099 (5) −0.0015 (4) 0.0026 (4) 0.0009 (4)
P5 0.0110 (5) 0.0100 (5) 0.0089 (5) −0.0003 (4) 0.0027 (4) 0.0002 (4)
P6 0.0111 (6) 0.0112 (5) 0.0111 (5) 0.0000 (4) 0.0032 (4) 0.0017 (4)
C1 0.024 (3) 0.021 (2) 0.014 (2) −0.0047 (19) 0.0099 (19) −0.0057 (19)
C2 0.020 (3) 0.031 (3) 0.030 (3) −0.004 (2) 0.006 (2) −0.009 (2)
C3 0.021 (3) 0.056 (4) 0.034 (3) −0.010 (3) 0.007 (2) −0.016 (3)
C4 0.039 (4) 0.067 (5) 0.032 (3) −0.035 (3) 0.020 (3) −0.021 (3)
C5 0.050 (4) 0.041 (4) 0.040 (4) −0.030 (3)
| 393
| 4,145
| 417
| 239
| null | null |
github_plus_top10pct_by_avg
|
{D}$, and it is not difficult to see from Eqs. (\[Eqn: func\_bi\]) and (\[Eqn: multi\_bi\]), that the restriction **** of $\widehat{\mathcal{T}}$ to $\textrm{Map}(X,Y)$ is just $\mathcal{T}$.
Henceforth $\widehat{\mathcal{T}}$ and $\mathcal{T}$ will be denoted by the same symbol $\mathcal{T}$, and convergence in the topology of pointwise biconvergence in $(\textrm{Multi}(X,Y),\mathcal{T})$ will be denoted by $\rightrightarrows$, with the notation being derived from Theorem 3.1.
**Definition 3.2.** ***Functionization of a multifunction.*** *A net of functions* $(f_{\alpha})_{\alpha\in\mathbb{D}}$ *in* $\textrm{Map}(X,Y)$ *converges in* $(\textrm{Multi}(X,Y),\mathcal{T})$, $f_{\alpha}\rightrightarrows\mathscr{M}$, *if it biconverges pointwise in* $(\textrm{Map}(X,Y),\mathcal{T}^{*})$. *Such a net of functions will be said to be a* *functionization of* $\mathscr{M}$*.$\qquad\square$*
**Theorem 3.2.** *Let $(f_{\alpha})_{\alpha\in\mathbb{D}}$ be a net of functions in $\textrm{Map}(X,Y)$. Then $$f_{\alpha}\overset{\mathbf{G}}\longrightarrow\mathscr{M}\Longleftrightarrow f_{\alpha}\rightrightarrows\mathcal{M}.\qquad\square$$* **Proof.** If $(f_{\alpha})$ converges graphically to $\mathscr{M}$ then either $\mathcal{D}_{-}$ or $\mathcal{R}_{-}$ is nonempty; let us assume both of them to be so. Then the sequence of functions $(f_{\alpha})$ converges pointwise to a function $F$ on $\mathcal{D}_{-}$ and to functions $G$ on $\mathcal{R}_{-}$, and the local basic neighbourhoods of $F$ and $G$ generate the topology of pointwise biconvergence.
Conversely, for pointwise biconvergence on $X$ and $Y$, $\mathcal{R}_{-}$ and $\mathcal{D}_{-}$ must be non-empty.$\qquad\blacksquare$
Observe that the boundary of $\textrm{Map}(X,Y)$ in the topology of pointwise biconvergence is a “line parallel to the $Y$-axis”. We denote this closure of $\textrm{Map}(X,Y)$ as
**Definition 3.3.** $\textrm{Multi}_{\mid}((X,Y),\mathcal{T})=\mathrm{Cl}(\mathrm{Map}((X,Y),\mathcal{T})).$$\qquad\square$
The sense in which $\textrm{Multi}_{\mid}(X,
| 394
| 963
| 886
| 493
| 1,430
| 0.789713
|
github_plus_top10pct_by_avg
|
---C37 1.395 (6)
W1---S3 2.2240 (11) C33---C34 1.396 (6)
W1---S2 2.2579 (11) C33---H33 0.9500
W1---Ag2 2.9701 (4) C34---C35 1.391 (7)
W1---Ag1 2.9707 (5) C34---H34 0.9500
W2---S8 2.1470 (13) C35---C36 1.390 (7)
W2---S6 2.1945 (13) C35---H35 0.9500
W2---S7 2.1985 (11) C36---C37 1.396 (6)
W2---S5 2.2878 (11) C36---H36 0.9500
W2---Ag4 3.0410 (4) C37---H37 0.9500
W2---Ag3 3.1609 (4) C38---H38A 0.9900
Ag1---P1 2.3924 (12) C38---H38B 0.9900
Ag1---S1 2.5374 (12) C39---C40 1.396 (6)
Ag1---S2 2.5677 (12) C39---C44 1.398 (6)
Ag1---S5 2.7919 (12) C40---C41 1.390 (7)
Ag2---P2 2.3914 (12) C40---H40 0.9500
Ag2---S3 2.5132 (11) C41---C42 1.376 (7)
Ag2---S2 2.5772 (11) C41---H41 0.9500
Ag2---S5 2.8412 (12) C42---C43 1.389 (7)
Ag3---P4 2.4478 (12) C42---H42 0.9500
Ag3---P3 2.4602 (12) C43---C44 1.394 (7)
Ag3---S5 2.6096 (12) C43---H43 0.9500
Ag3---S6 2.7403 (13) C44---H44 0.9500
Ag4---P6 2.4485 (12) C45---C46 1.396 (7)
Ag4---P5 2.4601 (11) C45---C50 1.400 (6)
Ag4---S5 2.5984 (12) C46---C47 1.400 (7)
Ag4---S7 2.7248 (12) C46---H46 0.9500
P1---C1 1.826 (5) C47---C48 1.390 (8)
P1---C7 1.824 (5) C47---H47 0.9500
P1---C13 1.831 (4) C48---C49 1.371 (8)
P2---C70 1.829 (5) C48---H48 0.9500
P2---C64 1.830 (5) C49
| 395
| 4,265
| 449
| 297
| null | null |
github_plus_top10pct_by_avg
|
der 2) defines the transformation of the space by the following formula: $b_z(f_1)=f_2$, $b_z(f_2)=f_1$, $b_z(f_3)=f_4$, $b_z(f_4)=f_3$.
Obviously, the restriction of the epimorphism $\omega: \Z/2 \int
\D_4 \to \Z/2$ to the subgroups $\I_{2,x}, \I_{2,y} \subset \Z/2
\int \D_4$ is trivial and the restriction of this homomorphism to the subgroup $\I_{2,z}$ is non-trivial.
The subgroup $\I_3 \subset \I_{2,x}$ is defined as the subgroup with the generators $c_x, b_x, a_x^2$. This is an index 2 subgroup isomorphic to the group $\Z/2^3$. The image of this subgroup in $\Z/2 \int \D_4$ coincides with the intersection of arbitrary pair of subgroups $\I_{2,x}$, $\I_{2,y}$, $\I_{2,z}$. The subgroup $\I_3 \subset \I_{2,y}$ is generated by $c_y, b_y,
a^2_y$. Moreover, one has $c_y=b_x$, $b_y=c_x$, $a^2_y=a^2_x$. It is easy to check that the following relations hold: $c_z=a^2_x$, $a^2_z=c_x=b_y$, $b_z=b_x=c_y$. Therefore $Ker(\omega
\vert_{\I_2,z})$ coincides with the subgroup $\I_3 \subset
\I_{2,z}$.
The subgroups $\I_{2,x}, \I_{2,y}, \I_{2,z}, \I_3$ in $\Z/2 \int
\D_4$ are well-defined. There is a natural projection $\pi_b: \I_3
\to \I_b$.
We will also consider the subgroup $\I_{2,x \downarrow} \subset
\Z/2 \int \D_4$ from geometrical considerations. This subgroup is a quadratic extension of the subgroup $\I_{2,x}$ such that $\I_{2,x}=Ker \omega \vert_{\I_{2,x
\downarrow}} \subset \I_{2,x\downarrow}$. An algebraic definition of this group will not be required.
In the following lemma we will describe the structure group of the framing of the triad $(L^{n-4k}_{int} \cup_{\Lambda}
L^{n-4k}_{ext})$. The framings of the spaces of the triad will be denoted by $(\Psi_{\int}
\cup_{\Psi_\Lambda} \cup \Psi_{ext}, \zeta_{int}
\cup_{\zeta_\Lambda} \cup \zeta_{ext})$.
### Lemma 1 {#lemma-1 .unnumbered}
There exists a generic regular deformation $g_1 \to g_2$ of the caliber $3 \varepsilon_3$ such that the immersed manifold $g_2(N^{n-2k}_{ext})$ admits a reduction of the structure group of the $\D_4$-framing to the subgroup $\I_b \s
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| 450
| null | null |
github_plus_top10pct_by_avg
|
Magnesium (g) 0.17 0.05
Sodium (g) 1.0 0.3
Potassium (g) 2.8 0.8
Chloride (g) 3.0 0.9
Iron (mg) 57.0 17.0
Copper (mg) 6.9 2.0
Zinc (mg) 69.0 20.0
Manganese (mg) 24.0 6.9
Selenium (mg) 0.05 0.01
Iodine (mg) 1.0 0.3
Vitamin A (IU) 6990 2001
Vitamin D3 (IU) 242 70
Vitamin E (IU) 276 80
Thiamin (mg) 9.0 2.6
Riboflavin (mg) 18.0 5.2
Pyridoxine (mg) 8.0 2.3
Niacin (mg) 56.0 16.2
Pantothenic acid (mg) 16.0 4.6
Cobalamin (mg) 0.06 0.02
Folic acid (mg) 1.5 0.4
Choline (mg) 860 249
^\*^All nutrients listed on an energy basis.
In dogs that successfully reached target weight, detailed evaluation was conducted after the weight loss. At this stage, body weight was recorded, and body composition assessed by DEXA. The detailed re-evaluation assessment was not conducted in dogs failing to complete, either because they were euthanased (for unrelated reasons) before reaching target weight or were lost to follow-up.
Laboratory analyses
-------------------
All blood and urine samples were taken after a fast of at least 16 h, from each dog, both before initiating the weight loss programme and when target weight was successfully achieved. A complete blood count was performed using whole blood from EDTA tubes. Serum was analysed for a
| 397
| 4,914
| 312
| 198
| null | null |
github_plus_top10pct_by_avg
|
square root (\[eq:squareroot\]) can be written in the form $$c_1^{\rm rep}({\cal E}) \: \equiv \:
c_1^{\rm rep}(T \mathfrak{X}) \mbox{ mod } 2$$ applying the Chern-rep’s discussed in sections \[sect:possible-anomcanc\] and appendix \[app:chern-reps\]. We will leave such an interpretation to future work.
Spectrum result and Serre duality
---------------------------------
Finally, we are ready to associate sheaf cohomology groups to elements of the spectrum. A general element of the spectrum will have the form $$\lambda_-^{a_1} \cdots \lambda_-^{a_m} \psi_+^{\overline{\imath}_1} \cdots
\psi_+^{\overline{\imath}_k} | 0 \rangle ,$$ where each $\lambda$ and $\psi$ has some unspecified moding, such that the sum of the modings equals the vacuum energy computed earlier. Canonical commutation relations descend to statements of the form $$\{ \lambda_{p}^a, \lambda_{-p}^{\overline{b}} \} \: \propto \: h^{a
\overline{b}}, \: \: \:
\{ \psi_p^i, \psi^{\overline{\jmath}}_{-p} \} \: \propto \: g^{i
\overline{\jmath}} ,$$ where $p$ is a moding. So long as the modings are all negative, both holomorphic and antiholomorphic-indexed fermions can appear in states. For zero modes, our Fock vacuum conventions are such that only $\lambda_{-,0}^{\overline{a}}$ and $\psi_{+,0}^i$ contribute.
In any event, it should now be clear, following [@dist-greene], that on component $\alpha$, states of the form[^22] $$\prod_n \left(
\lambda_{-,n}^{a_1} \cdots \lambda_{-,n}^{a_{m_n}}
\lambda_{-,n}^{\overline{b}_1} \cdots
\lambda_{-,n}^{\overline{b}_{p_n}}
\psi_{+,n}^{j_1} \cdots \psi_{+,n}^{j_{\ell_n}}
\psi_{+,n}^{\overline{\imath}_1} \cdots
\psi_{+,n}^{\overline{\imath}_{k_n}} \right) | 0 \rangle ,$$ (where the fermion modings add up to the vacuum energy in the $\alpha$ sector) are counted by the sheaf cohomology group $$\label{eq:countstates1}
H^{k_0}\left( I_{\mathfrak{X}}|_{\alpha},
\left( \wedge^{m_0} {\cal E}_0^{\alpha *} \right)
\otimes_{n>0}\left( \wedge^{m_n} {\cal E}_n^{\alpha }
\otimes \wedge^{p_n} {\cal E}_n^{\alpha *}
\otimes
| 398
| 720
| 540
| 443
| 3,806
| 0.769995
|
github_plus_top10pct_by_avg
|
of the tensor $B$ at the first non-trivial order in $f^2$ : $$\begin{aligned}
{B^{ac}}_{ed} &=& -i \frac{g}{2(c_++c_-)}
({f^c}_{eg} {f^{ag}}_d (-1)^{ed} + {f^c}_{dg} {f^{ag}}_e) + O(f^4). \end{aligned}$$
5\. A similar analysis for the other two first-order poles proportional respectively to $1/( z - w)$ and $( z - w)/(\bar z - \bar w)^2$ gives respectively the tensors $A$ and $C$ in equations (\[euclidOPEs\], \[ABC\]). The details of the calculation are very similar to the calculation we just discussed.
Remarks on higher order terms in $f^2$ {#remarks-on-higher-order-terms-in-f2 .unnumbered}
--------------------------------------
To discuss a few aspects of the higher order terms that we encountered, it is useful to define the following tensor: $$\begin{aligned}
{S^{ac}}_{ed} &=&
{f^c}_{eg} {f^{ag}}_d (-1)^{ed} + {f^c}_{dg} {f^{ag}}_e.\end{aligned}$$ It is manifestly graded symmetric in the lower indices. Let’s also check that it is graded symmetric in the upper indices: $$\begin{aligned}
{S^{ca}}_{ed} &=&
{f^a}_{eg} {f^{cg}}_d (-1)^{ed} + {f^a}_{dg} {f^{cg}}_e
\nonumber \\
&=& {f^{ag}}_e (-1)^{g+eg+1+ed}
{f^c}_{dg} (-1)^{gd+1}
+ (-1)^{g+1+gd+1+eg} {f^c}_{eg} {f^{ag}}_d
\nonumber \\
&=& {f^{ag}}_e (-1)^{ac}
{f^c}_{dg}
+ (-1)^{ac} {f^c}_{eg} {f^{ag}}_d
\nonumber \\
&=& (-1)^{ac} {S^{ac}}_{ed}.\end{aligned}$$ Therefore, $S$ is a linear operator that acts on the space of (graded) symmetric two-tensors.
The higher order term in the last line in the above explicit calculation gives rise to the square of the linear operator $S$. We computed it for $psl(2|2)$ for which it simplifies to $$\begin{aligned}
{S^{ac}}_{gh} {S^{gh}}_{ed} &=& 8 ( \kappa^{ac} \kappa_{de}
+ ( \delta^a_e \delta^c_d + (-1)^{ed} \delta^a_d \delta^c_e)).\end{aligned}$$ We also have the equality $S^3=16S$. When we take a supertrace of $S^2$, it can be shown to be zero because the superdimension of $psl(2|2)$ is $-2$.
Using some of these properties, it is clear that at higher order the structure of a pole in the $j^a \cdot M
| 399
| 2,726
| 628
| 404
| null | null |
github_plus_top10pct_by_avg
|
\kappa^{ca}j^b_{L,z}(w)
+ \delta_{\bar n,0} \frac{n!}{(x-w)^{n+3}} c_1 c_2 {f^{cab}}
+ \frac{c_1 \kappa^{cb} \p^n \bar \p ^{\bar n} j^a_{L,z}(w)}{(x-w)^2}+ ...
\end{aligned}$$ Resumming the series, we get: $$\begin{aligned}
:j^a_{L,z}(z) & j^b_{L,z}(w): j^c_{L,z}(x) = \sum_{n,\bar n=0}^{\infty} \frac{(z-w)^n }{n ! }\frac{ (\bar z - \bar w)^{\bar n}}{ \bar n !}
\left[ \delta_{\bar n,0}\frac{(n+1)!}{(x-w)^{n+2}} c_1 \kappa^{ca}j^b_{L,z}(w) \right. \cr
& \qquad \left.
+ \delta_{\bar n,0} \frac{n!}{(x-w)^{n+3}} c_1 c_2 {f^{cab}}
+ \frac{c_1 \kappa^{cb} \p^n \bar \p ^{\bar n} j^a_{L,z}(w)}{(x-w)^2}+ ... \right] \cr
& = \frac{c_1 \kappa^{ca}j^b_{L,z}(w)}{(x-z)^2}
+ \frac{c_1 c_2 {f^{cab}}}{(x-z)(x-w)^2}
+ \frac{c_1 \kappa^{cb} j^a_{L,z}(z)}{(x-w)^2}
+...\end{aligned}$$ After gathering all terms, we obtain: $$\begin{aligned}
j^a_{L,z}(z) & j^b_{L,z}(w) j^c_{L,z}(x) =
\frac{c_1 \kappa^{ab}j^c_{L,z}(x)}{(z-w)^2} + \frac{c_1 c_2 {f^{abc}}}{(z-w)(w-x)^2} + \frac{c_1 \kappa^{ca}j^b_{L,z}(w)}{(x-z)^2} \cr
& \qquad + \frac{c_1 c_2 {f^{cab}}}{(x-z)(x-w)^2}
+ \frac{c_1 \kappa^{cb} j^a_{L,z}(z)}{(x-w)^2}
+... \cr
& = \frac{c_1 c_2 {f^{abc}}}{(z-x)(x-w)(w-z)} + \frac{c_1 \kappa^{ab}j^c_{L,z}(x)}{(z-w)^2}+ \frac{c_1 \kappa^{ca}j^b_{L,z}(w)}{(x-z)^2}
+\frac{c_1 \kappa^{cb} j^a_{L,z}(z)}{(x-w)^2}+ \mathcal{O}(f^0) +... \nonumber\end{aligned}$$ which is manifestly invariant under permutation of the currents.
The OPE $j^a_{L,z}(z) j^b_{L,z}(w) j^c_{L,\bar z}(x)$ {#the-ope-ja_lzz-jb_lzw-jc_lbar-zx .unnumbered}
-----------------------------------------------------
We now consider the OPE involving two $z$-components and one $\bar z$-component of the left current: j\^a\_[L,z]{}(z) j\^b\_[L,z]{}(w) j\^c\_[L,|z]{}(x). First we will take first the OPE between the two $z$-components of the current: $$\begin{aligned}
[ j^a_{L,z}(z) & j^b_{L,z}(w) ] j^c_{L,\bar z}(x) =
\left(
\frac{c_1 \kappa^{ab}}{(z-w)^2} + \frac{c_2 {f^{ab}}_d j^d_{L,z}(w)}{z-w}+ \frac{(c_2-g) {f^{ab}}_d j^d_{L,\bar z}(w)(\bar z - \bar w)}{(z-w)^2} \right. \
| 400
| 1,691
| 824
| 453
| null | null |
github_plus_top10pct_by_avg
|
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