text
large_stringlengths 384
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al length should be $2\sqrt{2}\pi$.
Q:
Limit a date in input type date
I would like to limit the date so that the user does not have to select a date of less than one year, but I wish that it is done automatically compared to the date of the system. If anyone has ideas I'm grateful.
A:
You can get the current date and subtract an year from the current year and set min attribute
var dtToday = new Date();
var month = dtToday.getMonth() + 1;
var day = dtToday.getDate();
var year = dtToday.getFullYear();
if(month < 10)
month = '0' + month.toString();
if(day < 10)
day = '0' + day.toString();
var minDate = (year-1) + '-' + month + '-' + day;
document.getElementById('dt').setAttribute('min', minDate);
<input type="date" id="dt">
Q:
J2Objc Eclipse Plugin "error: --ignore-missing-imports is no longer supported"
When I use the J2Objc Eclipse Plugin I get the following error while translating my code:
Executing with switches: [ -g --no-package-directories -x objective-c -use-arc --verbose --ignore-missing-imports --prefixes /Users/mg/Documents/Grails/GGTS3.6.2/TEST2Objectc/.TEST2Objectc-prefixes ]
/Applications/J2Objc/j2objc-0.9.6/j2objc -g --no-package-directories -x objective-c -use-arc --verbose --ignore-missing-imports --prefixes /Users/mg/Documents/Grails/GGTS3.6.2/TEST2Objectc/.TEST2Objectc-prefixes -encoding UTF-8 -d /Users/mg/Documents/Grails/GGTS3.6.2/TEST2Objectc/src /Users/mg/Documents/Grails/GGTS3.6.2/TEST2Objectc/src/java/ios/Test.java
error: --ignore-missing-imports is no longer supported
I do not see any option to change the --ignore-missing-imports flag.
How can I fix this error?
A:
--ignore-missing-imports flag has been removed by J2Objc developer
Because
That flag is only useful when doing a first
pass over a large project, and shouldn't be used normally since all that
does is ignore an error that will show up when compiling the generated
files.
You should uncheck "Continue translation if an imported class is not fo
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| 2,968
| 551
| 163
| 52
| 0.831045
|
github_plus_top10pct_by_avg
|
}{75}(-\frac{45}{13}m^2r^2+\frac{45}{13}(\alpha^2r^2-\frac{1}{18})e^2rm+e^4)ra^2 \nonumber\\
&+\frac{7}{25}e^4r^5\alpha^2)\alpha a^2r^2\cos^4(\theta)-180a^2(a^4m^2r^2\alpha^2+((\frac{71}{45}\alpha^2r^4-r^2)m^2-\frac{1}{18}e^2r(\alpha^2r^2-20)m-\frac{13}{45}e^4)a^2-\frac{7}{30}e^2\alpha^2r^4 \nonumber\\
&(e^2-\frac{19}{7}mr))r^2\cos^3(\theta)-150\alpha(((\frac{34}{75}r^3\alpha^2-\frac{38}{25}r)m+e^2)ma^4+\frac{11}{75}r(-\frac{34}{11}m^2r^2+\frac{20}{11}e^2(\alpha^2r^2+\frac{9}{20})rm \nonumber\\
&+e^4)a^2+\frac{2}{75}e^4r^5\alpha^2)r^4\cos^2(\theta)+40(a^4m^2r^2\alpha^2+((\frac{9}{10}\alpha^2r^4-r^2)m^2-\frac{1}{4}e^2r(\alpha^2r^2-6)m-\frac{11}{20}e^4)a^2-\frac{1}{10}(e^2 \nonumber\\
&-\frac{3}{2}mr)e^2\alpha^2r^4)r^4\cos(\theta)+10\alpha(((\frac{1}{5}r^3\alpha^2-\frac{6}{5}r)m+e^2)a^2+\frac{1}{5}r^2(e^2-mr))mr^6)\sin^2(\theta)+(2\alpha a^6(a^4m^2\alpha^2+ \nonumber\\
&(3\alpha^2e^2mr-m^2)a^2+2\alpha^2e^4r^2)\cos^9(\theta)+2\alpha^2a^6((e^2m-18m^2r)a^2+2re^4-20e^2mr^2)\cos^8(\theta)-68\alpha a^4(m^2(\alpha^2r^2 \nonumber\\
&-\frac{3}{17})a^4+(-m^2r^2 +\frac{57}{34}e^2r(\alpha^2r^2+\frac{5}{57})m)a^2+\frac{21}{34}e^4r^4\alpha^2)\cos^7(\theta)+40a^4(a^4m^2r\alpha^2-\frac{9}{20}((-\frac{142}{9}r^3\alpha^2+\frac{20}{9}r)m \nonumber\\
&+e^2(\alpha^2r^2-\frac{5}{9}))ma^2-\frac{21}{20}e^2\alpha^2(e^2-\frac{30}{7}mr)r^3)\cos^6(\theta)+60\alpha a^2(((3r^3\alpha^2-\frac{19}{5}r)m+e^2)ma^4+(-3r^3m^2+\frac{17}{6}e^2 \nonumber\\
&(\alpha^2r^2+\frac{1}{17})r^2m+\frac{11}{30}re^4)a^2+\frac{8}{15}e^4r^5\alpha^2)r\cos^5(\theta)-180a^2(a^4m^2r^2\alpha^2+((\frac{71}{45}\alpha^2r^4-r^2)m^2+\frac{1}{18}e^2r(\alpha^2r^2+15)m \nonumber\\
&-\frac{11}{90}e^4)a^2 -\frac{8}{45}e^2r^4\alpha^2(e^2-3mr))r\cos^4(\theta)-200(((\frac{17}{50}r^3\alpha^2-\frac{17}{10}r)m+e^2)ma^4+\frac{13}{50}(-\frac{17}{13}m^2r^2+\frac{15}{26}e^2(\alpha^2r^2 \nonumber\\
&-\frac{3}{5}) rm+e^4)ra^2+\frac{1}{100}e^4r^5\alpha^2)\alpha r^3\cos^3(\theta)+96r^3(a^4m^2r^2\alpha^2+((\frac{3}{8}\alpha^2r^4-r^2)m^2+\frac{5}{48}e^2r(\alpha^2r^2+15)m \nonumbe
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github_plus_top10pct_by_avg
|
)
C27---H27 0.9500 N2---C80 1.481 (7)
C28---C29 1.392 (7) C79---H79 0.9500
C28---H28 0.9500 C80---H80A 0.9800
C29---C30 1.401 (7) C80---H80B 0.9800
C29---H29 0.9500 C80---H80C 0.9800
C30---C31 1.376 (7) C81---H81A 0.9800
C30---H30 0.9500 C81---H81B 0.9800
C31---H31 0.9500 C81---H81C 0.9800
S4---W1---S1 107.81 (4) C25---C24---H24 119.8
S4---W1---S3 108.47 (4) C20---C25---C24 120.0 (5)
S1---W1---S3 109.03 (4) C20---C25---H25 120.0
S4---W1---S2 108.04 (4) C24---C25---H25 120.0
S1---W1---S2 111.20 (4) C27---C26---C31 118.3 (4)
S3---W1---S2 112.14 (4) C27---C26---P5 118.7 (3)
S4---W1---Ag2 131.67 (3) C31---C26---P5 123.0 (3)
S1---W1---Ag2 120.49 (3) C28---C27---C26 121.5 (5)
S3---W1---Ag2 55.67 (3) C28---C27---H27 119.2
S2---W1---Ag2 57.14 (3) C26---C27---H27 119.2
S4---W1---Ag1 136.25 (3) C27---C28---C29 119.8 (5)
S1---W1---Ag1 56.40 (3) C27---C28---H28 120.1
S3---W1---Ag1 115.24 (3) C29---C28---H28 120.1
S2---W1---Ag1 56.88 (3) C28---C29---C30 119.2 (5)
Ag2---W1---Ag1 78.214 (10) C28---C29---H29 120.4
S8---W2---S6 110.73 (6) C30---C29---H29 120.4
S8---W2---S7 109.18 (5) C31---C30---C29 120.2 (4)
S6---W2---S7 109.38 (5) C31---C30---H30 119.9
S8---W2---S5 108.25 (5) C29---C30---H30 119.9
S6---W2---S5 110.66 (4) C30---C31---C26 120.9 (4)
S7---W2---S5 108.61 (4) C30---C31---H31 119.5
S8---W2---Ag4 148.67 (5) C26---C31---H31 119.5
S6---W2---Ag4 100.53 (4) C33---C32-
| 403
| 5,222
| 469
| 199
| null | null |
github_plus_top10pct_by_avg
|
t.$$
in $\mathcal{R}(\mu_{\nu})$ to be eventually in every neighbourhood of $g$ in the sense that $\lim_{n\rightarrow\infty}\int_{-1}^{1}\mid g-g_{n}\mid=0$.
\(b) *The inverse $(\mu-\nu)^{-1}$ exists but is not continuous.* The inverse exists because, as noted earlier, $0$ is the only functional solution of Eq. (\[Eqn: eigen\]). Nevertheless although the net of functions $$\delta_{\nu\varepsilon}(\mu)=\frac{1}{\tan^{-1}(1+\nu)/\varepsilon+\tan^{-1}(1-\nu)/\varepsilon}\left(\frac{\varepsilon}{(\mu-\nu)^{2}+\varepsilon^{2}}\right),\qquad\varepsilon>0$$
is in the domain of $\mu_{\nu}$ because $\int_{-1}^{1}\delta_{\nu\varepsilon}(\mu)d\mu=1$ for all $\varepsilon>0$, $$\lim_{\varepsilon\rightarrow0}\int_{-1}^{1}\mid\mu-\nu\mid\delta_{\nu\varepsilon}(\mu)d\mu=0$$
implying that $(\mu-\nu)^{-1}$ is unbounded.
Taken together, (a) and (b) show that functional solutions of Eq. (\[Eqn: eigen\]) lead to state 2-2 in Table \[Table: spectrum\]; hence $\nu\in[-1,1]=C\sigma(\mu)$.
\(c) The two integral constraints in (b) also mean that $\nu\in C\sigma(\mu)$ is a *generalized eigenvalue* of $\mu$ which justifies calling the graphical limit $\delta_{\nu\varepsilon}(\mu)\overset{\mathbf{G}}\rightarrow\delta_{\nu}(\mu)$ a *generalized,* or singular, *eigenfunction*, see Fig. \[Fig: Poison\] which clearly indicates the convergence of the net of functions[^26].
From the fact that the solution Eq. (\[Eqn: CaseSolution\_FR\]) of the transport equation contains an integral involving the multifunction $\phi(\mu,\nu)$, we may draw an interesting physical interpretation. As the multi appears *every where* on $V(\mu)$ (that is there are no chaotic orbits but only the multifunctions that produce them), we have here a situation typical of *maximal ill-posedness* characteristic of chaos: note that both the functions comprising $\phi_{\varepsilon}(\mu,\nu)$ are non-injective. As the solution (\[Eqn: CaseSolution\_FR\]) involves an integral over all $\nu\in V(\mu)$, the singular eigenfunctions — that collectively may be regarded as repre
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github_plus_top10pct_by_avg
|
he last component, we define $$\label{def_cyclic_compos}
\alpha\circ_{m+1} \beta:=\tau_{n+m} (\tau^{-1}_{m+1}(\alpha)\circ_m
\beta)\stackrel{\eqref{compos_cyclic3}}{=} \tau_{n+1}(\beta) \circ_1
\alpha$$ $$\begin{pspicture}(1,1.6)(10.5,5.6)
\psline[linestyle=dashed](2,2)(1.2,2.9)
\psline(2,2)(1.6,2.9)
\psline(2,2)(2,2.9)
\psline(2,2)(2.4,2.9)
\psline[linestyle=dashed](2,2)(2.8,2.9)
\rput[b](3,2){$\alpha$} \rput[b](2.4,3.4){$\beta$}
\psline[linestyle=dashed](2.8,3)(2.8,3.5)
\psline[linestyle=dashed](2.8,3.5)(3,4)
\psline(2.8,3.5)(2.8,4)
\psline(2.8,3.5)(2.6,4)
\rput[b](3.5,3){$:=$}
\psline[linestyle=dashed](5,2)(4.2,2.9)
\psline[linestyle=dashed](4.2,3)(4.3,3.1)(5,3.25)(5.7,3.4)(5.8,3.5)
\psline(5,2)(4.6,2.9) \psline(4.6,3)(4.2,3.5)
\psline(5,2)(5,2.9) \psline(5,3)(4.6,3.5)
\psline(5,2)(5.4,2.9) \psline(5.4,3)(5,3.5)
\psline[linestyle=dashed](5,2)(5.8,2.9) \psline[linestyle=dashed](5.8,3)(5.4,3.5)
\rput[b](6,2){$\alpha$} \rput[b](6.4,3.1){$\tau_{m+1}^{-1}$}
\psline[linestyle=dashed](5.4,3.6)(5.4,4.1)
\psline[linestyle=dashed](5.4,4.1)(5.6,4.5)
\psline(5.4,4.1)(5.4,4.5)
\psline(5.4,4.1)(5.2,4.5)
\rput[b](5.2,3.8){$\beta$}
\psline[linestyle=dashed](5.8,3.6)(5.8,4.5)
\psline(4.2,3.6)(4.2,4.5)
\psline(4.6,3.6)(4.6,4.5)
\psline(5,3.6)(5,4.5)
\psline(4.2,4.6)(4.4,5.3)
\psline(4.6,4.6)(4.8,5.3)
\psline(5 ,4.6)(5.2,5.3)
\psline(5.2,4.6)(5.4,5.3)
\psline(5.4,4.6)(5.6,5.3)
\psline[linestyle=dashed](5.6,4.6)(5.8,5.3)
\psline[linestyle=dashed](5.8,4.6)(5.6,4.8)(5,4.95)(4.4,5.1)(4.2,5.3)
\rput[b](6.4,4.7){$\tau_{n+m}$}
\rput[b](7.3,3){$=$}
\psline[linestyle=dashed](8.55,2)(8.1,2.9)
\psline(8.55,2)(8.4,2.9)
\psline(8.55,2)(8.7,2.9)
\psline[linestyle=dashed](8.55,2)(9,2.9)
\rput[b](9.7,2){$\tau_{n+1}(\beta)$}
\psline[linestyle=dashed](8.1,3)(8.1,3.5)
\psline[linestyle=dashed](8.1,3.5)(7.8,4)
\psline(8.1,3.5)(8 ,4)
\psline(8.1,3.5)(8.2,4)
\psline(8.1,3.5)(8.4,4)
\rput[b](8.5,3.5){$\alpha$}
\end{pspicture}$$ where the last equal
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github_plus_top10pct_by_avg
|
60
Zhao et al[@b15-ott-10-5355] 2016 HNF1A-AS1 43 OS 60
Li et al[@b28-ott-10-5355] 2015 HOTTIP 68 OS 60
Sun et al[@b17-ott-10-5355] 2015 HULC 78 OS 60
Tian et al[@b31-ott-10-5355] 2015 MEG3 64 OS 60
**Abbreviations:** lncRNA, long noncoding RNA; OS, overall survival.
######
HRs of lncRNA expression in osteosarcoma
LncRNA HR (OS) 95% CI *P*-value lnHR SE Related to poor prognosis
----------- --------- -------- ----------- ------- ------- --------------------------- ------
TUG1 2.78 1.29 6.00 0.009 1.02 0.39 High
TUG1 3.6 1.01 12.8 0.035 1.28 0.65 High
UCA1 2.52 1.32 4.83 0.011 0.92 0.33 High
UCA1 3.13 1.29 7.55 0.015 1.14 0.45 High
BCAR4 3.22 0.89 7.88 0.014 1.17 0.55 High
BCAR4 2.32 1.24 5.62 0.018 0.84 0.40 High
HULC 2.27 0.61 8.44 0.016 0.82 0.67 High
HULC 2.28 1.48 5.43 0.009 0.83 0.33 High
HIF2PUT 5.48 1.99 12.29 0.01 1.70 0.46 High
MALAT1 3.16 1.56 6.88 0.003 1.15 0.38 High
HNF1A-AS1 2.64 1.39 7.42 0.005 0.97 0.43 High
HOTTIP 2.89 1.37 7.06 0.007 1.06 0.42 High
91H 3.13 1.32 7.49 0.010 1.04 0.44 High
CCAL 3.18 1.64 9.94 0.021 1.16 0.46 High
MEG3 0.81
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|
phi^{(0)}_{m,n}\big)^2 \phi^{(0)}_{m+1,n} \phi^{(1)}_{m-1,n} \big(\phi^{(1)}_{m,n}\big)^2 \phi^{(1)}_{m+1,n} \phi^{(2)}_{m-1,n} \phi^{(2)}_{m,n} \phi^{(2)}_{m+1,n},\\
P^{(3)}_{m,n} = 2 + 2 P^{(0)}_{m,n} + 2 P^{(1)}_{m,n}+ P^{(2)}_{m,n}.
\end{gathered}$$
Miura transformations and relation to Bogoyavlensky lattices {#sec:Miura}
============================================================
In this section we discuss Miura transformations for the reduced systems and their symmetries which bring the latter to polynomial form. In the lowest dimensional case ($N=3$) the polynomial system is directly related to the Bogoyavlensky lattice (see (\[eq:Bog\]) below), whereas the higher dimensional ones result in systems which generalise (\[eq:Bog\]) to $k$ component systems.
The reduced system in $\boldsymbol{N=3}$ {#the-reduced-system-in-boldsymboln3 .unnumbered}
----------------------------------------
The Miura transformation [@14-6] $$\begin{gathered}
\psi_{m,n} = \frac{P^{(0)}_{m,n}}{P^{(1)}_{m,n}} - 1,\end{gathered}$$ where $P^{(0)}_{m,n}$ and $P^{(1)}_{m,n}$ are given in (\[eq:N3-P-G\]), maps equation (\[eq:MX2\]) to $$\begin{gathered}
\label{eq:MX2a}
\frac{\psi_{m+1,n+1}+1}{\psi_{m,n}+\psi_{m,n+1}+1} + \frac{\psi_{m+1,n}}{\psi_{m,n+1}} = 0,\end{gathered}$$ and its symmetry to $$\begin{gathered}
\label{eq:Bog}
\partial_{t_2} \psi_{m,n} = \psi_{m,n} (\psi_{m,n}+1) (\psi_{m+2,n} \psi_{m+1,n} - \psi_{m-1,n} \psi_{m-2,n}),\end{gathered}$$ which is related to the Bogoyavlensky lattice [@B] $$\begin{gathered}
\partial_{t_2} \chi_{m,n} = \chi_{m,n}(\chi_{m+2,n} + \chi_{m+1,n} - \chi_{m-1,n} - \chi_{m-2,n}),\end{gathered}$$ through the Miura transformation $$\begin{gathered}
\chi_{m,n} = \psi_{m+1,n} \psi_{m,n} (\psi_{m-1,n}+1).\end{gathered}$$
The reduced system in $\boldsymbol{N=5}$ {#the-reduced-system-in-boldsymboln5 .unnumbered}
----------------------------------------
The Miura transformation $$\begin{gathered}
\psi_{m,n}^{(0)} = \frac{2 P^{(0)}_{m,n}}{P^{(2)}_{m,n}},\qquad \psi_{m,n}^{(1)} = \frac{P^{
| 407
| 212
| 616
| 506
| 3,001
| 0.775512
|
github_plus_top10pct_by_avg
|
----- --------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
**Name** **Experiment: nonstructural carbohydrate and saccharification**
Sin 1 *sinensis* 2 Allison *et al*. ([2011](#gcbb12419-bib-0002){ref-type="ref"}), da Costa *et al*. ([2014](#gcbb12419-bib-0011){ref-type="ref"}), Jensen *et al*. ([2011](#gcbb12419-bib-0019){ref-type="ref"}), Jensen *et al*. ([2013](#gcbb12419-bib-0500){ref-type="ref"}), Robson *et al*., ([2013a](#gcbb12419-bib-0501){ref-type="ref"},[b](#gcbb12419-bib-0502){ref-type="ref"})
Sin 2 *sinensis* 2
Sin 3 *sinensis* 2
Sin 4 *sinensis* 2
Sin 5 *sinensis* 2 Japan
Sin 6 *sinensis* 2 Japan
Sin 7 *sinensis* 2 South Korea
Sin 8 *sinensis*
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github_plus_top10pct_by_avg
|
^s$ and $\mu$ be non-zero partitions such that up to permutation of the parts of each $\nu^p$ we have $\sum_{p=1}^s\nu^p=\mu.$ Then $$\sum_{p=1}^s \nrm_\mu(\nu^p)\leq \nrm_\mu(\mu).$$ Equality holds if and only if:
\(i) $s=1$ and $\mu=\nu^1$.
or
\(ii) $\nu^1,\ldots,\nu^s$ and $\mu$ all are rectangular of the same length.
This is just a restatement of the inequality of §\[appendix\] with $x_{i,k}=\nu_{\sigma_k(i)}^k$, for the appropriate permutations $\sigma_k$, where $1\leq i \leq l(\mu),1\leq k \leq s$.
\[sigma-rectang\] If the partitions $\mu,\nu$ are rectangular of the same length then $$\sigma_\mu(\nu)=0.$$
Direct calculation.
From the definition we get $$2n\Delta(\muhat)= \delta(\muhat)n^2+\sum_{i=1}^k\nrm_{\mu^i}(\mu^i)$$ and similarly $$2n\Delta(\nuhat^p)=\delta(\muhat)n_p^2 +
\sum_{i=1}^k\nrm_{\mu^i}(\nu^{i,p}), \qquad \qquad p=1,\ldots,s$$ hence $$2n\sum_{p=1}^s\Delta(\nuhat^p)=\delta(\muhat)\sum_{p=1}^sn_p^2 +
\sum_{i=1}^k\sum_{p=1}^s\nrm_{\mu^i}(\nu^{i,p}).$$ Since $n=\sum_{p=1}^sn_p$ and $\delta(\muhat)\geq 0$ we get from Lemma \[nrm-ineq\] that $$\sum_{p=1}^s\Delta(\nuhat^p)\leq\Delta(\muhat)$$ as claimed.
Clearly, equality cannot occur if $\delta(\muhat)>0$ and $s>1$. If $\delta(\muhat)=0$ and $s>1$ it follows from Lemmas \[nrm-ineq\], \[sigma-rectang\] and that $\Delta(\muhat)=\Delta(\nuhat^p)=0$ for $p=1,2,\ldots,s$. Now (ii) is a consequence of Proposition \[affine-descrip\].
Proof of Theorem \[connectedness\]
----------------------------------
### Step I {#step-1}
Let $$\label{calA-defn}
\calA_{\lambda\muhat}(q):=
q^{(1-g)|\lambda|}\left(q^{-n(\lambda)}
H_{\lambda}(q)\right)^{2g+k-2}
\prod_{i=1}^k\left\langle
h_{\mu^i}(\x_i),
s_\lambda(\x_i\y)\right\rangle,$$ so that by Lemma \[specializ\] $$\Omega\left(\sqrt{q},1/\sqrt{q}\right) = \sum_{\lambda, \muhat}
\calA_{\lambda\muhat}(q)\, m_\muhat.$$It is easy to verify that $\calA_{\lambda\muhat}$ is in $\Q(q)$.
For a non-zero rational function $\calA\in \Q(q)$ we let $v_q\left(\calA\right)\in \Z$ be its valuation at $q$. We w
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|
ntial of metric tensor
As I understand so far, the metric tensor of a Riemannian manifold is an $n \times n$ matrix in many specific examples. As such it could formally be the curl of some vector potential or just the derivative.
I wonder if this is indeed possible and if yes, if it is interesting or really just a formal coincidence.
A:
If I do not misunderstand your question your are asking if it is possible to define a more primitive object than the metric tensor, on a smooth manifold $M$, from which we can derive the metric tensor $g$, isn't it?. Such a more primitive object of course must be called potential. This approach recall me the so called Kaehler manifolds https://en.wikipedia.org/wiki/K%C3%A4hler_manifold
Kaehler manifolds form a subclass of Riemannian manifolds. For them there is indeed a concept of potential. Namely, around each point of a Kaehler manifold the metric tensor can be recovered from a function called potential. The recovering procedure is something like taking the Hessian of the potential.
The following post develops the idea of Hessian type metric on a Riemannian manifold: https://mathoverflow.net/questions/122308/when-a-riemannian-manifold-is-of-hessian-typ
Q:
Closing of TCP socket - What is different when connection is closed by debugger
I create a socket connection to a PLC:
IPEndPoint endPoint = new IPEndPoint(plcAddress, PORT);
m_socket = new Socket(AddressFamily.InterNetwork, SocketType.Stream, ProtocolType.Tcp);
m_socket.Connect(endPoint);
m_stream = new NetworkStream(m_socket);
m_writer = new StreamWriter(m_stream);
m_reader = new StreamReader(m_stream);
When I close my program or the user clicks on logout then I call this code:
if (m_reader != null) m_reader.Close();
if (m_writer != null) m_writer.Close();
if (m_stream != null) m_stream.Close();
if (m_socket != null)
{
m_socket.Shutdown(SocketShutdown.Both);
m_socket.Disconnect(false);
m_socket.Close();
m_socket.Dispose();
m_socket = null;
}
But the PLC does not realize that the connection was
| 410
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| 435
| 0.809832
|
github_plus_top10pct_by_avg
|
um state $| 0_{\text{in}}\rangle$ is determined by $\hat{a}_{\text{k}}| 0_{\text{in}}\rangle = 0$, where $\hat{a}_{\text{k}}$ is the initial annihilation operator for $\tau_i$. The relation between annihilation and creation operators for the initial and final states is given by the Bogoliubov transformation $$\begin{aligned}
\hat{b}_{{\bf k}} &=& B_{+}(k) \hat{a}_{{\bf k}} + B_{-}(k)^{*} \hat{a}_{-{\bf k}}^{\dagger} \ , \label{Bog1} \\
\hat{b}_{{\bf k}}^{\dagger} &=& B_{+}(k)^{*}\hat{a}_{{\bf k}}^{\dagger} + B_{-}(k) \hat{a}_{-{\bf k}} \label{Bog2} \end{aligned}$$ where $|B_{+}|^2-|B_{-}|^2=1$. Because we are working in the Heisenberg description the vacuum state does not change during the evolution. It results that $\hat{b}_{{\bf k}}| 0_{\text{in}}\rangle=B_{-}(k)^{*} \hat{a}_{-{\bf k}}^{\dagger}| 0_{\text{in}}\rangle $ is differ from zero when $B_{-}(k)^{*}$ is a nonzero function. This means that in the final state graviton field considered is no more in the vacuum state without particles. The number of produced particles in the final state is given by $$\bar{n}_{{\bf k}} = \frac{1}{2} \langle 0_{\text{in}} |\left[ \hat{b}_{{\bf k}}^{\dagger}\hat{b}_{{\bf k}}+
\hat{b}_{-{\bf k}}^{\dagger}\hat{b}_{-{\bf k}} \right]| 0_{\text{in}} \rangle =|B_{-}(k)|^2. \label{particles}$$ Using relations (\[sol11\])and (\[sol22\]) and the Bogoliubov transformation (\[Bog1\]) and (\[Bog2\]) we obtain $$\begin{aligned}
B_{-}(k)&=&
\frac{f_i(k,\tau_i)g_f(k,\tau_f) -g_i(k,\tau_i) f_f(k,\tau_f)}{f_f^*(k,\tau_f)g_f(k,\tau_f)-g_f^*(k,\tau_f)f_f(k,\tau_f)}
= i\left[ f_i(k,\tau_i)g_f(k,\tau_f) -g_i(k,\tau_i) f_f(k,\tau_f) \right] \ , \\
B_{+}(k)&=&
\frac{f_i(k,\tau_i)g_f^*(k,\tau_f) -g_i(k,\tau_i) f_f^*(k,\tau_f)}{f_f(k,\tau_f)g_f^*(k,\tau_f)-g_f(k,\tau_f)f_f^*(k,\tau_f)}
=-i \left[ f_i(k,\tau_i)g_f^*(k,\tau_f) -g_i(k,\tau_i) f_f^*(k,\tau_f) \right] \end{aligned}$$ where simplifications come from the Wronskian condition (\[Wronskian\]). In the calculations we set $\tau_{{i}}=\tau_1=-20$ and $\tau_{{f}}=\tau_2=-1$. Thes
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lements of $\cH$ share a common element, while Chvátal [@Chva] handled the case for which the maximal sets of $\cH$ can be partitioned into two sunflowers (see definition below), each with core size 1. In [@Chva] is also found the case for compressed $\cH$; Snevily [@Snev] strengthened this to $\cH$ being merely compressed with respect to some element (which also implies [@Scho]). Miklos [@Mikl] (and later Wang [@Wang]) verified the conjecture for $\cH$ satisfying $\i(\cH)\ge |\cH|/2$, and Stein [@Stei] verified it for those $\cH$ having $m$ maximal sets, every $m-1$ of which form a sunflower. Most recently, Borg [@Borg] solved a weighted generalization of [@Snev].\
In this paper, we prove Conjecture \[chvatal\] for $\cH\sse \binom{[n]}{\leq 3}$. We also prove a slightly weaker result, one that makes an additional assumption on the size of the maximum intersecting family in $\cH$. The advantage of this assumption is that the proof becomes significantly simpler, and the technique, which employs the famous Sunflower Lemma of Erdős and Rado, could potentially be extended for downsets containing larger subsets.
Main Results {#main-results .unnumbered}
------------
We verify Conjecture \[chvatal\] for all downsets consisting of sets of size at most $3$.
\[completechvatal\] Let $\cH\subseteq \binom{[n]}{\le 3}$ be a downset. Then $\cH$ is EKR. Moreover $\cH$ is strictly EKR, unless one of the following holds.
1. \[case:1\] There is a subset $K\in\binom{[n]}{4}$ such that
- $\binom{K}{3}\subseteq \cH$,
- for all $H\in\cH $, $H\subseteq K$ or $K\cap H=\emptyset$, and
- the largest star in $\cH$ has size $7$.
2. \[case:2\] There are subsets $K\in\binom{[n]}{3}$ and (possibly empty) $M\sse [n]\setminus K$, and a subfamily $\cZ=\binom{K}{2}\cup\{Z\in\binom{K\cup M}{3}\mid |Z\cap K|=2 \}\sse\cH$ such that either
- $K\notin\cH$ and the largest star in $\cH$ has size $|\cZ|=3|M|+3$, or
- $K\in\cH$ and the largest star in $\cH$ has size $|\cZ|+1=3|M|+4$.
We also prove the following w
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case, we define $\rho_{{\mbox{\boldmath $\alpha$}}}(s_i)$ to be $$\rho_{{\mbox{\boldmath $\alpha$}}}(s_i)\ :\ v_{P}
\longmapsto a_d v_{P}.$$ Here $a_d$ is the one defined by .
Suppose that a tableau $p_1$ of $\mathbb{T}({\mbox{\boldmath $\alpha$}})$ goes through $\widetilde{\emptyset}$, $\widetilde{{\mbox{\tiny\yng(1)}}}$ and $\widetilde{{\mbox{\tiny\yng(2)}}}$ at the 0-th, the 1-st and the 2-nd coordinates respectively, then for the standard vector $u_1$ which corresponds to $p_1$ we have $$\rho_{{\mbox{\boldmath $\alpha$}}}(s_1) u_1 = u_1.$$ For the standard vector $v_2$ which corresponds to $p_2$, a tableau of $\mathbb{T}({\mbox{\boldmath $\alpha$}})$ which goes through $\widetilde{\emptyset}$, $\widetilde{{\mbox{\tiny\yng(1)}}}$ and $\widetilde{{\mbox{\tiny\yng(1,1)}}}$ at the 0-th, the 1-st and the 2-nd coordinates respectively, we have $$\rho_{{\mbox{\boldmath $\alpha$}}}(s_1) u_2 = -u_2.$$
Let $\lambda^{(1)} = (3)$, $\lambda^{(2)} = (2,1)$ and $\lambda^{(3)} = (1,1,1)$ be partitions of 3. Suppose that tableaux $q_1$ and $q_2$ of $\mathbb{T}({\mbox{\boldmath $\alpha$}})$ both go through $\widetilde{{\mbox{\tiny\yng(1)}}}$ and $\widetilde{{\mbox{\tiny\yng(2)}}}$ at the 1-st and the 2-nd coordinates respectively, and tableaux $q_3$ and $q_4$ of $\mathbb{T}({\mbox{\boldmath $\alpha$}})$ both go through $\widetilde{{\mbox{\tiny\yng(1)}}}$ and $\widetilde{{\mbox{\tiny\yng(1,1)}}}$ at the 1-st and the 2-nd coordinates respectively. Further, the tableaux $q_1$, $q_2$, $q_3$ and $q_4$ go through $\widetilde{\lambda^{(1)}}$, $\widetilde{\lambda^{(2)}}$, $\widetilde{\lambda^{(2)}}$ and $\widetilde{\lambda^{(3)}}$ at the 3-rd coordinates respectively. Then we have $$\rho_{{\mbox{\boldmath $\alpha$}}}(s_2) (v_1\ v_2\ v_3\ v_4)
= (v_1\ v_2\ v_3\ v_4)
\begin{pmatrix}
1 & 0 & 0 & 0\\
0 & -1/2& 3/(4c) & 0\\
0 & c & 1/2 & 0\\
0 & 0 & 0 & -1
\end{pmatrix}.$$ Here $v_i$ is the standard vector which corresponds to $q_i$.
### Reductive Case {#reductive-case .unnumbered}
Consider the case a tableau $P$ is reductive at $i
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{f}}_0 &= (\psi_0, \phi_0) =
([{\mathit{f}}(\psi) \xi_0], [(\ell(\Delta(\lambda, \psi)))({\mathit{f}}(\psi) \xi_0)]([{\mathit{f}}(\psi) \xi_0])).\end{aligned}$$
Due to conjointness, $\psi_0 = {\mathit{f}}(\psi) \xi_0 = \phi_0 \xi_0$ throughout: $$\begin{aligned}
\lambda_0 &= \Delta(\lambda, \psi),\\
{\mathit{f}}_0 &= (\ell(\Delta(\lambda, \psi)))(\psi_0),\\
{\mathbf{f}}_0 &= (\psi_0, \phi_0) = (\psi_0, [(\ell(\Delta(\lambda, \psi)))(\psi_0)](\psi_0)])).\end{aligned}$$
Substituting $\lambda_0 = \Delta(\lambda, \psi)$ and ${\mathsf{a}}_0 = \ell(\lambda_0)$ into the last two formulas, $$\begin{aligned}
\lambda_0 &= \Delta(\lambda, \psi),\\
{\mathit{f}}_0 &= (\ell(\lambda_0)(\psi_0) = {\mathsf{a}}_0(\psi_0),\\
{\mathbf{f}}_0 &= (\psi_0, \phi_0) = (\psi_0, [(\ell(\lambda_0))(\psi_0)](\psi_0)])) = (\psi_0, [{\mathsf{a}}_0(\psi_0)](\psi_0)])).\end{aligned}$$
Finally, substituting ${\mathit{f}}_0 = {\mathsf{a}}_0(\psi_0)$ into the last two formulas, $$\begin{aligned}
\lambda_0 &= \Delta(\lambda, \psi),\\
{\mathit{f}}_0 &= {\mathit{f}}_0,\\
{\mathbf{f}}_0 &= (\psi_0, {\mathit{f}}_0(\psi_0)) = {\mathbf{f}}_0.\end{aligned}$$
Only the first of these is a [real]{} constraint; the others are identities.
### Solution set {#S:SOLUTION_SET}
A feasible set for an equation is the collection of values that satisfy the equation. Producing the solution for a system of constraining equations involves intersecting the individual feasible sets $Q_i$. The general solution set for the system of equations is $Q = \bigcap_i Q_i$.
The case of the converse automaton $\tilde{{\mathfrak{A}}}$ consists of three constraining equations (§\[S:CONSTRAINING\_EQUATIONS\]). First of these is $\lambda_0 = \Delta(\lambda, \psi)$. Let ${\mathbb{S}} = \Lambda \times {\mathscr{F}} \times (\;{\prod{\Psi}} \times {\prod{\Phi}})$ be a fully elaborated step space. In set-builder notation the feasible set is $Q_1 = \lbrace (\lambda, {\mathit{f}}, (\psi, \phi)) \in {\mathbb{S}} \colon \lambda_0 = \Delta(\lambda, \psi) \rbrace
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$ is of type II}\},\end{gathered}$$ which finishes the proof.
\[la9\] Let $F_j$ be the closed subgroup scheme of $\tilde{G}$ defined by the following equations:
- $m_{i,k}=0$ *if $i\neq k$*;
- $m_{i,i}=\mathrm{id}, z_i^{\ast}=0, m_{i,i}^{\ast}=0, m_{i,i}^{\ast\ast}=0$ *if $i\neq j$*;
- and for $m_{j,j}$, $$\left \{
\begin{array}{l l}
s_j=\mathrm{id~}, y_j=0, v_j=0, z_j=\pi z_j^{\ast} & \quad \textit{if $i$ is even and $L_i$ is \textit{of type} $\textit{I}^o$};\\
s_j=\mathrm{id~}, r_j=t_j=y_j=v_j=u_j=w_j=0, z_j=\pi z_j^{\ast} & \quad \textit{if $i$ is even and $L_i$ is \textit{of type} $\textit{I}^e$};\\
s_j=\mathrm{id~}, r_j=t_j=y_j=v_j=u_j=w_j=0 & \quad \textit{if $i$ is odd and $L_i$ is \textit{free of type I}}.\\
\end{array} \right.$$
Then $F_j$ 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 $1$, and has exactly two connected components.
A matrix form of an element $m$ of $F_j(R)$ for a $\kappa$-algebra $R$ is $$\begin{pmatrix} id&0& & \ldots& & &0\\ 0&\ddots&& & & &\\ & &id& & & & \\ \vdots & & &m_{j,j} & & &\vdots
\\ & & & & id & & \\ & & & & &\ddots &0 \\ 0& & &\ldots & &0 &id \end{pmatrix}$$
such that $$m_{j,j}=\left\{
\begin{array}{l l}
\begin{pmatrix}id&0\\0&1+2 z_j^{\ast} \end{pmatrix} & \quad \textit{if $j$ is even and $L_j$ is of type $I^o$};\\
\begin{pmatrix}id&0&0\\0&1+\pi x_j&2 z_j^{\ast}\\0&0&1 \end{pmatrix} & \quad \textit{if $j$ is even and $L_j$ is of type $I^e$};\\
\begin{pmatrix}id&0&0\\0&1+\pi x_j&0\\0&\pi z_j&1 \end{pmatrix} & \quad \textit{if $j$ is odd and $L_j$ is free of type $I$}.
\end{array}\right.$$ We emphasize that we have $2z_j^{\ast}$, not $\pi z_j$, when $i$ is even.
To prove the lemma, we consider the matrix equation $\sigma({}^tm)\cdot h\cdot m=h$. Recall that $h$, as an element of $\underline{H}(R)$, is as explained in Remark \[r33\].(2). Based on Equations (\[ea1\]) and (\[ea2\]), the diagonal $(i,i)$-blocks of $\sigma({}^tm)\cd
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mits a reduction to an $\I_b$-framing) of the normal bundle for the immersion $g$ of $N^{n-2k}$ into $\R^n$.
Therefore the characteristic number, given by the formula (8) in the case when the $\Z/2 \int \D_4$ framing over $L^{n-4k}$ is reduced to an $\I_4$-framing, coincides with the characteristic number, given by the formula (9). Proposition 2 is proved.
### Definition 7 {#definition-7 .unnumbered}
We shall say that a $\D_4$-framed immersion $(g,\Xi_N,\eta)$ admits a $\I_4$–structure (a cyclic structure), if for the double points manifold $L^{n-4k}$ of $g$ there exist mappings $\kappa_a:
L^{n-4k} \to K(\Z/2,1)$, $\mu_a: L^{n-4k} \to K(\Z/4,1)$ such that the characteristic number (8) coincides with Kervaire invariant, see Definition 2. $$$$
### Theorem 2 {#theorem-2 .unnumbered}
Let $(g, \Psi, \eta)$ be a $\D_4$-framed immersion, $g: N^{n-2k}
\looparrowright \R^n$, that represents a regular cobordism class in the image of the homomorphism $\delta: Imm^{sf}(n-k,k) \to
Imm^{\D_4}(n-2k,2k)$, $n-4k=62$, $n=2^l-2$, $l \ge 13$, and assume the conditions of the Theorem 1 hold, i.e. the residue class $\delta^{-1}(Imm^{sf}(n-k,k)$ (this class is defined modulo odd torsion) contains a skew-framed immersion that admits a retraction of order $62$.
Then in the $\D_4$-framed cobordism class $[(g, \Psi, \eta)] =
\delta[(f, \Xi, \kappa)] \in Imm^{\D_4}(n-2k,2k)$ there exists a $\D_4$-framed immersion that admits an $\I_4$–structure (a cyclic structure). $$$$
Proof of Theorem 2
==================
Let us formulate the Geometrical Control Principle for $\I_b$–controlled immersions.
Let us take an $\I_b$–controlled immersion (see Definition 4) $(g,\Xi_N,\eta;(P,Q),\kappa_{Q,1}, \kappa_{Q,2})$, where $g:N
\looparrowright \R^n$ is a $\D_4$-framed immersion, equipped with a control mapping over a polyhedron $i_P: P \subset \R^n$, $dim(P)=2k-1$; $Q
\subset P$ $dim(Q)=dim(P)-1$. The characteristic classes $\kappa_{Q,i} \in H^1(Q;\Z/2)$, $i=1,2$ coincide with characteristic classes $\kappa_{i,N_Q} \in N_Q^{n-2k-1}$ by me
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line{N},L)$ is integer-similar to $count(\underline{M},\underline{N},L)$
- $count(\underline{M},\underline{N},L)$ is not integer-similar to $count(\underline{M}+1,\underline{N},L)$
Note that the last one is a counterexample because $count(\underline{M}+1,\underline{N},L)$ has integer expressions on $[1,1]$ and $[1,2]$, while $count(\underline{M},\underline{N},L)$ does not have any subterms on these positions. $\hfill \square$
\[th:analysis1\] Let $N_b$ and $N_e$ be nodes in a moded SLD-tree for a moded query $Q$. Let $Q'$ be the moded atom obtained by applying to $Q$ all substitutions on input variables from $N_0$ to $N_b$. Every query in $Den(Q')$ is either non-terminating or terminates due to the evaluation of an integer condition if the following properties hold:
- $A_b^1$ is an ancestor of $A_e^1$
- no substitutions on input variables occur from $N_b$ to $N_e$
- $A_e^1$ is moded more general than $A_b^1$
- $A_e^1$ is integer-similar to $A_b^1$ $\hfill \square$
\[example:mmg\_adaption\] The path between nodes $N_5$ and $N_9$ in Figure \[fig:count\_to\] satisfies the conditions of Theorem \[th:analysis1\]. There are no substitutions on input variables from $N_0$ to $N_5$ and thus, every query in $Den(\leftarrow count\_to(\underline{N},L))$ is either non-terminating or fails due to the evaluation of an integer condition. Note that although $\leftarrow count\_to(0,L)$ has a succeeding derivation to $N_2$, its derivation to $N_9$ fails due to the integer condition $0 > \underline{N}$. $\hfill \square$
To verify the last property automatically, we strengthen Proposition \[prop:mmg\] to imply both the moded more general relation and the integer-similar to relation.
\[prop:mmg\_int\_ins\] Let $A$ and $B$ be moded atoms. Let $A_1$ and $B_1$ be renamings of these atoms such that they do not share variables. $A$ is moded more general than $B$ and $A$ is integer-similar to $B$, if $A_1$ and $B_1$ are unifiable with most general unifier $\lbrace V_1\setminus t_1,\ldots,
V_n \setminus t_n \rbrace$, such
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ar performance, except for the Spearman’s footrule. The proposed data-driven rank-breaking achieves a slightly worse correlation compared to other approaches. However, note that none of the algorithms are necessarily maximizing the Kendall correlation, and are not expected to be particularly good in this metric.
[ C[2.5cm]{} | C[1.5cm]{} C[2.cm]{} C[1.5cm]{} C[1.5cm]{} C[2cm]{} ]{} & MLE under PL & data-driven RB & GMM & Borda count & Spearman’s footrule\
$n = 500$, $\ell = 9$ & 0.306 & 0.291 & 0.315 & 0.315 & 0.159\
$n = 5000$, $\ell = 9$ & 0.309 & 0.309& 0.315 &0.315 & 0.079\
$n = 5000$, $\ell = 2$ & 0.199 &0.199 & 0.201&0.200 & 0.113\
$n = 5000$, $\ell = 5$ & 0.217& 0.200& 0.217& 0.295& 0.152\
We compare our algorithm with the GMM algorithm on two other real-world data-sets as well. We use jester data set [@GRG01] that consists of over $4.1$ million continuous ratings between $-10$ to $+10$ of $100$ jokes from $48,483$ users. The average number of jokes rated by an user is $72.6$ with minimum and maximum being $36$ and $100$ respectively. We convert continuous ratings into ordinal rankings. This data-set has been used by [@MP00; @PD05; @CMR07; @LM07] for rank aggregation and collaborative filtering.
Similar to the settings of sushi data experiments, we take the estimated PL weights of the 100 jokes over all the rankings as ground truth. Figure \[fig:jest\] shows comparative performance of the data-driven rank-breaking and the GMM for the two scenarios. We first fix $\ell = 10$ and vary $n$ to simulate random-$10$ separators scenario (left). We next take all the rankings $n = 73421$ and vary $\ell$ to simulate random-$\ell$ separators scenario (rights). Since sets have different sizes, while varying $\ell$ we use full breaking if the setsize is smaller than $\ell$. Each point is averaged over $100$ instances. The mean squared error is plotted for both algorithms.
![jester data set: The data-driven rank-breaking achieves smaller error compared to the state-of-the-art GMM approach. []{data-label="fig:jest
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thcal{S}_{\vdash E(x)}=\mathcal{S}_{E}$ associated to $\vdash E(x)$ by the function $f$ (Sec. 3.2). Yet, whenever $\pi _{S}$ is recursively defined on the whole $\psi _{A}^{Q}$, new subsets of states are introduced (as $\mathcal{S}_{\delta _{1}}\cup \mathcal{S}_{\delta _{2}}$) which do not necessarily belong to $\mathcal{L(S)}$. If an af $\delta $ is associated by $f$ with a subset that does not belong to $\mathcal{L(S)}$, no empirical procedure exists in QM which allows one to determine the justification value $\pi _{S}(\delta )$.
We are thus led to introduce the subset $\psi _{AD}^{Q}$ $\subset \psi
_{A}^{Q}$ of all *pragmatically decidable*, or *p-decidable*, afs of $\mathcal{L}_{Q}^{P}$. An af $\delta $ of $\mathcal{L}_{Q}^{P}$ is p-decidable iff an empirical procedure of proof exists which allows one to establish whether $\delta $ is justified or unjustified, whatever the state $S$ of $x$ may be.
Because of the remark above, the subset of all p-decidable afs of $\mathcal{L}_{Q}^{P}$ can be characterized as follows.
$\psi _{AD}^{Q}=\{\delta \in \psi _{A}^{Q}\mid $ $\mathcal{S}_{\delta }\in
\mathcal{L(S)}\}$.
Let us discuss some criteria for establishing whether a given af $\delta \in
$ $\psi _{A}^{Q}$ belongs to $\psi _{AD}^{Q}$.
C$_{1}$. *All elementary afs of* $\psi _{A}^{Q}$* belong to* $\psi _{AD}^{Q}$*.*
C$_{2}$. *If* $\delta \in $* *$\psi _{AD}^{Q}$*, then* $N\delta \in $* *$\psi _{AD}^{Q}$* *
Indeed, $S_{\delta }\in \mathcal{L(S)}$ implies $S_{\delta }^{\bot }\in
\mathcal{L(S)}$.
C$_{3}$. *If* $\delta _{1}$*,* $\delta _{2}\in $* *$\psi _{AD}^{Q}$*, then* $\delta _{1}K$* *$\delta _{2}\in $* *$\psi _{AD}^{Q}$
Indeed, $S_{\delta _{1}}\in \mathcal{L(S)}$ and $S_{\delta _{2}}\in
\mathcal{L(S)}$ imply $S_{\delta _{1}}\cap S_{\delta _{2}}\in \mathcal{L(S)}
$, since $S_{\delta _{1}}\cap S_{\delta _{2}}=S_{\delta _{1}}\Cap S_{\delta
_{2}}$ because of known properties of the lattice $(\mathcal{L(S)},\subset
) $ (Sec. 2.2).
C$_{4}$. *If* $\delta _{1}$*,* $\delta _{2}\in $* *$\psi _{AD}^{
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inequality, and follows from Lemma \[l:M\_is\_regular\] and Lemma \[l:eldan-matrix\].
\[l:eldan-matrix\] Let $A$, $B$ be positive definite matrices. Then $$\begin{aligned}
\tr\lrp{\lrp{\sqrt{A} - \sqrt{B}}^2} \leq \tr\lrp{(A-B)^2 A^{-1}}
\end{aligned}$$
[Defining $f$ and related inequalities]{} \[s:defining-q\]
In this section, we define the Lyapunov function $f$ which is central to the proof of our main results. Here, we give an overview of the various functions defined in this section:
1. $g(z): \Re^d \to \Re^+$: A smoothed version of $\lrn{z}_2$, with bounded derivatives up to third order.
2. $q(r): \Re^+ \to \Re^+$: A concave potential function, similar to the one defined in [@eberle2016reflection], which has bounded derivatives up to third order everywhere except at $r=0$.
3. $f(z) = q(g(z)): \Re^d \to \Re^+$, a concave function which upper and lower bounds $\lrn{z}_2$ within a constant factor, has bounded derivatives up to third order everywhere.
\[l:fproperties\] Let $\epsilon$ satisfy $\epsilon \leq \frac{\Rq}{\aq\Rq^2 + 1}$. We define the function $$\begin{aligned}
f(z) := q(g(z))
\end{aligned}$$ Where $q$ is as defined in Appendix \[ss:defining-q\], and $g$ is as defined in Lemma \[l:gproperties\] (with parameter $\epsilon$). Then
1. 1. $\nabla f(z) = q'(g(z)) \cdot \nabla g(z)$
2. For $\lrn{z}_2 \geq 2\epsilon$, $\nabla f(z) = q'(g(z)) \frac{z}{\|z\|_2}$
3. For all $z$, $\lrn{\nabla f(z)}_2 \leq 1$.
2. 1. $\nabla^2 f(z) = q''(g(z)) \nabla g(z) \nabla g(z)^T + q'(g(z)) \nabla^2 g(z)$
2. For $r\geq 2\epsilon$, $\nabla^2 f(z) = q''(g(z)) \frac{zz^T}{\|z\|_2^2} + q'(g(z)) \frac{1}{\|z\|_2} \lrp{I - \frac{zz^T}{\|z\|_2^2}}$
3. For all $z$, $\lrn{\nabla^2 f(z)}_2 \leq \frac{2}{\epsilon}$
4. For all $z,v$, $v^T \nabla^2 f(z) v \leq\frac{q'(g(z))}{\|z\|_2}$
3. For any $z$, $\lrn{\nabla^3 f(z)}_2 \leq \frac{9}{\epsilon^2}$
4. For any $z$, $f(z) \in \lrb{\frac{1}{2}\exp\lrp{-\frac{7\aq\Rq^2}{3}} g(\|z\|_2), g(\|z\|_2)} \in
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[Figure 2](#fig2-0192513X17710773){ref-type="fig"}, both paths are significant. First, as posited in Hypothesis 2, transnational parents report to be less happy than nontransnational parents. Second, although transnational parenting is significantly associated with family-to-work conflict as postulated in Hypothesis 1, it is not in the expected direction. Instead of transnational parents reporting family-to-work conflict less often they report family-to-work conflict more often. And this is a significant difference.
![Mediation model job instability with binary mediators.\
*Note*. Indirect effects (a1 \* b1 and a2 \* b2); direct effect (c'); total effect \[(a1 \* b1) + (a2 \* b2) + c'\]; percentage of total effect mediated = indirect effects/total effect (20%); Pseudo *R*^2^ = .20; Unstandardized ordinary least squares coefficients presented, paths a1 and a2 are unstandardized logit coefficients.\
Standard errors in parentheses.\
*Source*. TCRAf-Eu Angolan parent survey, The Netherlands 2010-2011.\
\**p* \< .05. \*\**p* \< .01. \*\*\**p* \< .001 (one-tailed test).](10.1177_0192513X17710773-fig2){#fig2-0192513X17710773}
######
Test of Mediation With Bootstrapped Results for Job Instability.
Mediator Β coefficient Bias-corrected CI
------------------------------------- --------------- ------------------- ------
Indirect effect
Happiness 0.07 0.01 0.15
Conflict −0.02 −0.08 0.03
Total 0.05 −0.03 0.13
Direct effect 0.18 0.05 0.33
Total effect 0.23 0.09 0.38
Proportion of total effect mediated 0.20
*Note*. The way to interpret the confidence intervals (CIs) is
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i, i-1}+\delta_{i+1}v_{i+1}\cdot {}^tm_{i, i+1} = \pi m_{i,i}^{\ast\ast}$$ such that $ m_{i,i}^{\ast\ast} \in M_{1\times n_i}(B\otimes_AR)$. This equation is considered in $B\otimes_AR$ and $\pi$ stands for $\pi\otimes 1\in B\otimes_AR$. Here, $v_{i-1}$ (resp. $v_{i+1}$)$=(0,\cdots, 0, 1)$ of size $1\times n_{i-1}$ (resp. $1\times n_{i+1}$).\
To simplify notation, each element $$((m_{i,j})_{i\neq j}, (m_{i,i})_{\textit{$L_i$ of type II, or bound of type I with i odd}},
(s_i, y_i, v_i, z_i)_{\textit{$L_i$ of type $I^o$ with i even}},$$ $$(s_i, v_i, z_i, r_i, t_i, y_i, x_i, u_i, w_i)_{\textit{$L_i$ of type $I^e$ with i even, or free of type I with i odd}},$$ $$(z_i^{\ast})_{\textit{$L_i$ of type I with i even}}, (m_{i,i}^{\ast}, m_{i,i}^{\ast\ast})_{\textit{$L_i$ bound of type I with i odd}} )$$ of $\underline{M}(R)$, for a $\kappa$-algebra $R$, is denoted by $(m_{i,j}, s_i \cdots w_i)$.\
In the next section, we need a description of an element of $\underline{M}(R)$ and its multiplication for a $\kappa$-algebra $R$. In order to prepare for this, we describe the multiplication explicitly only for a $\kappa$-algebra $R$. To multiply $(m_{i,j}, s_i\cdots w_i)$ and $(m_{i,j}', s_i'\cdots w_i')$, we form the matrices $m=\begin{pmatrix} \pi^{max\{0,j-i\}}m_{i,j} \end{pmatrix}$ and $m'=\begin{pmatrix} \pi^{max\{0,j-i\}}m_{i,j}' \end{pmatrix}$ with $s_i\cdots w_i$ and $s_i'\cdots w_i'$ and write the formal matrix product $\begin{pmatrix} \pi^{max\{0,j-i\}}m_{i,j} \end{pmatrix}\cdot \begin{pmatrix} \pi^{max\{0,j-i\}}m_{i,j}' \end{pmatrix}=\begin{pmatrix} \pi^{max\{0,j-i\}}\tilde{m}_{i,j}'' \end{pmatrix}$ with $$\tilde{m}_{i,i}''=\left\{
\begin{array}{l l}
\begin{pmatrix} \tilde{s}_i''&\pi \tilde{y}_i''\\ \pi \tilde{v}_i''&1+\pi \tilde{z}_i'' \end{pmatrix} & \quad \textit{if $i$ is even and $L_i$ is \textit{of type $I^o$}};\\
\begin{pmatrix} \tilde{s}_i''&\tilde{r}_i''&\pi \tilde{t}_i''\\ \pi \tilde{y}_i''&1+\pi \tilde{x}_i''&\pi \tilde{z}_i''\\ \tilde{v}_i''&\tilde{u}_i''&1+\pi \tilde{w}_i'' \end{pmatrix} & \q
| 422
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| 0.772697
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|
0.678 65.4 66.7 0.036
A β~**1**\ --\ **42**~/A β~**1**\ --\ **40**~ \<0.095 85.2 79.3 0.857 79.3 85.2 0.001
t-Tau/A β~**1**\ --\ **42**~ \>0.298 77.8 82.8 0.853 80.8 80.0 0.004
p-Tau ^181^ /Aβ~1\ --42~ Combination \>0.059 81.5 86.2 0.891 84.6 83.3 0.001
A β~1\ --42~+ p-Tau ^181^ 92.6 89.7 0.935 89.3 92.9
p-Tau ^181^ /Ap~1\ --42~ + t-Tau 92.6 86.2 0.930 81.5 93.1
Aβ, beta-amyloid protein; AD, Alzheimer\'s disease; aMCI, amnestic mild cognitive impairment; AUC, area under the curve; CSF, cerebrospinal fluid; NPV, negative predictive value; PPV, positive predictive value; p-Tau^181^, tau protein phosphorylated at threonine 181; SE, sensitivity; SP, specificity; t-Tau, total tau protein.
######
Diagnostic cutoff values in differentiating patients with preclinical AD (*n* = 14), prodromal AD (*n* = 27), and amyloid-positive AD dementia (*n* = 31) from normal amyloid-negative subjects (*n* = 73)
Preclinical AD versus normal Prodromal AD versus normal AD dementia versus normal
---------------------------------- ------------------------------ ---------------------------- --------------------------- ------- --------- ------ ------ ------- --------- ------ ------- -------
CSF Aß~**1**\ --\ **42**~, pg/mL \<833.0 92.9 86.3 0.947 \<752.0 88.9 93.2 0.961 \<618.4 80.6 100.0 0.971
CSF t-Tau, pg/mL \>253.5 71.4 65.8
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26.0 ± 6.0 29.7 ± 5.3^§^ 24.8 ± 5.9 24.1 ± 6.5^†^
Trunk fat% 13.4 ± 3.1 15.3 ± 2.7^§^ 12.8 ± 3.0 12.4 ± 3.4^†^
Muscle% 68.2 ± 5.9 64.6 ± 5.2^§^ 69.4 ± 5.9 70.2 ± 6.4^†^
Leg-muscle% 12.6 ± 1.1 11.8 ± 1.0^§^ 12.8 ± 1.1 12.8 ± 1.2^†^
Trunk muscle% 33.9 ± 2.9 32.3 ± 2.5^§^ 34.6 ± 2.9 35.1 ± 3.5^†^
ASM index 8.24 ± 0.99 8.17 ± 1.04 8.29 ± 1.28 8.13 ± 1.24
Data were expressed as mean ± standard deviation. eGFR, estimated glomerular filtration rate; HbA1c, glycosylated hemoglobin; HDL, high-density lipoprotein; LDL, low-density lipoprotein; TG, triglyceride; BMI, body mass index; ASM index, appendicular skeletal muscle mass index.
\* p \< 0.001 elderly vs. non-elderly. ‡ p \< 0.001 non-low protein vs. low protein group. † p \< 0.05 elderly vs. non-elderly. § p \< 0.05 non-low protein vs. low protein group.
######
Comparisons of characteristics and body compositions of non-elderly patients in different protein intake groups at baseline and 1-year follow-up.
Non-low protein group, n = 43 Low protein group, n = 13
--------------------------- ------------------------------- --------------------------- -------------- --------------
BMI (kg/m^2^) 23.9 ± 3.9 24.0 ±3.7 23.4 ± 4.4 23.3 ± 4.6
waist circumference (cm) 83.3 ± 12.1 81.6 ± 9.4 83.6 ± 15.7 85.1 ± 15.8
eGFR (mL/min/1.73m^2^) 24.5 ±10.2 21.9 ± 11.3^\*^ 19.5 ± 11.1 19.3 ± 14.0
Serum albumin (mg/dL) 4.3 ± 0.3 4.5 ± 0.4 4.5 ± 0.3 4.4 ± 0.3
Hemoglobin level ( g/dL) 11.6 ± 2.1 12.7 ± 5.8 10.4 ± 1.7 10.9 ± 2.3
Hb
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. . In , , & (Eds.), [**]{} (pp. ). : volume . (). . , [**]{}, . , & (). In , & (Eds.), [**]{} (pp. ). , & (). . , [ ** ]{}, . , , , , , , , , , & (). . , [ ** ]{}, . , , , , & (). . , [**]{}, . , & (). . In [**]{} (pp. ). volume . , & (). . , [ ** ]{}, . (). . , [ ** ]{}, . , , & (). . , [**]{}, . , & (). . , [**]{}, . , & (). . ( ed.). : . (). . , [ ** ]{}, . , & (). . , [ ** ]{}, . , , & (). . , [ ** ]{}, . , , & (). . , [ ** ]{}, . , & (). . , [ ** ]{}, . , & (). . , [ ** ]{}, . , , & (). . , [**]{}, . , , & (). . , [ ** ]{}, . , , & (). . , [ ** ]{}, . (). , [**]{}, . , , , , & (). . In , , & (Eds.), [**]{} (pp. ). : volume . (). . In [**]{} (pp. ). . (). . , [ ** ]{}, . , & (). . , [ ** ]{}, . , , & (). . , [ ** ]{}, . , & (). . , [ ** ]{}, . , , , & (). . , [ ** ]{}, . , , & (). . , [**]{}, . , & (). . , [ ** ]{}, . , , & (). . , [ ** ]{}, . (). . , [**]{}, . , , & (). . , [ ** ]{}, . , & (). . , [ ** ]{}, . , & (). . In , , & (Eds.), [**]{} (pp. ). : volume . , & (). . , [ ** ]{}, . , , , , & (). . , [ ** ]{}, . , , & (). . , [**]{}, . (). . In , & (Eds.), [**]{} (pp. ). . , , & (). . , [ ** ]{}, . , , & (). . , [**]{}, . , & (). . , [ ** ]{}, . , , , , , , & (). . , [ ** ]{}, . (). . , [**]{}.
---
abstract: 'A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively applies binary splits to divide the set of classes into two subsets, and trains a binary classifier for each split. Many methods have been proposed to perform this split, each with various advantages and disadvantages. In this paper, we present a simple, general method for improving the predictive performance of nested dichotomies produced by any subset selection techniques that employ randomness to construct the subsets. We provide a theoretical expectation for performance improvements, as well as empirical results showing that our method improves the root mean squared error of nested dichotomies, regardless of whether they are employed as an individual
| 425
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varepsilon),(r_1,r_2),(r_1r_5,r_2r_6),(r_1r_6,r_2r_5),(r_2,r_1), (r_2r_7,r_1r_8),(r_2r_7r_9,r_1r_8r_{10})\}.$$ (See figures \[figure\_stratST\]-\[figure\_stratSR\]).\
Subsequently: $$\begin{aligned}
S_1 & := &\{(\varepsilon,\varepsilon),(r_5,r_6),(r_6,r_5)\}\\
S_2 & := &\{(\varepsilon,\varepsilon)\}\\
S_3 & := &\{ (\varepsilon,\varepsilon),(r_7,r_8),(r_7r_9,r_8r_{10})\}\\
S_4 & := &\{ (\varepsilon,\varepsilon),(r_9,r_{10})\}\\
S_5 & := &\{ (\varepsilon,\varepsilon)\}\\
S_6 & := & {{\rm INDSTR}}(S_2,S_5)= S_2^{-1} \circ S_5= \{ (\varepsilon,\varepsilon)\}\end{aligned}$$
(90,90) (DE)(0,30)[$(D,E)$]{} (ED)(60,30)[$(E,D)$]{} (CC)(30,60)[$(C,C)$]{} (AB)(60,90)[$(A,B)$]{} (APBP)(90,60)[$(A',B')$]{} (ASBS)(90,30)[$(A'',B'')$]{} (DEBOT)(90,0)[$(D,E)$]{} (AB,CC)[$(y,x)$]{} (CC,DE)[$(x,y)$]{} (CC,ED)[$(y,x)$]{} (AB,APBP)[$(x,y)$]{} (APBP,ASBS)[$(x,x)$]{} (ASBS,DEBOT)[$(x,x)$]{}
(90,90) (DE)(0,30)[$(D,E)$]{} (ED)(60,30)[$(E,D)$]{} (CC)(30,60)[$(C,C)$]{} (AB)(60,90)[$(A,B)$]{} (APBP)(90,60)[$(A',B')$]{} (ASBS)(90,30)[$(A'',B'')$]{} (DEBOT)(90,0)[$(D,E)$]{} (AB,CC)[$(r_1,r_3)$]{} (CC,DE)[$(r_5,r_6)$]{} (CC,ED)[$(r_6,r_5)$]{} (AB,APBP)[$(r_2,r_4)$]{} (APBP,ASBS)[$(r_7,r_8)$]{} (ASBS,DEBOT)[$(r_9,r_{10})$]{}
$S$ is a prefix of D-strategy w.r.t. $(A(\bot),B(\bot))$. \[S\_is\_strategy\]
Let us check that $S$ fulfills the critetium given by Lemma \[L-characterisation\_PDstrategies\]. Here $n=3$. Point (1) is easily checked.\
Let $\beta \in ({\cal R}\times{\cal R})^{*}$ such that $\beta \backslash S = \{(\varepsilon,\varepsilon)\}$. Either (${{\rm NEXT}}((A,B),\beta)\in \{(E,D),(D,E)\}$, while $D \not{\!\!\sim_1} E$) or $|\beta| = 3$. Hence Point (2) holds.
For proving the equivalences of the members of the basis we shall use the “trivial” prefixes of strategies, consisting of 2-tuples of identical rules on both sides: $$\begin{aligned}
{\rm Id_{C,1}} & := & \{(\varepsilon,\varepsilon), (r_5,r_5),(r_6,r_6)\})\\
{\rm Id_{D,2}} & := & \{(\varepsilon,\varepsilon), (r_{11},r_{11}), (r_{11}r_{14},r_{11}r_{14})\})\\
{\rm Id_{E,2
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0.5567 0.3044 0.043\*
C78 0.8173 (3) 0.6276 (4) 0.2097 (2) 0.0303 (12)
H78A 0.7921 0.6525 0.1773 0.045\*
H78B 0.8199 0.5581 0.2078 0.045\*
H78C 0.8583 0.6550 0.2177 0.045\*
O2 0.9365 (2) 0.6952 (4) 0.83007 (18) 0.0508 (13)
N2 0.8745 (2) 0.6405 (3) 0.75669 (18) 0.0266 (10)
C79 0.8866 (3) 0.6654 (4) 0.8036 (2) 0.0352 (14)
H79 0.8546 0.6604 0.8186 0.042\*
C80 0.9225 (3) 0.6454 (5) 0.7310 (3) 0.0405 (15)
H80A 0.9587 0.6772 0.7530 0.061\*
H80B 0.9072 0.6815 0.6997 0.061\*
H80C 0.9334 0.5808 0.7235 0.061\*
C81 0.8168 (3) 0.6078 (5) 0.7255 (3) 0.0424 (16)
H81A 0.7874 0.6068 0.7448 0.064\*
H81B 0.8213 0.5434 0.7135 0.064\*
H81C 0.8021 0.6507 0.6966 0.064\*
------ --------------- --------------- --------------- -------------------- --
Atomic displacement parameters (Å^2^) {#tablewrapadps}
=====================================
----- -------------- -------------- -------------- --------------- -------------- --------------
*U*^11^ *U*^22^ *U*^33^ *U*^12^ *U*^13^ *U*^23^
W1 0.00959 (9) 0.01051 (8) 0.00897 (8) 0.00050 (6) 0.00322 (7) 0.00076 (6)
W2 0.01041 (9) 0.02124 (10) 0.00953 (9) −0.00198 (7) 0.00248 (7) 0.00324 (7)
Ag1 0.01769 (18) 0.01876 (17) 0.01144 (16) 0.00004 (13) 0.00515 (13) 0.00419 (13)
Ag2 0.00979 (16) 0.01623 (16) 0.01571 (17) 0.00196 (12)
| 427
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ed haplotype frequency analysis for 2-SNP, 3-SNP, and 4-SNP windows showing the most significant results among all possible sliding windows
**HCV-1**
--------------------------------------------------------- ------------- ------------- -------- --------------
rs10907185-rs6603797 (S1-S2)
OMNIBUS \- \- \- 0.0208\*
AC 0.2 0.1158 1.91 0.0078\*
rs6603797-rs4648727-rs12126768 (S2-S3-S4)
OMNIBUS \- \- \- 0.054
CAT 0.1157 0.0673 1.81 0.0524
rs10907185-rs6603797-rs4648727-rs12126768 (S1-S2-S3-S4)
OMNIBUS \- \- \- 0.0397\*
ACAT 0.1163 0.0615 2.01 0.0261\*
**HCV-2**
**Haplotypes** **RVR (+)** **RVR (−)** **OR** ***P*value**
rs4648727-rs12126768 (S3-S4)
OMNIBUS \- \- \- 0.0546
AT 0.1139 0.0278 4.50 0.0265\*
rs6603797-rs4648727-rs12126768 (S2-S3-S4)
OMNIBUS \- \- \- 0.1099
CAT
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|
R}}$ a root system of type ${\mathcal{C}}$. We say that ${\mathcal{R}}$ is *finite*, if $R^a$ is finite for all $a\in A$. The following lemmata are well-known for traditional root systems.
[@p-CH08 Lemma 2.11] Let ${\mathcal{C}}$ be a connected Cartan scheme and ${\mathcal{R}}$ a root system of type ${\mathcal{C}}$. The following are equivalent.
1. ${\mathcal{R}}$ is finite.
2. $R^a$ is finite for at least one $a\in A$.
3. ${\mathcal{W}}({\mathcal{R}})$ is finite.
\[le:Rfincond\]
[@a-HeckYam08 Cor.5] Let ${\mathcal{C}}$ be a connected Cartan scheme and ${\mathcal{R}}$ a finite root system of type ${\mathcal{C}}$. Then for all $a\in A$ there exist unique elements $b\in A$ and $w\in {\mathrm{Hom}}(b,a)$ such that $|R^a_+|=\ell (w)\ge \ell (w')$ for all $w'\in {\mathrm{Hom}}(b',a')$, $a',b'\in A$. \[le:longestw\]
The Weyl groupoid of a bicharacter {#ssec:Weylgroupoid}
----------------------------------
Let $I$ be a non-empty finite set. Recall that a bicharacter on ${\mathbb{Z}}^I$ with values in ${{\Bbbk }^\times }$ is a map $\chi :{\mathbb{Z}}^I\times {\mathbb{Z}}^I\to {{\Bbbk }^\times }$ such that $$\begin{aligned}
\chi (a+b,c)=&\chi (a,c)\chi (b,c),&
\chi (c,a+b)=&\chi (c,a)\chi (c,b)
\label{eq:bichar}\end{aligned}$$ for all $a,b,c\in {\mathbb{Z}}^I$. Then $\chi (0,a)=\chi (a,0)=1$ for all $a\in {\mathbb{Z}}^I$. Let ${\mathcal{X}}$ be the set of bicharacters on ${\mathbb{Z}}^I$. If $\chi \in {\mathcal{X}}$, then $$\begin{aligned}
\label{eq:chiop}
\chi {^\mathrm{op}}: & {\mathbb{Z}}^I\times {\mathbb{Z}}^I\to {{\Bbbk }^\times },&
\chi {^\mathrm{op}}(a,b)=&\,\chi (b,a),\\
\label{eq:chiinv}
\chi ^{-1} : & {\mathbb{Z}}^I\times {\mathbb{Z}}^I\to {{\Bbbk }^\times },&
\chi ^{-1}(a,b)=&\,\chi (a,b)^{-1},
\intertext{and for all $w\in {\mathrm{Aut}}_{\mathbb{Z}}({\mathbb{Z}}^I)$ the map}
\label{eq:w*chi}
w^*\chi : & {\mathbb{Z}}^I\times {\mathbb{Z}}^I\to {{\Bbbk }^\times },&
w^*\chi (a,b)=&\,\chi (w^{-1}(a),w^{-1}(b)),\end{aligned}$$ are bicharacters on ${\mathbb{Z}}^I$. The equat
| 429
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}-\sqrt{2{\sigma^2_{R_\psi}}}\mathrm{erf}^{-1}\left(1-2\epsilon\right),$$ respectively, where $F_{R_\psi}^{-1}(x)$ denotes the approximated inverse cdf of $R_{\psi}$.
Substituting and into completes the proof.
Proof of Corollary \[Cor:outGlsngrO\] {#App:proofCor:outGlsngrO}
=====================================
As $\Psi\rightarrow\infty$, we have $1-2\epsilon^{\frac{1}{\Psi}}\rightarrow-1$. From the tail region approximation for the inverse error function, we note that $$\label{eq:appinverflargexneg}
\mathrm{erf}^{-1}(x)= -\sqrt{-\ln\left(1-x^2\right)} \quad \text{as} \quad x\rightarrow -1.$$ Based on and , as $\Psi\rightarrow\infty$, $G_{R^{\mathrm{out}}}(\Psi)$ is asymptotically equivalent to $$\begin{aligned}
&G_{R^{\mathrm{out}}}(\Psi)\sim
\frac{{\bar{R}_{\psi}}}{{\bar{R}_{\psi}}-\sqrt{2{\sigma^2_{R_\psi}}}\mathrm{erf}^{-1}\left(1-2\epsilon\right)}+\notag\\
&
\frac{\sqrt{2{\sigma^2_{R_\psi}}}}{{\bar{R}_{\psi}}-\sqrt{2{\sigma^2_{R_\psi}}}\mathrm{erf}^{-1}\left(1-2\epsilon\right)}\sqrt{-\ln\left(1-\left(1-2{\epsilon}^{\frac{1}{\Psi}}\right)^2\right)}
\notag\\
&\sim \frac{\sqrt{2{\sigma^2_{R_\psi}}}}{{\bar{R}_{\psi}}-\sqrt{2{\sigma^2_{R_\psi}}}\mathrm{erf}^{-1}\left(1-2\epsilon\right)}\sqrt{-\ln\left(1-{\epsilon}^{\frac{1}{\Psi}}\right)}
\notag\\
& \stackrel{(a)}{\sim}\frac{\sqrt{2{\sigma^2_{R_\psi}}}}{{\bar{R}_{\psi}}-\sqrt{2{\sigma^2_{R_\psi}}}\mathrm{erf}^{-1}\left(1-2\epsilon\right)}\sqrt{\ln(\Psi)},\end{aligned}$$ where $(a)$ is derived by analyzing the Taylor series of $\sqrt{-\ln\left(1-{\epsilon}^{\frac{1}{\Psi}}\right)}$ at $\Psi\rightarrow\infty$. This completes the proof.
[10]{} \[1\][\#1]{} url@samestyle \[2\][\#2]{} \[2\][[l@\#1=l@\#1\#2]{}]{}
B. He and H. Jafarkhani, “Millimeter wave communications with reconfigurable antennas,” in *Proc. IEEE ICC*, May 2018. \[Online\]. Available: <http://arxiv.org/abs/1806.00051>
T. S. Rappaport, R. W. Heath, R. C. Daniels, and J. N. Murdock, *Millimeter Wave Wireless Communications*.1em plus 0.5em minus 0.4emPrentice Hall, 2014.
Z. Pi and
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he teams participating in this competition were provided with two datasets for training and testing phases, respectively. After training their designed ML frameworks, the teams were allowed to produce a prediction label list for the test samples, and to submit those predictions to the competition platform under a limited number of rights so as to check the accuracy of their models. In this way, they could change their learning algorithm or make some modifications on it like parameter tuning or utilizing some preprocessing techniques.
At the end of the competition, the teams were requested to propose their default ML frameworks so that they could be evaluated on a testing set in terms of accuracy, sensitivity, and specificity. Based on each evaluation metric, the teams were ranked. Ultimately, the overall competition rank was defined by the summation of the three metric ranks of each team.
Analysis of Machine Learning Methods in the Brain Network Classification Kaggle Competition
-------------------------------------------------------------------------------------------
In this section, we provide an overview of the machine learning pipelines that have been proposed by the top 20 leading teams in the competition. All methods laying the foundation of those pipelines are examined under three major ML categories: (1) preprocessing techniques, (2) dimensionality reduction methods, and, (3) learning models (Figure \[fig:trend\]).
![Trends of machine learning methods for brain network classification in Kaggle competition. The thickness of the link between two objects indicates the relative quantity of usage from left to right.[]{data-label="fig:trend"}](Fig1.png){width="100.00000%"}
### Preprocessing Techniques
Preprocessing techniques are the algorithms on the front line of a machine learning pipeline composed of several steps such as data preparation, dimension reduction, model training, validation, and testing. The main reason why they are commonly adopted is that they can improve poor-quality data in some asp
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|
--------------------------------------------------
Coming back to the general language $\mathcal{L}^{P}$, we remind that a notion of pragmatic validity (invalidity) is introduced in it by means of the following definition.
*Let* $\delta \in \psi _{A}$*. Then,* $\delta $* is* pragmatically valid*, or* p-valid* (*pragmatically invalid*, or* p-invalid*) iff for every* $\sigma \in \Sigma $* and* $\pi _{\sigma }\in \Pi _{\sigma }$*,* $\pi _{\sigma }(\delta
)=J$* (*$\pi _{\sigma }(\delta )=U$*).*
By using the notions of justification in $\mathcal{L}_{Q}^{P}$, one can translate the notion of p-validity (p-invalidity) within $\mathcal{L}_{Q}^{P} $ as follows.
*Let* $\delta \in \psi _{A}^{Q}$*. Then,* $\delta $*is p-valid (p-invalid) iff, for every* $S\in S$*,* $\pi _{S}(\delta
)=J$* (*$\pi _{S}(\delta )=U$*).*
The notion of p-validity (p-invalidity) can then be characterized as follows.
*Let* $\delta \in \psi _{A}^{Q}$*. Then,* $\delta $*is p-valid (p-invalid) iff* $S_{\delta }=S$* (*$S_{\delta
}=\emptyset $*).*
The set of all p-valid afs plays in $\mathcal{L}_{Q}^{P}$ a role similar to the role of tautologies in classical logic, and some afs in it can be selected as axioms if one tries to construct a p-correct and p-complete calculus for $\mathcal{L}_{Q}^{P}$. We will not deal, however, with this topic in the present paper.
Furthermore, let us observe that a binary relation can be introduced in the general language $\mathcal{L}^{P}$ by means of the following definition.
*For every* $\delta _{1}$*,* $\delta _{2}\in \psi _{A}$*,* $\delta _{1}\prec $* *$\delta _{2}$* iff a proof exists that* $\delta _{2}$* is justified whenever* $\delta _{1}$*is justified (equivalently,* $\delta _{1}\prec \delta _{2}$* iff* $\delta _{1}C\delta _{2}$* is justified*).
The set-theoretical pragmatics introduced in Sec. 3.2 allows one to translate the above definition in $\mathcal{L}_{Q}^{P}$ as follows.
*For every* $\delta _{1}$*,* $\delta _{2}\in \psi _{A}^{Q}$*,* $\delta _{1}\prec $* *$\delta _{2}$* iff for every* $S\
| 432
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| 0.770362
|
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|
pes that the program can execute along with the probabilities they will occur. One can easily envision its extension to smaller program units.
### Extended operational profile {#S:EXTENDED_OP_PROFILE}
We shall extend run types into steps, the elementary quantum of automata. This detaches the operational profile concept from notions such as run types which are part of human understanding rather than algorithmic structure (however, the idea pops up elsewhere). Despite appearances, this extension is not so large – the only addition is a method for counting step events.
### Counting {#S:COUNTING}
Let $\{{\mathit{s}}_n\}$ be a walk (infinite sequence of steps) and let $Z$ be an arbitrary reference set of steps (members of step space ${\mathbb{S}} = \Lambda \times {\mathscr{F}} \times {\mathbf{F}}$). Simply summarized, $N_Z(\{{\mathit{s}}_n\},k)$ denotes the number of occurrences of any member of $Z$ before or at the ${{k}^{\text{th}}}$ automaton step.
Details follow for those interested. When the ${{i}^{\text{th}}}$ step of the walk is a member of $Z$ (${{\mathit{s}}_i} \in Z$), then $\{{\mathit{s}}_n\}$ is said to *arrive* at $i$.
\[D:ARRIVAL\] An *arrival* function is a sequence $\varphi \colon \{1,2,\cdots\} \to \{n_1,n_2,\cdots\}$ mapping each arrival, as identified by its ordinal occurrence number $i$, into its frame sequence number $n_i$.
The arrival function assumes the natural order, that is, $i < j$ implies $n_i < n_j$.
A related function counts *how many* arrivals occur within a given interval:
\[D:COUNTING\] Suppose $\{{\mathit{s}}_n\}$ is a walk and $Z$ is a set of steps. Let $\varphi$ be an arrival function. The *counting* function $N_Z \colon {\mathbb{S}}^{{\mathbb{N}}} \times {\mathbb{Z}^+}\to {\mathbb{Z}^+}$ induced by $\varphi$ is $$N_Z(\{{\mathit{s}}_n\}, k) = \max_{\varphi(i) \leq k} \: i ,$$ and for completeness set $\max(\varnothing) = 0$.
### Normal operations {#S:NORMAL_OPERATIONS}
The idea behind [normal operations]{} is a long program run following a software usage pattern. Inter
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| 2,656
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| 566
| 640
| 0.803516
|
github_plus_top10pct_by_avg
|
not, while the continuous and residual spectra together comprise the boundary spectrum. Thus a $\lambda$ can be both in the point and the continuous or residual spectra which need not be disjoint. The continuous and residual spectra are included in the boundary spectrum which may also contain parts of the point spectrum.
Function $\textrm{Int}(\sigma(f))$ $\textrm{Bdy}(\sigma(f))$ $P\sigma(f)$ $C\sigma(f)$ $R\sigma(f)$
------------------ --------------------------- --------------------------- -------------- -------------- --------------
$f_{\textrm{a}}$ $(0,1)$ $\{0,1\}$ $[0,1]$ $\{1\}$ $\{0\}$
$f_{\textrm{b}}$ $(0,1)$ $\{0,1\}$ $[0,1]$ $\{1\}$ $\{0\}$
$f_{\textrm{c}}$ $(0,\infty)$ $\{0\}$ $[0,\infty)$ $\{0\}$ $\emptyset$
$f_{\textrm{d}}$ $(0,2)$ $\{0,2\}$ $(0,2)$ $\{0,2\}$ $\emptyset$
$f_{\textrm{e}}$ $(0,1)$ $\{0,1\}$ $(0,1)$ $\{1\}$ $\{0\}$
$f_{\textrm{f}}$ $(0,1)$ $\{0,1\}$ $(0,1)$ $\{0,1\}$ $\emptyset$
: \[Table: Appel\_multi\][Nonlinear spectra of functions of Fig. \[Fig: Appel\]. Compare the present point spectra with the usual linear spectra of Table \[Table: Appel\_spectra\].]{}
**Example 6.1.** To see how these concepts apply to linear mappings, consider the equation $(D-\lambda)y(x)=r(x)$ where $D=d/dx$ is the differential operator on $L^{2}[0,\infty)$, and let $\lambda$ be real. For $\lambda\neq0$, the unique solution of this equation in $L^{2}[0,\infty)$, is
$$\begin{aligned}
y(x)= & \left\{ \begin{array}{ll}
{\displaystyle e^{\lambda x}\left(y(0)+\int_{0}^{x}e^{-\lambda x^{\prime}}r(x^{\prime})dx^{\prime}\right)}, & \lambda<0\\
{\displaystyle e^{\lambda x}\left(y(0)-\int_{x}^{\infty}e^{-\lambda x^{\prime}}r(x^{\prime})dx^{\prime}\right),} &
| 434
| 3,263
| 1,097
| 389
| null | null |
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|
0.0981 2.26 (0.85, 6.02)
**rs6603797** **rs6603797**
**Males** **Males**
C/C 45 (81.8) 50 (67.6) \- C/C 60 (80.0) 12 (92.3) \-
C/T 9 (16.4) 24 (32.4) \- C/T 15 (20.0) 1 (7.7) \-
T/T 1 (1.8) 0 (0.0) 0.0672 1 T/T 0 (0.0) 0 (0.0) \- 1
C/C + C/T 54 (98.2) 74 (100.0) 0.2442 \- C/C + C/T 75 (100.0) 13 (100.0) \- \-
**Females** **Females**
C/C 42 (79.2) 66 (79.5) 1.91 (0.19, 18.97) C/C 69 (83.1) 19 (79.2) 1.82 (0.16, 21.12)
C/T 10 (18.9) 14 (16.9) 2.14 (0.19, 23.72) C/T 12 (14.5) 4 (16.6) 1.50 (0.11, 21.31)
T/T 1 (1.9) 3 (3.6) 0.8179 1 T/T 2 (2.4) 1 (4.2) 0.8601 1
C/C + C/T 52 (98.1) 80 (96.4) 0.5609 1.95 (0.20, 19.26) C/C + C/T 81 (97.6) 23 (95.8) 0.6461 1.76 (0.15, 20.30)
**rs4648727** **rs4648727**
**Males** **Males**^**a**^
A/A 4 (7.3) 5 (6.8) 1.20 (0.29, 5.02) A/A 9 (12.0) 0 (0.0)
| 435
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|
$\left\langle n\right|\hat{\Omega}_{m}^+\left|n'\right\rangle$ simply by increasing the Lamb-Dicke parameter. The quantum Rabi frequencies become an oscillating function of $n$ due to the presence of the Laguerre polynomials in Eq. (\[Omegme\]). These oscillations can strongly influence the system dynamics as thoroughly studied in [@gregorio].
Results {#tfti}
=======
The work protocol we have in mind is now explained. First, the work parameter $\lambda_t$ here has to do with the application of the laser on the ion. More specifically, we take $\lambda_i=0$ and $\lambda_f=\Omega$ in a sudden quench of the system Hamiltonian. This means an abrupt change from $$\begin{aligned}
\label{h0}
\hat{\mathcal H}(\lambda_i)= \hbar\nu\hat{a}^{\dagger}\hat{a} +
\frac{ \hbar \omega_0 }{2} \hat{\sigma}_{z}\end{aligned}$$ to $$\label{hf}
\!\!\!\hat{\mathcal H}(\lambda_f) =
\hat{\mathcal H}(\lambda_i) + \frac{\hbar \Omega}{2}
\left[ \hat{\sigma}_{+} \,
\text{e}^{ i \eta ( \hat{a} + \hat{a}^{\dagger} )
} +
\hat{\sigma}_{-} \,
\text{e}^{ - i \eta ( \hat{a} + \hat{a}^{\dagger} )
}
\right]\!,$$ or, if we want to explore the sidebands, an abrupt change to $$\begin{aligned}
\label{hs}
\hat{\mathcal H}(\lambda_f) = \hat{\mathcal H}(\lambda_i) +
\hbar ( \hat{\Omega}_{m}^\pm \hat{\sigma}_{+} +
\hat{\Omega}_{m}^\mp \hat{\sigma}_{-} ).\end{aligned}$$ The above Hamiltonians, Eq. (\[hf\]) and Eq. (\[hs\]), correspond to the sudden application of the laser field, i.e., the result of taking the limit of $t\rightarrow 0$ in Eq. (\[Hamint\]) and in Eq. (\[hamrwa\]), respectively.
It is well known that the Hamiltonian (\[hf\]) can not be diagonalized exactly, so that much of the analytical advances take place with the sideband Hamiltonians in Eq. (\[hs\
| 436
| 2,957
| 612
| 429
| null | null |
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|
Count
-------------------------------------------------------------------------------- -----------------------------------------------
$\overline{\partial} X^{1-2}_{-1} \otimes \left( \psi^{1-2}_{-1/2}, gravity, tensor multiplet contributions
\overline{\psi}^{1-2}_{-1/2} \right)$
$\left( \lambda^{1-6}_{-1/2}, \overline{\lambda}^{1-6}_{-1/2} \right)^2 vector in adjoint of $so(12)$
\otimes \left( \psi^{1-2}_{-1/2},\overline{\psi}^{1-2}_{-1/2} \right)$
$\left( \lambda^7_{-1/2} \lambda^8_{-1/2}, vectors in adjoint of $U(1)^2$
\overline{\lambda}^7_{-1/2} \overline{\lambda}^8_{-1/2} \right) \otimes
\left( \psi^{1-2}_{-1/2},\overline{\psi}^{1-2}_{-1/2} \right)$
$\left( \lambda^7_{-1/2} \overline{\lambda}^7_{-1/2}, vectors in adjoint of $U(1)^2$
\lambda^8_{-1/2} \overline{\lambda}^8_{-1/2} \right) \otimes
\left( \psi^{1-2}_{-1/2},\overline{\psi}^{1-2}_{-1/2} \right)$
$\lambda^8_{-1/2}\left( \lambda^{1-6}_{-1/2}, \overline{\lambda}^{1-6}_{-1/2} half-hypermultiplet in ${\bf 12}$ of $so(12)$
\right) \otimes \left( \psi^3_{-1/2}, \overline{\psi}^4_{-1/2} \right)$
$\overline{\lambda}^8_{-1/2} \left( \lambda^{1-6}_{-1/2}, half-hypermultiplet in ${\bf 12}$ of $so(12)$
\overline{\lambda}^{1-6}_{-1/2}\right) \otimes \left(
\overline{\psi}^3_{-1/2}, \psi^4_{-1/2} \right)$
$\lambda^7_{-1/2} \left( \lambda^{1-6}_{-1/2}, \overline{\lambda}^{1-6}_{-1/2} half-hypermultiplet in ${\bf 12}$ of $so(12)$
\right) \otimes \left(
\overline{\psi}^3_{-1/2}, \psi^4_{-1/2} \right)$
$\overline{\lambda}^7_{-1
| 437
| 4,018
| 319
| 282
| null | null |
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|
egin{aligned}
{\rm Observable} &: &~~~~SU(4) \times SU(2)_L
\times U(1)_R \times{U(1)}^3 \nonumber\\
{\rm Hidden} &: &~~~~SU(2)_A \times U(1)_A \times SU(2)_B
\times U(1)_B \times SU(2)_C \times U(1)_C
\times SO(4)_2 \nonumber\end{aligned}$$ The string states arising in other sectors transform under these gauge group factors. Additional space–time vector bosons that enhance the NS observable and/or hidden gauge groups may arise from additional sectors. In order to preserve the above gauge groups, all these additional space–time vector bosons need to be projected out. These additional space–time vector bosons arise from the following 36 sectors $$\mathbf{G}_{Enh} =
\left\{ \begin{array}{ccccc}
\,\,\,\, z_1 ,&
\,\,\,\, z_1 + \beta ,&
\,\,\,\, z_1 + 2\beta ,\\
\,\,\,\,\, z_1 + \alpha ,&
\,\,\,\,\, z_1 + \alpha + \beta ,&
\,\,\, z_1 + \alpha + 2\beta ,\\
\,\, z_2 ,&
\,\,\,\,\,\,\,\, z_2 + \beta ,&
\,\,\,\,\,\, z_2 + 2\beta ,\\
\,\,\,\,\, z_2 + \alpha ,&
\,\,\,\,\, z_2 + \alpha + \beta ,&
\,\,\, z_2 + \alpha + 2\beta ,\\
\,\, z_1 + z_2 ,&
\,\,\,\,\,\,\,\, z_1 + z_2 + \beta ,&
\,\,\,\,\,\, z_1 + z_2 + 2\beta ,\\
\,\,\,\,\, z_1 + z_2 + \alpha ,&
\,\,\,\,\, z_1 + z_2 + \alpha + \beta ,&
\,\,\, z_1 + z_2 + \alpha + 2\beta ,\\
\,\, \beta ,&
\,\,\,\,\,\,\,\, 2\beta ,&
\,\,\, \alpha,\\
\,\,\,\,\, \alpha + \beta ,&
\,\,\,\,\, \alpha + 2\beta ,&
\,\, x,\\
\,\,\,\,\, z_1 + x + \beta ,&
\,\,\,\,\, z_1 + x + 2\beta ,&
\,\, z_1 + x + \alpha,\\
\,\,\,\,\, z_1 + x + \alpha + \beta ,&
\,\,\, z_2 + x + \beta ,&
\,\,\,\,\, z_2 + x + \alpha + \beta ,\\
\,\,\, z_1 + z_2 + x + \beta ,&
\,\, z_1 + z_2 + x + 2\beta,&
\,\,\,\,\, z_1 + z_2 + x + \alpha + \beta ,\\
\,\, x + \beta,&
\,\,\,\,\, x + \alpha ,&
\,\,\, x + \alpha + \beta ,\\
\end{array} \right\}, \label{ggsectors1}$$\
where $x = 1 + S + \textstyle\sum_{i = 1}^{6} e_i + z_1 + z_2$.
The Matter Content {#analysis2}
---
| 438
| 2,687
| 502
| 394
| null | null |
github_plus_top10pct_by_avg
|
0.40 \[-0.66, 1.46\] 0.46
FES -- Social orientation^2^ -0.31 \[-0.62, 0.01\] 0.06 0.06 \[-0.16, 0.29\] 0.58 0.07 \[-0.19, 0.32\] 0.62 -0.52 \[-1.34, 0.30\] 0.22
PSS -- Cancer appraisal 0.48 \[0.37, 0.58\] \<0.001^\*\*^ 0.40 \[0.33, 0.47\] \<0.001^\*\*^ 0.38 \[0.29, 0.46\] \<0.001^\*\*^ -0.03 \[-0.10, 0.04\] 0.43
**Control variables**
Family member (Mother vs. Patient) -1.85 \[-4.34, 0.64\] 0.15 2.47 \[0.50, 4.45\] 0.02^\*^ -0.33 \[-2.61, 1.94\] 0.77 -0.79 \[-2.78, 1.20\] 0.44
Family member (Father vs. Patient) -0.78
| 439
| 4,770
| 822
| 301
| null | null |
github_plus_top10pct_by_avg
|
tions \[setth\] and \[typeVcomps\] contain the successive reductions bringing a given germ $\alpha(t)$ centered at a point of ${{\mathscr S}}$ into one of the forms given in §\[germlist\], or establishing that it does not contribute a component of the PNC. This analysis will conclude the proof of Theorem \[mainmain\].
Two examples {#twoexamples}
------------
The two examples that follow illustrate the main result, and show that components of all types may already occur on curves of degree 4. Simple translations are used to bring the marker germs provided by §\[germlist\] into the form given here.
Consider the reducible quartic ${{\mathscr C}}_1$ given by the equation $$(y+z)(xy^2+xyz+xz^2+y^2z+yz^2)=0\,.$$ It consists of an irreducible cubic with a node at $(1:0:0)$ and a line through the node and the inflection point $(0:1:-1)$. The other inflection points are $(0:1:0)$ and $(0:0:1)$. According to Theorem \[mainmain\] and the list in §\[germlist\], the PNC for ${{\mathscr C}}_1$ has one component of type I, one component of type II, one component of type III, corresponding to the triple point $(1:0:0)$, and four components of type IV: one for each of the inflection points $(0:1:0)$ and $(0:0:1)$, one for the node $(0:1:-1)$ and the tangent line $x=y+z$ to the cubic at that point, and one for the triple point $(1:0:0)$ and the two lines in the tangent cone $y^2+yz+z^2=0$ to the cubic at that point. Here is a schematic drawing of the curve, with features marked by the corresponding types (four points are marked as $\text{IV}_i$, since four different points are responsible for the presence of type IV components):
A list of representative marker germs is as follows: $${\rm I}:
\begin{pmatrix}
1 & 0 & 0\\
0 & 1 & 0\\
0 & -1 & t
\end{pmatrix};\quad
{\rm II}:
\begin{pmatrix}
2 & 0 & 0\\
-3 & t & 0\\
6 & 0 & t^2
\end{pmatrix};\quad
{\rm III}:
\begin{pmatrix}
1 & 0 & 0\\
0 & t & 0\\
0 & 0 & t
\end{pmatrix};$$ and, for type IV: $$\begin{pmatrix}
t & 0 & 0\\
0 & 1 & 0\\
-t & 0 & t^
| 440
| 327
| 774
| 530
| 1,575
| 0.788083
|
github_plus_top10pct_by_avg
|
delta_{i+2}'(m_{i+2, i}^{\#})^2\right)+
\left(\delta_{i-3}(m_{i-3, i}^{\natural})^2+\delta_{i+3}(m_{i+3, i}^{\natural})^2\right).
\end{array} \right.$$ Here, $\mathcal{P}^i_{1, 2}, \mathcal{P}^i_{2, 3}$ are suitable polynomials with variables in the entries of $m_{i-1, i}, m_{i+1, i}$ and
- $m_{i\pm 1,i}^{\prime}$ is the $(n_i-1)$-th column vector of the matrix $m_{i\pm 1,i}$.
- $\delta_{j}^{\prime} = \left\{
\begin{array}{l l}
1 & \quad \textit{if $j$ is odd and $L_j$ is \textit{free of type I}};\\
0 & \quad \textit{otherwise}.
\end{array} \right.$
- $m_{i\pm 2, i}^{\#}$ is the $(n_{i\pm 2}\times n_i-1)$-th entry of $m_{i\pm 2, i}$.
- $m_{i\pm 3, i}^{\natural}= \left\{
\begin{array}{l l}
\textit{the $n_{i\pm 3}\times (n_i-1)$-th entry of $m_{i\pm 3, i}$} & \quad \textit{if $L_{i \pm 3}$ is of type $I^o$};\\
\textit{the $(n_{i\pm 3}-1)\times (n_i-1)$-th entry of $m_{i\pm 3, i}$} & \quad \textit{if $L_{i \pm 3}$ is of type $I^e$}. \end{array} \right.$
In the right hand side of the equation including $\mathcal{X}_{i,2,2}(m)$, the term $1/2({}^tm_{i-1, i}'h_{i-1}m_{i-1, i}'+{}^tm_{i+1, i}'h_{i+1}m_{i+1, i}')$ should be interpreted as follows. We formally compute $1/2({}^tm_{i-1, i}'h_{i-1}m_{i-1, i}'+{}^tm_{i+1, i}'h_{i+1}m_{i+1, i}')$ and it is of the form $1/2(2X)$. Then the term $1/2({}^tm_{i-1, i}'h_{i-1}m_{i-1, i}'+{}^tm_{i+1, i}'h_{i+1}m_{i+1, i}')$ is defined as the modified $X$ by letting each term having $\pi$ as a factor in $X$ be zero.
These equations are considered in $(B\otimes_AR)/(\pi\otimes 1)(B\otimes_AR)$. Since $m$ actually belongs to $\mathrm{Ker~}\varphi(R)/\tilde{G}^1(R)$, we have the following equations by the argument made at the beginning of this step: $$\label{24}
\left \{
\begin{array}{l}
\mathcal{X}_{i,1,2}(m)=\bar{a}_ir_i+{}^tv_i+{}^ty_iz_i+\mathcal{P}^i_{1, 2}=\bar{b}_i=0;\\
\mathcal{X}_{i,1,3}(m)=\bar{a}_it_i+{}^ty_i=\bar{e}_i=0
| 441
| 3,519
| 447
| 309
| 2,626
| 0.778316
|
github_plus_top10pct_by_avg
|
X_H,\nu)$, given in , on the set $X_H$ of cosets with respect to $H$. We may thus assume that $(X,\mu)=(X_H,\nu)$.
Assume that $(X_H,\nu)$ is an $S$-torsor. We show that $H=E(H)^{\uparrow}$. It is enough to verify that $H\subseteq E(H)^{\uparrow}$. Let $s\in H$. Since $(X_H,\nu)$ is free, the equalities $$s\cdot x = {\mathbf d}(s)\cdot x=x$$ imply that there is some $c\leq s, {\mathbf d}(s)$ such that $c\cdot x=x$. Therefore $c\in E(H)$ and $s\geq c$, so that we have the inclusion $H\subseteq E(H)^{\uparrow}$.
Conversely, assume that $(X_H,\mu)$ is universal and let $s,t\in S$ and $x\in X_H$ be such that $s\cdot x=t\cdot x$. Then there are some $e,f\in E(H)$ such that $s\geq e$, $t\geq f$ such that $e\cdot x$ and $f\cdot x$ are defined, and then of course $e\cdot x=f\cdot x=x$. We put $h=ef$. Then $s,t\geq h$ and $h\cdot x=x$, so that $(X_H,\mu)$ is an $S$-torsor.
The following result follows from Proposition \[prop:torsors\] and [@FH Proposition 3.9] stated there without proof.
\[prop:ff\] The equivalence in Proposition \[prop:trans\] restricts to an equivalence between the category of universal $S$-sets and the category of filtered functors on $L(S)$. Consequently, the category of points of the topos ${\mathcal B}(S)$ is equivalent to the category of universal $S$-sets.
Let $(X,\mu)$ be a universal $S$-set. Assume that we have two objects $(e,x)$ and $(f,y)$ and two arrows $$(e,x) {\mathrel{
\settowidth{\@tempdima}{$\scriptstyle(f,s)$}
\settowidth{\@tempdimb}{$\scriptstyle(f,t)$}
\ifdim\@tempdimb>\@tempdima \@tempdima=\@tempdimb\fi
\mathop{\vcenter{
\offinterlineskip\ialign{\hbox to\dimexpr\@tempdima+2em{##}\cr
\rightarrowfill\cr\noalign{\kern.3ex}
\rightarrowfill\cr}}}\limits^{\!(f,s)}_{\!(f,t)}}} (f,y)$$ in the category of elements $\int_{L(S)}\Phi(X,\mu)$. This implies that ${\mathbf d}(s)={\mathbf d}(t)=e$ and $s\cdot x=t\cdot x=y$. Since $(X,\mu)$ is free, there is $c\leq c,s$ such that $c\cdot x=y$. Since $c\leq s$ we have that $c=sg$ for some $g\in E(S)$ where we may assume that
| 442
| 1,467
| 478
| 474
| 4,142
| 0.767811
|
github_plus_top10pct_by_avg
|
{\hat{T}}^{\chi }_{p,\Lambda }=\ker {\hat{T}}^{\chi ,-}_{p,\Lambda }
= & \, U^-(\chi )F_p{\otimes }{\mathbb{K}}_{{t}_p^\chi (\Lambda )},\\
{\operatorname{Im}}{\hat{T}}^{\chi }_{p,\Lambda }={\operatorname{Im}}{\hat{T}}^{\chi ,-}_{p,\Lambda }
= & \, U^-(\chi )F_p^{{b}-1} {\otimes }{\mathbb{K}}_\Lambda .
\end{aligned}$$
Let $q=\chi ({\alpha }_p,{\alpha }_p)$, $\chi '=r_p(\chi )$, and $\Lambda '={t}_p^\chi (\Lambda )$. We prove the claims about ${\hat{T}}^\chi _{p,\Lambda }$ in (i). The rest is analogous. By Lemma \[le:EmFn\], for all $m\in \{0,1,\dots ,{b}-1\}$, $$\begin{aligned}
{\hat{T}}^\chi _{p,\Lambda }(F_p^mv_{\Lambda '})
=&{T}_p(F_p^m)F_p^{{b}-1}v_\Lambda
=(K_p^{-1}E_p)^mF_p^{{b}-1}v_\Lambda \\
=&aE_p^mF_p^{{b}-1}v_\Lambda =a'F_p^{{b}-1-m}
\prod _{j=1}^m (q^{j+1-{b}}\Lambda (K_pL_p^{-1})-1) v_\Lambda
\end{aligned}$$ for some $a,a'\in {{\Bbbk }^\times }$. Thus, ${\hat{T}}^\chi _{p,\Lambda }(F_p^mv_{\Lambda '})=0$ if and only if $q^j=q^{{b}-1}\Lambda (K_pL_p^{-1})^{-1}$ for some $j\in \{1,2,\dots ,m\}$. By the assumption on $\Lambda (K_pL_p^{-1})$, this is equivalent to $j={b}-t$ for some $j\in \{1,2,\dots ,m\}$. Therefore ${\hat{T}}^\chi _{p,\Lambda }(F_p^mv_{\Lambda '})=0$ if and only if $m\ge {b}-t$.
Let $F\in U^-(\chi ')$. By Lemma \[le:Eheight\](ii), there exist unique $F'_m\in U^-_{p,K}(\chi ')$, where $m\in \{0,1,\dots ,{b}-1\}$, such that $F=\sum _{m=0}^{{b}-1}F'_mF_p^m$. By the previous paragraph, and since $\Lambda (K_pL_p^{-1})\in {\Bbbk }$, for each $m\in \{0,1,\dots ,{b}-1-t\}$ there is a unique $a_m\in {{\Bbbk }^\times }$ such that $${\hat{T}}^\chi _{p,\Lambda }(F v_{\Lambda '})=\sum _{m=0}^{{b}-1-t}
a_m{T}_p (F'_m)F_p^{{b}-1-m}v_\Lambda \in U^-(\chi ){\otimes }1_\Lambda .$$ By Lemma \[le:Eheight\](ii), the latter expression is zero if and only if ${T}_p(F'_m)=0$ for all $m\in \{0,1,\dots ,{b}-1-t\}$. Therefore, Lemma \[le:TpU+U+\] and relations $F'_m\in U^-_{i,K}(\chi ')$ imply that ${\hat{T}}^\chi _{p,\Lambda }(F v_{\Lambda '})=0$ if and only if $F'_m=
| 443
| 1,484
| 471
| 524
| null | null |
github_plus_top10pct_by_avg
|
patial three-cycles (in the simplest scenario), since the theory admits no D0-branes. For the time being, we work in the type-IIA framework, returning later to the type-IIB version of D-foam phenomenology.
![*Left: schematic representation of a generic D-particle space-time foam model, in which matter particles are treated as open strings propagating on a D3-brane, and the higher-dimensional bulk space-time is punctured by D-particle defects. Right: details of the process whereby an open string state propagating on the D3-brane is captured by a D-particle defect, which then recoils. This process involves an intermediate composite state that persists for a period $\delta t \sim \sqrt{\alpha '} E$, where $E$ is the energy of the incident string state, which distorts the surrounding space time during the scattering, leading to an effective refractive index but *not* birefringence.*[]{data-label="fig:recoil"}](recoil2_sarbennickJE.eps "fig:"){width="7.5cm"} ![*Left: schematic representation of a generic D-particle space-time foam model, in which matter particles are treated as open strings propagating on a D3-brane, and the higher-dimensional bulk space-time is punctured by D-particle defects. Right: details of the process whereby an open string state propagating on the D3-brane is captured by a D-particle defect, which then recoils. This process involves an intermediate composite state that persists for a period $\delta t \sim \sqrt{\alpha '} E$, where $E$ is the energy of the incident string state, which distorts the surrounding space time during the scattering, leading to an effective refractive index but *not* birefringence.*[]{data-label="fig:recoil"}](restore.eps "fig:"){width="7.5cm"}
Within this approach, a photon propagating on the D3-brane (represented as an open-string state) interacts with ‘flashing’ D-particles at a rate proportional to their local density $n_{D0}$. During each such interaction, a simple string amplitude calculation or the application of the quantum-mechanical uncertainty principle
| 444
| 176
| 1,412
| 333
| null | null |
github_plus_top10pct_by_avg
|
parators ]{}
Figure \[fig:sushi\_10\_ken\] illustrates the Kendall rank correlation of the rankings estimated by the two algorithms and the ground truth. Larger value indicates that the estimate is closer to the ground truth, and the data-driven rank-breaking outperforms the state-of-the-art GMM approach.
![The data-driven rank-breaking achieves larger Kendall rank correlation compared to the state-of-the-art GMM approach. []{data-label="fig:sushi_10_ken"}](sushi10_n_ken-eps-converted-to.pdf "fig:"){width=".3\textwidth"} (-100,100) (-220,50) (-90,-7)[sample size ]{} ![The data-driven rank-breaking achieves larger Kendall rank correlation compared to the state-of-the-art GMM approach. []{data-label="fig:sushi_10_ken"}](sushi10_l_ken-eps-converted-to.pdf "fig:"){width=".3\textwidth"} (-100,100) (-115,-7 )[number of separators ]{}
To validate whether PL model is the right model to explain the sushi data set, we compare the data-driven rank-breaking, MLE for the PL model, GMM for the PL model, Borda count and Spearman’s footrule optimal aggregation. We measure the Kendall rank correlation between the estimates and the samples and show the result in Table \[tab:sushi\_10\_all\]. In particular, if $\sigma_1,\sigma_2,\cdots, \sigma_n$ denote sample rankings and $\widehat{\sigma}$ denote the aggregated ranking then the correlation value is $(1/n)\sum_{i = 1}^n \big(1-\frac{4\mathcal{K}(\widehat{\sigma},\sigma_i)}{\kappa(\kappa-1)}\big)$, where $\mathcal{K}(\sigma_1,\sigma_2) = \sum_{i < j \in [\kappa]} \mathbb{I}_{\{(\sigma_1^{-1}(i) - \sigma_1^{-1}(j))(\sigma_2^{-1}(i) - \sigma_2^{-1}(j)) < 0 \}}$. The results are reported for different number of samples $n$ and different values of $\ell$ under the top-$\ell$ separators scenarios. When $\ell=9$, we are using all the complete rankings, and all algorithms are efficient. When $\ell < 9$, we have partial orderings, and Spearman’s footrule optimal aggregation is NP-hard. We instead use scaled footrule aggregation (SFO) given in [@DKNS01]. Most approaches achieve simil
| 445
| 99
| 216
| 442
| 986
| 0.796302
|
github_plus_top10pct_by_avg
|
-\frac{1}{\sqrt{2}} & 0 & 0\\
0 & 0 & 0 & 0 & 0 & \frac{1}{\sqrt{2}} & 0 & -\frac{1}{\sqrt{2}} & 0\\
0 & \frac{1}{\sqrt{3}} & 0 & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{6}} & 0 & 0 & 0 & -\frac{1}{\sqrt{6}}\\
0 & 0 & \frac{1}{\sqrt{3}} & 0 & 0 & -\frac{1}{\sqrt{6}} & \frac{1}{\sqrt{3}} & -\frac{1}{\sqrt{6}} & 0\\
\frac{1}{\sqrt{3}} & 0 & 0 & 0 & \frac{1}{\sqrt{3}} & 0 & 0 & 0 & \frac{1}{\sqrt{3}}
\end{array}\right].\label{b2}$$ Eqs. (\[b1\]) and (\[b2\]) allow us to compute all eigenvalues of arbitrary operator $X{\left(\varphi,\psi\right)}$. In all examples given below the largest eigenvalue $\lambda_{max}$ correspond to the scalar component in the decomposition (\[b3\]). All of them involve three orbits (N=3 in eq. (\[b4\])).
:
- First orbit\
${\left|\varphi_1\right>}={\left|x_0^1\right>},\quad {\left|\psi_1\right>}={\left|x_1^4\right>}$\
$\lambda_{max}\simeq 7,40$
- Second orbit\
${\left|\varphi_2\right>}={\left|x_0^1\right>},\quad {\left|\psi_2\right>}={\left|x_0^7\right>}$\
$\lambda_{max}\simeq 4,57$
- Third orbit\
${\left|\varphi_3\right>}={\left|x_0^1\right>},\quad {\left|\psi_3\right>}={\left|x_1^5\right>}$\
$\lambda_{max}\simeq 4,12$
The maximal eigenvalue of the operator $X$ defined by eq. (\[b4\]):\
$\lambda_{max}(X)\simeq 16,09$.\
:
- First orbit\
${\left|\varphi_1\right>}={\left|x_0^1\right>},\quad {\left|\psi_1\right>}={\left|x_2^3\right>}$\
$\lambda_{max}\simeq 5,21$
- Second orbit\
${\left|\varphi_2\right>}={\left|x_0^1\right>},\quad {\left|\psi_2\right>}={\left|x_1^6\right>}$\
$\lambda_{max}\simeq 5,30$
- Third orbit\
${\left|\varphi_3\right>}={\left|x_0^1\right>},\quad {\left|\psi_3\right>}={\left|x_0^1\right>}$\
$\lambda_{max}\simeq 8,00$
The maximal eigenvalue of $X$:\
$\lambda_{max}(X)\simeq 18,51$.
:
- First orbit\
${\left|\varphi_1\right>}={\left|x_0^1\right>},\quad {\left|\psi_1\right>}={\left|x_2^5\right>}$\
$\lambda_{max}\simeq 3,35$
- Second orbit\
${\left|\varphi_2\right>}={\left|x_0^1\right>},\qu
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|
$. A subject is an active entity which operates on segments of a GWV partition. The extended GWV policy is as follows.
$$\label{eq:gwv_pikeos}
\begin{aligned}
& current(st1) = current(st2) \; \wedge \\
& currentsubject(st1) = currentsubject(st2) \; \wedge \\
& select(seg,st1) = select(seg,st2) \; \wedge \\
& selectlist(segs,st1) = selectlist(segs,st2) \\
& \Rightarrow \\
& select(seg,next(st1)) = select(seg,next(st2))
\end{aligned}$$
where $segs = diastrong(seg,current(st1)) \cap segsofpartition(current(st1))$. The extended GWV policy has been applied to formally specify the PikeOS [@Tverdy11].
The GWV policy is only applicable to a class of systems in which strict temporal partitioning is utilized and kernel state cannot be influenced by execution of code within partitions. The GWV theorem has been shown to hold for the AAMP7G’s hardware-based separation kernel [@Wilding10]. The original GWV theorem is only applicable to such strict static schedulers. The GWV policy is sound but not complete [@Grev05]. In GWV, $dia$ function only expresses the direct interaction between segments. It is extended by multiple active “Agent” in GWVr1 [@Grev05] that moving data from one segment to another segment is under control of one agent. GWVr1 is similar to the $diaStrong$ function in [@Tverdy11]. For more dynamic models, a more general GWV theorem, GWVr2 [@Grev05], uses a more generalized influence between segments, the information flow graph, to specify the formal security policy. The information flow graph enables system analysis and can be used as foundation for application-level policies. The GWVr2 is used to formal analysis for the INTEGRITY-178B separation kernel [@Richards10]. More theoretical discussion of GWVr1 and GWVr2 is in [@Greve10].
- Noninterference
The concept of noninterference is introduced in [@Goguen82] to provide a formal foundation for the specification and analysis of security policies and the mechanisms to enforce them. The intuitive meaning of noninterference is that a security domain $u$
| 447
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| 0.788932
|
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|
:
$$\label{eq:pks}
P_{KS}(i,j)=\frac{A(i,j)}{\lambda}\frac{\Psi_j}{\Psi_i}.$$
We have $ \forall i$ $ \sum_j P_{KS}(i,j) =1$. Moreover, using the fact that $A$ is symmetric we find:
$$\label{eq:sta}
\sum_j P_{KS}(j,i)\Psi^2_j=\sum_j \frac{A(j,i)\Psi_i\Psi_j}{\lambda}=\Psi^2_i.$$
Hence, $P_{KS}^t \Psi^2=\Psi^2$ and the stationary density of $P_{KS}$ is $\pi_{stat}=\Psi^2$.
Using Eqs. (\[eqhks\]) and (\[eq:pks\]), we have:
$$\label{eq:pks2}
h_{KS}=-\frac{1}{\lambda}\sum_{(i,j)} A(i,j) \Psi_i \Psi_j \log(\frac{A(i,j)}{\lambda}\frac{\Psi_i}{\Psi_j}).$$
Eq. (\[eq:pks2\]) can be split in two terms:
$$\begin{aligned}
\label{eq:pks3}
h_{KS}&=&\frac{1}{\lambda}\sum_{(i,j)} A(i,j)\Psi_i\Psi_j\log(\lambda)\nonumber\\
&-&\frac{1}{\lambda}\sum_{(i,j)} A(i,j)\Psi_i\Psi_j\log(A(i,j)\frac{\Psi_j}{\Psi_i}).\end{aligned}$$
The first term is equal to $\log(\lambda)$ because $\Psi$ is an eigenvector of $A$ and the second term is equal to $0$ due to the symmetry of $A$. Thus:
$$\label{eq:pks4}
h_{KS}=\log(\lambda).$$
Moreover, for a Markov chain the number of trajectories of length $n$ is equal to $ N_n=\sum_{(i,j)} (A^n)(i,j)$. For a Markov chain the KSE can be seen as the time derivative of the path entropy leading that KSE is maximal when the paths are equiprobable. For an asymptotic long time the maximal KSE is:
$$\label{eq:pks5}
h_{KS_{max}}=\frac{\log(N_n)}{n} \rightarrow\log(\lambda),$$
by diagonalizing $A$. Using Eqs. (\[eq:pks4\]) and (\[eq:pks5\]) we find that $P_{KS}$ defined as in Eq. (\[eq:pks\]) maximises the KSE. Finally $P_{KS}$ verifies $\pi_{stat_i}P_{KS}(i,j)=\pi_{stat_j}P_{KS}(j,i)$ $\forall$ $(i,j)$ and thus $P_{KS}$ is reversible.
In a similar way, we can search for a transition matrix $P_{mix}$ which minimizes the mixing time -or, equivalently the transition matrix minimizing its second eigenvalue $\lambda(P)$. This problem is much more difficult to solve than the first one, given that the eigenvalues of $P_{mix}$ can be complex. Nevertheless, two cases where the matrix $P_{mix}$ is diagonaliz
| 448
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| 3,933
| 0.769197
|
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|
o Hive, Can anybody please help me with the below Error I receive when trying to create the following table:
hive> create table Employees(
> name String,
> salary float,
> subordinates array<string>,
> deductions map<string,float>,
> address struct<street:string,city:string,state:string>)
> row format serde
> 'org.apache.hadoop.hive.contrib.serde2.MultiDelimitSerDe' << **this one is present in "hive-contrib"**
> with serdeproperties ("field.delim"=",")
> location 'Mytable/employee'; **<< This is in my HDFS location.**
The error is:
FAILED: Execution Error, return code 1 from org.apache.hadoop.hive.ql.exec.DDLTask. MetaException(message:java.lang.IllegalArgumentException: java.net.URISyntaxException: Relative path in absolute URI: hdfs://localhost:9000./Mytable/employee)**
My data takes the form:
JSON :
{
"name":"Manager",
"salary":10000.0,
"subordinates": ["Emp1", "Emp2"],
"deductions":{
"State Tax":0.1,
"Insurance":2,
},
"address":{
"street":"1 Ave",
"city":"Chicago",
"state":"IL"
}
}
Thanks in advance.
A:
location should be an absolute path. If you really want your data to be in hdfs://localhost:9000/Mytable/employee, you should replace the last line with:
location '/Mytable/employee';
Q:
Google maps are offset north using ggmap()?
I'm trying to match up images generated with ggmap to some other geo data and running into odd behaviour.
The simplest way I can explain is that if I run the following to request a Stamen map, it will overlay nicely with my other data.
map_out <- ggmap::get_map("54.5234,-3.0232", zoom =12, source = "stamen", maptype = "watercolor")
ggmap::ggmap(map_out)
If I run exactly the same thing but requesting a Google Map, the image is offset to the north west.
map_out <- ggmap::get_map("54.5234,-3.0232", zoom =12, source = "google", maptype = "terrain")
ggmap::ggmap(map_out)
The coordinates on the two plots are identical but the Google one is offset north west. I'm blaming the Google map because Stamen matches up with other data so
| 449
| 324
| 76
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| 325
| 0.813363
|
github_plus_top10pct_by_avg
|
in this section is to investigate the response of an spatially extended detector, working in its co-moving frame and coupled to the Minkowski vacuum state of the scalar field, following De Bievre and Merkli [@DeBievre:2006pys]. We consider the corresponding centre of mass, with co-ordinates $(x_0(\tau))$, of the detector to follow the Rindler trajectory with uniform acceleration $g$. We work in Rindler co-ordinates with the following form of the metric $$ds^2 = \exp{(2 g z)} \left( - dt^2 + dz^2 \right) + d x^2_{\perp}
\label{rindlermetric}$$
We further assume the usual monopole interaction Hamiltonian term proportional to the value of the field on the trajectory, but now the field is replaced by the smeared field $\phi(\tau)$ obtained through $$\phi(\tau) = \int dz d^2 x_{\perp} e^{g z} f \left(z, x_{\perp}, z_0(\tau), x_{\perp 0}(\tau) \right) \phi(x)
\label{smeared}$$ where $dz d^2 x_{\perp} e^{g z}$ is the 3-spatial volume of the $t = $ constant hypersurface and $f \left(z, x_{\perp}, z_0(\tau), x_{\perp 0}(\tau) \right)$ is the profile function which encodes the spatial geometry of the extended detector itself. For the particular detector considered, $z_0(\tau) =0 = x_{\perp 0}(\tau) $, the detector is centred, with its centre of mass at the origin.
The pullback of the Wightman function relevant for calculating the detector response function is $$\begin{aligned}
W(\tau,\tau^\prime) = \langle 0_M | \phi(\tau) \phi(\tau^\prime) | 0_M \rangle
\label{whitmannfunction}\end{aligned}$$ with the transition rate being $${\dot {\cal F}}(E) = 2 \operatorname{Re}\int_0^\infty ds \,e^{-i E s} \, W(\tau,\tau - s)$$
The quantised scalar field in terms of the mode solutions for the metric in Eq.(\[rindlermetric\]) is $$\phi(x) = \int d\omega \int d^2 k_{\perp} \left[ {\hat a}_{\omega, k_{\perp}} v_{\omega, k_{\perp}}(x) + {\hat a}^{\dagger}_{\omega, k_{\perp}} v^{\star}_{\omega, k_{\perp}}(x) \right]
\label{field}$$ where the mode solutions are given in terms of the modified Bessel function as $$v_{\omega, k_{\perp}
| 450
| 2,817
| 605
| 477
| 3,752
| 0.770324
|
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|
m:cramer\_rao\_position\_p\] {#sec:proof_cramer_rao_position_p}
-------------------------------------------------
Let $H(\theta) \in \mathcal{S}^d$ be Hessian matrix such that $H_{i\i}(\theta) = \frac{\partial^2\L(\theta)}{\partial\theta_i \partial \theta_{\i}}$. The Fisher information matrix is defined as $I(\theta) = -\E_\theta[H(\theta)]$. Fix any unbiased estimator $\widehat{\theta}$ of $\theta \in \Omega_b$. Since, $\widehat{\theta} \in \mathcal{U}$, $\widehat{\theta} - \theta$ is orthogonal to ${\boldsymbol{1}}$. The Cramér-Rao lower bound then implies that ${\E[{\|\widehat{\theta} - \theta^*\|}^2] \geq \sum_{i = 2}^d \frac{1}{\lambda_i(I(\theta))}}$. Taking the supremum over both sides gives $$\begin{aligned}
\sup_{\theta}\E[{\|\widehat{\theta} - \theta\|}^2] \;\; \geq \;\; \sup_{\theta} \sum_{i=2}^d \frac{1}{\lambda_i(I(\theta))} \geq \sum_{i = 2}^d \frac{1}
{\lambda_i(I({\boldsymbol{0}}))}\;.\end{aligned}$$ The following lemma provides a lower bound on $\E_\theta[H({\boldsymbol{0}})]$, where ${\boldsymbol{0}}$ indicates the all-zeros vector.
\[lem:cr\_lem\] Under the hypotheses of Theorem \[thm:cramer\_rao\_position\_p\], $$\begin{aligned}
\label{eq:cr0}
\E_\theta[H({\boldsymbol{0}})] \;\;\succeq\;\; - \sum_{j=1}^n \frac{2p\log(\kappa_j)^2}{\kappa_j(\kappa_j-1)} \sum_{\i<i \in S_j}(e_i - e_{\i})(e_i - e_{\i})^{\top} \,.\end{aligned}$$
Observe that $I({\boldsymbol{0}})$ is positive semi-definite. Moreover, $\lambda_1(I({\boldsymbol{0}}))$ is zero and the corresponding eigenvector is the all-ones vector. It follows that $$\begin{aligned}
I(0) &\preceq & \sum_{j=1}^n \frac{2p\log(\kappa_j)^2}{\kappa_j(\kappa_j-1)} \sum_{\i<i \in S_j}(e_i - e_{\i})(e_i - e_{\i})^{\top} \\
& \preceq & 2p\log(\kappa_{\max})^2 \underbrace{\sum_{j=1}^n \frac{1}{\kappa_j(\kappa_j-1)} \sum_{\i<i \in S_j}(e_i - e_{\i})(e_i - e_{\i})^{\top}}_{=L}\;,\end{aligned}$$ where $L$ is the Laplacian defined for the comparison graph $\H$, Definition \[def:comparison\_graph1\], as $\ell_j = 1$ for all $j \in [n]$ in this s
| 451
| 967
| 536
| 508
| null | null |
github_plus_top10pct_by_avg
|
= -( + )which we can finally rewrite in the expected form: T(w) j\^a\_[L,z]{}(z) = :j\^[|b]{}\_[R,z]{}j\^[|c]{}\_[R,z]{}:(w)\_[|b |c]{} j\^a\_[L,z]{}(z) = + , thus completing our consistency check.
The associativity of the current algebra {#associativity}
----------------------------------------
In this appendix we address the issue of the associativity of the current algebra . We will prove the associativity of this current algebra at the first non-trivial order in $f^2$.
The OPE $j^a_{L,z}(z) j^b_{L,z}(w) j^c_{L,z}(x)$ {#the-ope-ja_lzz-jb_lzw-jc_lzx .unnumbered}
------------------------------------------------
First we consider the OPE between three $z$-components of the left-current: j\^a\_[L,z]{}(z) j\^b\_[L,z]{}(w) j\^c\_[L,z]{}(x). We will compute this OPE using the current algebra at the order of the poles. Moreover we will only compute the lowest-order terms in the $f^2$ expansion. In this case these are terms of order $f^{-2}$. To prove associativity we will first compute the OPE between the first two currents, then compute the OPE of the result with the third current, and show that the result is invariant under permutation of the currents. We start out with: $$\begin{aligned}
j^a_{L,z}(z) & j^b_{L,z}(w) j^c_{L,z}(x) =
\left(
\frac{c_1 \kappa^{ab}}{(z-w)^2} + \frac{c_2 {f^{ab}}_d j^d_{L,z}(w)}{z-w}+ \frac{(c_2-g) {f^{ab}}_d j^d_{L,\bar z}(w)(\bar z - \bar w)}{(z-w)^2} \right. \cr
& \left. \qquad
+ :j^a_{L,z}(z) j^b_{L,z}(w): + ...
\right) j^c_{L,z}(x).\end{aligned}$$ The ellipses stand for lower-order terms in the OPEs, that we do not keep track of. We obtain : $$\begin{aligned}
j^a_{L,z}(z) & j^b_{L,z}(w) j^c_{L,z}(x) =
\frac{c_1 \kappa^{ab}j^c_{L,z}(x)}{(z-w)^2} + \frac{c_1 c_2 {f^{abc}}}{(z-w)(w-x)^2} + :j^a_{L,z}(z) j^b_{L,z}(w):j^c_{L,z}(x) + ...\end{aligned}$$ up to a contact terms. We now have to compute the OPE involving the regular operator $:j^a_{L,z}(z) j^b_{L,z}(w):$. In order to use the techniques presented in appendix \[compositeOPEs\] we rewrite both currents as being evaluated at
| 452
| 404
| 816
| 596
| 3,741
| 0.770399
|
github_plus_top10pct_by_avg
|
$(-,-)$ -1/3 -1/3
$\left( \, \textbf{4} \, , \textbf{1} , \, +1 \, \right)$ $(-,-,-)$ $(-,-)$ -1 -1
Here $``+"$ and $``-"$, label the contribution of an oscillator with fermion number $F = 0$ or $F = -1$, to the degenerate vacuum. These states correspond to particles of the Standard Model. More precisely we can decompose these representations under $SU(3) \times SU(2) \times U(1)$ as $$\begin{aligned}
\label{16decomposition}
\left( \textbf{4} , \textbf{2} , 0 \right)&
= \left(\textbf{3},\textbf{2},+\frac{1}{6}\right)_{Q} +
\left(\textbf{1},\textbf{2},-\frac{1}{2}\right)_{L}, \nonumber \\
\left( \overline{\textbf{4}} , \textbf{1} , -1 \right) &=
\left(\overline{\textbf{3}},\textbf{1},-\frac{2}{3}\right)_{u^c}+
\left(\textbf{1},\textbf{1},0\right)_{\nu^c},\nonumber\\
\left( \overline{\textbf{4}} , \textbf{1} , +1 \right)&=
\left(\overline{\textbf{3}},\textbf{1},+\frac{1}{3}\right)_{d^c}+
\left(\textbf{1},\textbf{1},+1 \, \right)_{e^c}. \nonumber\end{aligned}$$ Where $L$ is the lepton–doublet; $Q$ is the quark–doublet; $d^c,~u^c,~e^c$ and $\nu^c$ are the quark and lepton singlets. Because of the $\alpha$- and $\beta$-projections, which projects on incomplete $\textbf{16}$ and $\overline{\textbf{16}}$ representations, complete families and anti–families are formed by combining states from different sectors.
Nonviability of the $SU(4) \times SU(2) \times U(1)$ model {#nonv}
==========================================================
We now discuss why in our free fermionic construction, the $SU(4) \times SU(2) \times U(1)$ GUT models are not viable. As mentioned in the previous section, the matter content comes from the $\bf{16}$ of $SO(10)$. However, with the addition of the $\alpha$ and $\beta$ basis vectors from eq. (\[421\]), the $\bf{16}$ representation is broken by the GGSO projections that are in general given by $$\label{gso}
e^{i\pi v_i\cdot F_{\xi}} |S_{\xi}> =
\delta_{{\xi}}\ C\binom {\xi} {v_i}^* |S_{\xi}>.$$ Here $\delta
| 453
| 935
| 811
| 578
| 2,470
| 0.77949
|
github_plus_top10pct_by_avg
|
Meier biochemical recurrence free survival curves. Number of AA patients in BCR curves with deletion (red) or without deletion (blue) is marked above the X-axis.](gr3){#f0015}
######
Patient-specific features included in the study (patient number: GP02-18; Race: African American: AA, Caucasian American: CA; prostate specific antigen: PSA).
Summary of information on patient and tumor
--------------------------------------------- ---- ---- ----------- ----- ------ ---- ----------- ----- ----
GP02 AA 68 7 (4 + 3) T3C 7 − 6 (3 + 3) 100 80
GP04 AA 51 7 (3 + 4) T3A 8.3 − 7 (3 + 4) 95 80
GP10 AA 53 7 (3 + 4) T3C 6.5 − 7 (3 + 4) 95 90
GP18 AA 48 7 (3 + 4) T3A 3.7 − 6 (3 + 3) 100 80
GP12 AA 52 6 (3 + 3) TX 3.8 \+ 6 (3 + 3) 100 90
GP13 AA 59 6 (3 + 3) T2C 7.7 \+ 7 (3 + 4) 100 85
GP15 AA 44 6 (3 + 3) TX 9.1 \+ 6 (3 + 3) 92 80
GP06 CA 58 7 (4 + 3) T3C 7.4 − 7 (3 + 4) 100 95
GP11 CA 64 7 (3 + 4) T2C 11.6 − 6 (3 + 3) 95 90
GP16 CA 49 7 (4 + 3) T3A 22.7 − 7 (3 + 4) 85 90
GP01 CA 64 7 (3 + 4) T3B 11.4 \+ 7 (3 + 4) 95 80
GP07 CA 69 6 (3 + 3) TX 4 \+ 6 (3 + 3) 100 90
GP09 CA 60 6 (3 + 3) TX 2.8 \+ 7 (3 + 4) 97 80
| 454
| 3,507
| 386
| 367
| null | null |
github_plus_top10pct_by_avg
|
person in the office with access to InDesign, so I need our templates to be editable outside of InDesign, while retaining formatting. What I'm running into is that when I export to PDF, they are text-editable, but the PDF is treating text objects on separate pages as unlinked, even if they're linked in ID. So, for example, if I have a text object on page 1 that's linked with a text object on page 2 and I delete the text object on page 1, the text object on page 2 doesn't move to page 1; or, if I add more text to page 1, it doesn't move the text objects that follow it. Is it even possible to make that happen?
TL;DR: I want to be able to add or subtract text objects from an InDesign file exported to PDF and have other objects move accordingly. Can I do that?
Thanks!
A:
You can not reflow text across frames with anything other than InDesign. What you are seeking is not possible.
What you may be able to do is have everyone work on the text in a Word file. You can then link that text file to the InDesign document. So, changes to the Word file are automatically updated within InDesign. This will not allow others to view the overall InDesign layout though.
InDesign formatting can only really be edited with InDesign. Acrobat is for simple touch ups only and never intended to be a full fledged editor.
Q:
IE7 syntax error for if(...) return false
One of our advertisers has a landing page that contains the following Javascript function:
sfHover = function() {
if (!document.getElementsByTagName) return false;
var sfEls1 = document.getElementById("catmenu").getElementsByTagName("li");
for (var i=0; i<sfEls1.length; i++) {
sfEls1[i].onmouseover=function() {
this.className+=" sfhover1";
}
sfEls1[i].onmouseout=function() {
this.className=this.className.replace(new RegExp(" sfhover1\\b"), "");
}
}
var sfEls1 = document.getElementById("menu").getElementsByTagName("li");
for (var i=0; i<sfEls1.length; i++) {
sfEls1[i].onmouseover=
| 455
| 506
| 219
| 463
| 121
| 0.824253
|
github_plus_top10pct_by_avg
|
42& 0.33 & 0.09 & 0.28 & 0.71 & 0.09 \\
& &(24,\ 0) & & 0.84 & 1.30 & 0.83 & 1.11 & 0.82 \\
& &(24,\ 4) & & 1.27 & 1.31 & 1.27 & 1.30 & 1.26 \\
& &(24,\ 8) & & 1.32 & 1.33 & 1.33 & 1.34 & 1.32 \\
& &(24, 12) & & 1.35 & 1.34 & 1.35 & 1.36 & 1.35 \\
& &(24, 24) & & 1.39 & 1.36 & 1.37 & 1.38 & 1.37 \\
[6pt]
1 & 1 &(\ 0,\ 0)&10.4& 1.6 & 0.7 & 2.1 & 5.2 & 0.7 \\
& &(24,\ 0) & & 4.6 & 5.5 & 4.9 & 7.0 & 4.4 \\
& &(24,\ 4) & & 5.7 & 5.9 & 5.9 & 7.4 & 5.4 \\
& &(24,\ 8) & & 6.6 & 6.3 & 6.6 & 7.7 & 6.2 \\
& &(24, 12) & & 7.2 & 6.6 & 7.1 & 8.0 & 6.7 \\
& &(24, 24) & & 8.4 & 7.3 & 7.9 & 8.4 & 7.6 \\
[6pt]
1 &0.1&(\ 0,\ 0)&36.0& 6.8 & 2.4 & 7.2 & 18.0 & 2.4 \\
& &(24,\ 0) & & 18.7 & 25.8 & 18.9 & 26.1 & 18.2 \\
& &(24,\ 4) & & 25.5 & 26.8 & 25.7 & 28.9 & 25.0 \\
& &(24,\ 8) & & 28.1 & 27.7 & 28.2 & 30.2 & 27.6 \\
& &(24, 12) & & 29.7 & 28.4 & 29.5 & 30.9 & 28.9 \\
& &(24, 24) & & 32.4 & 30.0 & 31.3 & 32.0 & 30.8 \\
\hline
\end{array}
$
The risk is based on 100,000 independent replications of $X$ and $Y$ for some pairs of two eigenvalues of $\Th\Th^\top$. The simulation results are provided in Table \[tab:2\], where GB, JS, EM, MS1 and MS2 are the Bayesian predictive densities with the following priors.
[ ]{}
(\[eqn:pr\_Th\]) and (\[eqn:pr\_GB\]) with $a=1$, $b=3$ and $v_0=1$,
(\[eqn:pr\_js\]),
(\[eqn:pr\_em\]),
(\[eqn:pr\_MS1\]),
(\[eqn:pr\_MS2\]).
Note that GB, JS, EM and MS1 are minimax, while MS2 has not been shown to be minimax.
When the pair of eigenvalues of $\Th\Th^\top$ is $(0,\, 0)$, JS and MS2 are superior. When the pair of eigenvalues of $\Th\Th^\top$ is $(24,\, 24)$, JS has nice performance but it is bad if the two eigenvalues of $\Th\Th^\top$ are much different.
Our simulations suggest that MS2 is better than EM and MS1. When the two eigenvalues of $\Th\Th^\top$ are much different, namely they are $(24,\, 0)$ and $(24,\,
| 456
| 453
| 1,193
| 599
| null | null |
github_plus_top10pct_by_avg
|
{\sigma }_{i_{\nu +2-n}}\cdots {\sigma }_{i_{\nu -1}}({\alpha })>0$. Clearly, this has to be a simple root. Let $i_\nu \in I$ such that ${\alpha }=\al
_{i_\nu }$. Then the first claim follows from [@a-HeckYam08 Cor.3]. By Eq. for $\nu -1$ and by [@a-HeckYam08 Cor.3] we get $1_{r_{i_{\nu -n-1}}\cdots r_{i_2}r_{i_1}(\chi )}
{\sigma }_{i_{\nu -n}}{\sigma }_{i_{\nu +1-n}}\cdots {\sigma }_{i_{\nu -1}}({\alpha }_{i_\nu })<0$. Together with the first claim of the lemma this implies the second claim.
For each $\nu \in \{1,2,\dots,2n\}$ let $$\begin{aligned}
\label{eq:beta2n}
\beta _\nu =\beta _\nu ^\chi
=&1_\chi {\sigma }_{i_1}\dots {\sigma }_{i_{\nu -1}}({\alpha }_{i_\nu }),&
F_{\beta _\nu }=& F_{\beta _\nu }^\chi
={T}_{i_1}\dots {T}_{i_{\nu -1}}(F_{i_\nu }),\end{aligned}$$ where $F_{i_\nu }\in U^-(r_{i_{\nu -1}}\cdots r_{i_2}r_{i_1}(\chi ))$ and $F_{\beta _\nu }\in U(\chi )$. Since $$\ell (1_{r_{i_n}\cdots r_{i_2}r_{i_1}(\chi )}{\sigma }_{i_{n+1}}{\sigma }_{i_{n+2}}
\cdots {\sigma }_{i_{2n}})=n,$$ Lemma \[le:longestw\] implies that $$\begin{aligned}
1_\chi {\sigma }_{i_1}{\sigma }_{i_2}\dots {\sigma }_{i_n}=&
{\sigma }_{i_1}{\sigma }_{i_2}\dots {\sigma }_{i_n}1_{r_{i_n}\cdots r_{i_2}r_{i_1}(\chi )}\\
=&
(1_{r_{i_n}\cdots r_{i_2}r_{i_1}(\chi )}
{\sigma }_{i_{n+1}}{\sigma }_{i_{n+2}}\dots \s_{i_{2n}})^{-1}.\end{aligned}$$ Moreover, $$\begin{aligned}
\beta _\nu ^\chi =-\beta _{\nu -n}^\chi \in - R^\chi _+
\label{eq:betak>n}\end{aligned}$$ for all $\nu \in \{n+1,n+2,\dots ,2n\}$ by Lemma \[le:longlongw\]. In $U(\chi )$ we also get $$\begin{aligned}
F_{\beta ^\chi _\nu }=T_{i_1}\cdots T_{i_{\nu -n}}(F_{i_{\nu -n}})\in \fienz
K^{-1}_{\beta _{\nu -n}^\chi }E_{\beta ^\chi _{\nu -n}}
\label{eq:Fbetak}\end{aligned}$$ for all $\nu \in \{n+1,\dots ,2n\}$ by [@p-Heck07b Thm.6.19,Prop.6.8(ii)].
Verma modules and morphisms {#sec:Verma}
===========================
We consider Verma modules for the algebras $U(\chi )$, $\chi \in {\mathcal{X}}$. We observe that the fundaments of the theory of Ver
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to $z=0$. If $b=c$, then necessarily $s=0$: $$\alpha(t)=\begin{pmatrix}
1 & 0 & 0 \\
t^a & t^b & 0 \\
r(t) & 0 & t^b
\end{pmatrix}\quad,$$ and further $a<v(r)$ (cf. Lemma \[faber\]). The reader can verify that the limits of the branches collected in $G$ are supported on the kernel line $x=0$. The limit of each (formal) branch collected in $H(y,z)$ may be computed as in Definition \[branchlimit\], and is found to be given by a homogeneous equation in $x$ and $z$ only: that is, a $(0:1:0)$-star. It follows that the limit of ${{\mathscr C}}$ is again a kernel star, hence a rank-2 limit by Lemma \[rank2lemma\].
End of the proof of Proposition \[standardform\] {#Eop}
------------------------------------------------
By Lemma \[b=c\], we may now assume that $\alpha$ is given by $$\alpha(t)=\begin{pmatrix}
1 & 0 & 0\\
t^a & t^b & 0\\
r(t) & s(t)t^b & t^c
\end{pmatrix}$$ with the usual conditions on $r(t)$ and $s(t)$, and further $a<b<c$.
The limit of ${{\mathscr C}}$ under $\alpha$ is analyzed by studying limits of formal branches.
\[otherbranches\] The limits of formal branches that are not tangent to the line $z=0$ are necessarily $(0:0:1)$-stars. Further, if $a<v(r)$, then the limit of such a branch is the kernel line $x=0$.
\[tangentbranches\] The limit of a formal branch $z=f(y)$ tangent to the line $z=0$ is a $(0:0:1)$-star unless
- $r(t)\equiv f(t^a)\pmod{t^c}$;
- $s(t)\equiv f'(t^a)\pmod{t^{c-b}}$.
The limit of the branch is given by the dominant terms in $$r(t)+s(t)t^by+t^cz=f(t^a)+f'(t^a)t^by+\dots$$ If $r(t)\not\equiv f(t^a)\pmod{t^c}$, then the weight of the branch is necessarily $<c$, so the ideal of the limit is generated by a polynomial in $x$ and $y$, as needed. The same reasoning applies if $s(t)\not\equiv f'(t^a)\pmod{t^{c-b}}$.
To verify the condition on $\frac ca$ stated in Proposition \[standardform\], note that the limit of the formal branch $z=f(y)$ is now given by the dominant term in $$r(t)+s(t) t^b y+t^c z=f(t^a)+f'(t^a)t^b y+\frac{f''(t^a)t^{2b}y^2}2
+\dots:$$ the dominant
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weight will be less than $c$ (causing the limit to be a $(0:0:1)$-star) if $c>2b+v(f''(t^a))=2b+a(\lambda_0-2)$. The stated condition follows at once, completing the proof of Proposition \[standardform\].
Characterization of type V germs {#charaV}
--------------------------------
In the following, we will replace $t$ by a root of $t$ in the germ obtained in Proposition \[standardform\], if necessary, in order to ensure that the exponents appearing in its expression are relatively prime integers; the resulting germ determines the same component of the PNC.
In order to complete the characterization of type V germs given in §\[germlist\], we need to determine the possible triples $a<b<c$ yielding germs contributing components of the PNC. This determination is best performed in terms of $B=\frac ba$ and $C=\frac ca$. Let $$z=f(y)=\sum_{k\ge 0} \gamma_{\lambda_k} y^{\lambda_k}$$ with $\lambda_k\in {{\mathbb{Q}}}$, $1<\lambda_0<\lambda_1<\dots$, and $\gamma_{\lambda_k}\ne 0$, be a formal branch tangent to $z=0$. Every choice of such a branch and of a rational number $C=\frac ca>1$ determines a truncation $$f_{(C)}(y):=\sum_{\lambda_k<C} \gamma_{\lambda_k} y^{\lambda_k}\quad.$$
The choice of a rational number $B=\frac ba$ satisfying $1<B<C$ and $B\ge \frac{C-\lambda_0}2+1$ determines now a germ as prescribed by Proposition \[standardform\]: $$\alpha(t)=\begin{pmatrix}
1 & 0 & 0 \\
t^a & t^b & 0 \\
\underline{f(t^a)} & \underline{f'(t^a) t^b} & t^c\end{pmatrix}$$ (choosing the smallest positive integer $a$ for which the entries of this matrix have integer exponents). Observe that the truncation $\underline{f(t^a)}=f_{(C)}(t^a)$ is identically 0 if and only if $C\le\lambda_0$. Also observe that $\underline{f'(t^a)t^b}$ is determined by $f_{(C)}(t^a)$, as it equals the truncation to $t^c$ of ${(f_{(C)})}'(t^a)t^b$.
\[abc\] If $C\le\lambda_0$ or $B\ne \frac{C-\lambda_0}2+1$, then $\lim_{t\to
0}{{\mathscr C}}\circ\alpha(t)$ is a rank-2 limit.
We deal with the different cases separately.
\[Clelambda0\] I
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=======================================================================
The general second order differentiation $\mathcal{D}^{(m,h)}$ on the ten unknown $C$-functions, denoted as $\mathcal{D}^{(m,h)}_{AB}[\mathbf{C}(u)]$, can be written compactly by putting all $C$-functions together to form a vector $\mathbf{C}(u)$, $$\mathcal{D}^{(m,h)}_{AB}[\mathbf{C}(u)] = (\mathcal{A}_{AB} \partial^2_u
+ \mathcal{B}_{AB}\partial_u + \mathcal{C}_{AB})\cdot
\bigg(C_{TT}(u), \ldots, C_{\Phi u}(u)\bigg)^\text{T}.$$ Here $\mathcal{A}_{AB}$, $\mathcal{B}_{AB}$, and $\mathcal{C}_{AB}$ are covectors whose components are obtained by collecting coefficients in front of $C$-functions. We further stack all the covectors $\mathcal{A}_{AB}$ to form a matrix, and similarly do for $\mathcal{B}_{AB}$ and $\mathcal{C}_{AB}$. We label the resulting coefficient matrices as $\mathcal{A}, \mathcal{B}$, and $\mathcal{C}$ respectively. They are given in Tables \[tab:a-matrix-LEE\], \[tab:b-matrix-LEE\], \[tab:c-matrix-LEE-1\], \[tab:c-matrix-LEE-2\], and \[tab:c-matrix-LEE-3\]. They can also be computed using the companion <span style="font-variant:small-caps;">Mathematica</span> notebook `Sep-met-pert-in-NHEK-Poinc.nb`, or read from the precomputed expressions in `NHEK-precomputed.mx` [@NHEKsupplement].
$$\begin{array}{c|cccccccccc}
\mathcal{D}_{AB} & C_{TT}''(u) & C_{T\Phi }''(u) & C_{\Phi \Phi }''(u) & C_{RR}''(u) & C_{Ru}''(u) & C_{uu}''(u) & C_{TR}''(u) & C_{Tu}''(u) & C_{\Phi R}''(u) & C_{\Phi u}''(u)
\\
\noalign{\smallskip}
\hline \hline \noalign{\smallskip}
\mathcal{D}_{TT} & -\frac{2 \left(u^2-1\right)^2}{\left(u^2+1\right)^3} & \frac{u^6+5 u^4-9 u^2+3}{\left(u^2+1\right)^3} & -\frac{\left(u^4+6 u^2-3\right)^2}{8 \left(u^2+1\right)^3} & \frac{u^6+5 u^4-9 u^2+3}{2 \left(u^2+1\right)^3} & 0 & 0 & 0 & 0 & 0 & 0 \\
\mathcal{D}_{T \Phi} & -\frac{2 \left(u^2-1\right)^2}{\left(u^2+1\right)^3} & \frac{u^6+9 u^4-17 u^2+7}{2 \left(u^2+1\right)^3} & -\frac{u^6+5 u^4-9 u^2+3}{2 \left(u^2+1\right)^3} & \frac{2 \left(u^2-1\right)^2}{\le
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verb15]. The formal API specification covers the IPC, memory, file provider, port, and event, etc.
Formal Verification of Separation Kernels
-----------------------------------------
As introduced in [[[Section]{}]{}]{} \[sec:bg\], the typical properties of separation kernels are data separation, information flow security, fault isolation, and temporal separation. The first three properties are collectively called “spatial separation” properties. Therefore, we categorize formal verification work on separation kernels into spatial and temporal separation verification in this subsection.
### Spatial Separation Verification
Most related work on formally verifying separation kernels consider both the data separation and information flow security. Here, we present significant research work of spatial separation verification. Due to the importance of data separation and information flow security properties for separation kernels, we finally highlight a general verification approach for these properties.
- ED Separation Kenrel
A novel and practical approach to verify security of separation kernels code which substantially reduces the cost of verification is presented in [@Heitmeyer06; @Heitmeyer08]. The objective of this project is to provide evidence for a CC evaluation of the ED (Embedded Devices) separation kernel to enforce data separation. The ED separation kernel contains 3,000 lines of C and assembly code.
The code verification process consists of five steps: (1) Producing a Top-Level Specification (TLS) using a state machine model. (2) Formally expressing the security property as the data separation property of the state machine model. (3) Formally verifying that the TLS enforces data separation in TAME (Timed Automata Modeling Environment), a front end to the PVS theorem prover. (4) Partitioning the code into three categories, in which it is identified as “Other Code” such code not corresponding to any behavior defined by the TLS; “Other Code” is ignored in the verification, therefore great
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rings and dress induction theorem. , 80(1):90–105, 1983.
A. [Z]{}immermann. . , 73(1):15–17, 1999.
[Baptiste Rognerud\
EPFL / SB / MATHGEOM / CTG\
Station 8\
CH-1015 Lausanne\
Switzerland\
e-mail: baptiste.rognerud@epfl.ch]{}
---
author:
-
-
-
bibliography:
- '../bibliography.bib'
title: 'Generating Optimal Privacy-Protection Mechanisms via Machine Learning\'
---
---
abstract: 'Let $R$ be a ring spectrum and $ {\mathcal{E}}\to X$ an $R$-module bundle of rank $n$. Our main result is to identify the homotopy type of the group-like monoid of homotopy automorphisms of this bundle, $hAut^R({\mathcal{E}})$. This will generalize the result regarding $R$-line bundles proven by the authors in [@cjgauge]. The main application is the calculation of the homotopy type of $BGL_n(End (({\mathcal{L}}))$ where ${\mathcal{L}}\to X$ is any $R$-line bundle, and $End ({\mathcal{L}})$ is the ring spectrum of endomorphisms. In the case when such a bundle is the fiberwise suspension spectrum of a principal bundle over a manifold, $G \to P \to M$, this leads to a description of the $K$-theory of the string topology spectrum in terms of the mapping space from $M$ to $BGL (\Sigma^\infty (G_+))$.'
author:
- |
Ralph L. Cohen [^1]\
Department of Mathematics\
Stanford University\
Bldg. 380\
Stanford, CA 94305, USA
- |
John D.S Jones\
Mathematics Institute\
Zeeman Building\
Warwick University\
Coventry, CV4 7AL, UK
title: 'Homotopy automorphisms of $R$-module bundles, and the $K$-theory of string topology'
---
Introduction {#introduction .unnumbered}
============
Let $R$ be a ring spectrum. In several places in the recent literature, the notion of an $R$-module bundle ${\mathcal{E}}\to X$ of rank $n$ has been defined and described [@units], [@5author], [@lind]. This is a parameterized $R$-module spectrum ${\mathcal{E}}$ over $X$, where each fiber $E_x$ admits an $R$-module equivalence $E_x {\xrightarrow}{\simeq} \vee_{n} R$. In analogy to vector bundles, it was proved in [@lind] that eq
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MBE equation with $\lambda>0$ [@Xun; @Luis2019; @Luis2017], for which $\beta\approx 1/3$ and $1/5$ in $d=1$ and $d=2$, respectively[^1], while crossovers to the Edwards-Wilkinson universality class with $\beta=1/4$ in $d=1$ and $\beta=0$ (logarithmic growth) in $d=2$ are expected for the WV model [@wvbogo; @Vvedensky]. The simulations with the kinetic barrier, however, departs from the original dynamics after a transient which increases with the diffusion of particles. For long times, an evolution consistent with an uncorrelated growth [described by $\frac{\partial h}{\partial t}=\eta$, characterized by a growth exponent $\beta=1/2$ [@barabasi], is observed.]{} [This observation can be rationalized as follows. At long times, mounds interact weakly since the kinetic barrier reduces drastically inter-mound diffusion. Consider the idealized case of plateaus of size $L_0$ with an infinity barrier at their edges. A particle initially adsorbed on the top of a plateau will never slide down to its bottom. So, the probability that this plateau receives $R$ particles after one unity of time (deposition of $L$ particles) is a binomial distribution $$P(R)=\binom{L}{R} p^R (1-p)^{L-R}\simeq
\frac{1}{\sqrt{2\pi L_0}} e^{-\frac{(R-L_0)^2}{2L_0}},
\label{eq:PR}$$ where $p=L_0/L$ is the probability that a particle is deposited on this terrace and $1\ll L_0\ll L$ is assumed in the Gaussian limit in right-hand side of Eq. . We argue that this situation is similar to the weakly interacting mound observed in our simulations.]{}
![Characteristic length of mounds $\xi$ for WV (main plots) and DT (insets) models with and without the kinetic barrier in (a) one- and (b) two-dimensional substrates for different values of the parameter $N_s$ indicated in the legend.\[xi\]](xi_wvdt_1d.pdf "fig:"){width="0.8\linewidth"}\
![Characteristic length of mounds $\xi$ for WV (main plots) and DT (insets) models with and without the kinetic barrier in (a) one- and (b) two-dimensional substrates for different values of the parameter $N_s$
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A1c ( % ) (DM only) 7.1 ± 1.5 6.6 ±1.1 6.0 ± 0.4 6.0 ± 0.6
Total cholesterol (mg/dL) 175.3 ± 33.2 161.5 ± 47.9 147.9 ± 26.5 142.5 ± 28.0
HDL (mg/dL) 54.0 ± 15.3 53.6 ± 15.1 52.0 ± 11.6 46.2 ± 6.1
LDL (mg/dL) 93.8 ± 29.4 86.0 ± 33.9 78.1 ± 24.9 84.0 ± 30.7
TG (mg/dL) 154.7 ± 118.4 182.8 ± 241.7 116.0 ± 42.9 105.8 ± 35.8
**Body composition**
Fat % 24.8 ± 5.9 24.7 ± 5.9 24.1 ± 6.5 24.0 ± 7.2
Trunk fat % 12.8 ± 3.0 12.7 ± 3.0 12.4 ± 3.4 12.3 ± 3.7
Muscle % 69.4 ± 5.9 69.5 ± 5.9 70.2 ± 6.4 70.3 ± 7.2
Leg-muscle % 12.8 ± 1.1 12.8 ± 1.2 12.8 ± 1.2 12.9 ± 1.3
Trunk muscle % 34.6 ± 2.9 34.6 ± 2.8 35.1 ± 3.5 35.1 ± 3.7
ASM index 8.29 ± 1.28 8.54 ± 1.85 8.13 ± 1.24 8.08 ± 1.08
Data were expressed as mean ± standard deviation. ASM index, appendicular skeletal muscle mass index; BMI, body mass index.
\* p \< 0.05 compared with baseline.
######
Comparisons of characteristics and body compositions of elderly patients in different protein intake groups at baseline and 1-year follow-up.
Non-low protein group, n = 79 Low protein group, n = 24
--------------------------- ------------------------------- --------------------------- -------------- ------------------
BMI (kg/m^2^) 24.1 ± 3.1 23.9 ± 3.1
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me beyond numerical tolerance. With this in mind, it is interesting to see which features are found when the quantum-classical theory of Refs. [@qc-bracket; @kcmqc] is mapped onto a scheme of motion where phase space dependent wave fields, instead of operators, are used to represent the dynamics.
As it is well known [@ballentine], in standard quantum mechanics, the correspondence between dynamics in the Heisenberg and in the Schrödinger picture rests ultimately on the following operator identity: $$e^{\hat{Y}}\hat{X}e^{-\hat{Y}}=e^{[\hat{Y},\ldots]}\hat{X}\;,
\label{eq:expid}$$ where $[\hat{Y},\ldots]\hat{X}\equiv [\hat{Y},\hat{X}]$. Thus, in quantum-classical theory, one would like to derive an operator identity analogous to that in Eq. (\[eq:expid\]). However, as already shown in Ref. [@qc-stat], because of the non associativity of the quantum-classical bracket in Eq. (\[qclm\]), the identity that can be derived is $$\begin{aligned}
e^{\frac{it}{\hbar}~\left[\hat{H},
\ldots\right]_{\mbox{\tiny\boldmath$\cal D$}}}
\hat{\chi}&=&
{\cal S}\left(
e^{\frac{it}{\hbar}\overrightarrow{\mathcal H}}\hat{\chi}
e^{-\frac{it}{\hbar}\overleftarrow{\mathcal H}}\right)\;,
\label{eq:qc-ope-ide}\end{aligned}$$ where the two operators $$\begin{aligned}
\overrightarrow{\mathcal H}&=&\hat{H}
-\frac{\hbar}{2i}
\left\{\hat{H},\ldots\right\}_{\mbox{\tiny\boldmath$\cal B$}}
\label{eq:hright}\\
\overleftarrow{\mathcal H}&=&\hat{H}
-\frac{\hbar}{2i}
\left\{\ldots,\hat{H}\right\}_{\mbox{\tiny\boldmath$\cal B$}}
\label{eq:hleft}\end{aligned}$$ have been introduced and $\cal S$ is an ordering operator which is chosen so that the left and the right hand side of Eq. (\[eq:qc-ope-ide\]) coincide by construction [@qc-stat], when the exponential operators are substituted with their series expansion. The existence of such an ordering problem, and of the ordering operator $\cal S$, in Eq. (\[eq:qc-ope-ide\]) is caused by the Poisson bracket parts of the operators in Eqs. (\[eq:hright\]) and (\[eq:hleft\]). Hence, one can imagine that t
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^ = 233.99 (between trial variation in β)
\(viii\) σ ^2^ = 333.74 (residual variance)
**A1** Same as base case, except changed (i) K = 5
**A2** Same as base case, except changed (i) K = 20
**B1** Same as base case, except changed (ii) n ~i~ ∼U(30, 1000)
**B2** Same as base case, except changed (ii) n ~i~ ∼U(30, 100) for trials 1 to 5,
n ~i~ ∼U(900, 1000) for trials 6 to 10
**B1‐A1** Same as base case, except changed (i) and (ii) K = 5 and n ~i~ ∼U(30, 1000)
**B1‐A2** Same as base case, except changed (i) and (ii) K = 20 and n ~i~ ∼U(30, 1000)
**B2‐A1** Same as base case, except changed (i) and (ii) n ~i~ ∼U(30, 100) for trials 1 and 2, n ~i~ ∼U(900, 1000) for trials 3 to 5
**B2‐A2** Same as base case, except changed (i) and (ii) n ~i~ ∼U(30, 100) for trials 1 to 10, n ~i~ ∼U(900, 1000) for trials 11 to 20
**B3** Same as base case, except changed (ii) n ~i~ ∼U(30, 100)
**C1** Same as base case, except changed (vii) Halving τ ~β~ ^2^ to 117
**C2** Same as base case, except changed (vii) Doubling τ ~β~ ^2^ to 468
**D1** Same as base case, except changed (v) Halving τ ^2^ to 3.9
**D2** Same as base case, except changed (v)
| 466
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indicated in the legend.\[xi\]](xi_wvdt_2d.pdf "fig:"){width="0.8\linewidth"}
In addition, as can be seen in Fig. \[xi\], the characteristic lateral lengths of simulations with kinetic barrier saturate after an initial transient in values that increase with the parameter $N_s$ while the models without barrier present coarsening with $\xi\sim t^{1/z}$ [@barabasi]. The saturation implies that the aspect ratio (height/width) of the mounds remains increasing with time and the surface does not present slope selection forming columnar growth. This property is also reflected in the asymptotic interface width scaling as $w\sim t^{1/2}$. As explained previously, it can be interpreted as an uncorrelated evolution of the columns, in which the 1/2 exponent comes out. The results shown in the insets of Figs. \[width\] and \[xi\] corroborate that the DT model presents the same behavior of the WV model despite of the mounds are less evident in the former.
![\[current\_1d\] Evolution of the out-of-plane current for (a) WV and (b) DT models grown in one-dimensional substrates. Models with the kinetic barrier using $N_s =1$, $2$ and $10$ steps (indicated in the legend) and the original version are shown. ](jz_wv1d.pdf "fig:"){width="0.8\linewidth"}\
![\[current\_1d\] Evolution of the out-of-plane current for (a) WV and (b) DT models grown in one-dimensional substrates. Models with the kinetic barrier using $N_s =1$, $2$ and $10$ steps (indicated in the legend) and the original version are shown. ](jz_dt1d.pdf "fig:"){width="0.8\linewidth"}
Instability and mound formation can be investigated considering the surface currents [@Siegert1994; @Krug1993]; see [@Krug1997] for details. In this work, we investigated the out-of-plane component of the current defined as [@Leal_Jstat] $$J_z = \frac{1}{N}\sum_{(i,j)} \mathrm{sgn}(\delta h) D(i,j) P_{\delta h}(i,j)$$ where $\mathrm{sgn}(x)=1$ for $x>0$, $\mathrm{sgn}(x)=-1$ for $x<0$, and $\mathrm{sgn}(0)=0$ is the definition of sign function, $P_{\delta h}(i,j)$ is given by Eq. , and
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l{L}_{Q}^{P}$
-------------------------------------------------------
The notion of justification introduced in Sec. 3.2 is basic in our approach and must be clearly understood. So we devote this section to comments on it.
Whenever an elementary af $\vdash E(x)$ of $\mathcal{L}_{Q}^{P}$ is considered, the notion of justification obviously coincides with the notion of existence of an empirical proof of the truth of $E(x)$ because of assumption A$_{5}$ and proposition P in Sec. 3.2, which fits in with JR$_{1}$ in Sec. 3.1.
Whenever molecular afs of $\mathcal{L}^{P}$ are considered, one can grasp intuitively the meaning of the notion of justification for them by considering simple instances. Indeed, let $E(x)$ be a rf and let $x$ be in the state $S$. We get
$\pi _{S}(N\vdash E(x))=J$ iff $S\in \mathcal{S}_{E}^{\bot }$,
which means, shortly, that it is justified to assert that $E(x)$ cannot be asserted iff MQ entails that the truth value of $E(x)$ is *false* for every $x$ in the state $S$. This result, of course, fits in with JR$_{2}$ in Sec. 3.1.
Furthermore, let $E(x)$ and $F(x)$ be rfs, and let $x$ be in the state $S$. We get
$\pi _{S}(\vdash E(x)K\vdash F(x))=J$ iff $S\in \mathcal{S}_{E}\cap \mathcal{S}_{F}$,
$\pi _{S}(\vdash E(x)A\vdash F(x))=J$ iff $S\in \mathcal{S}_{E}\cup \mathcal{S}_{F}$.
The first equality shows that asserting $E(x)$ and $F(x)$ conjointly is justified iff both assertions are justified. The second equality shows that asserting $E(x)$ or asserting $F(x)$ is justified iff one of these assertions is justified. Both these results, of course, fit in with JR$_{3}$ in Sec. 3.1.
We add that
$\pi _{S}(\vdash E(x))=J$ implies $\pi _{S}(N\vdash E(x))=U$
and
$\pi _{S}(N\vdash E(x))=J$ implies $\pi _{S}(\vdash E(x))=U$
since $\mathcal{S}_{E}\cap \mathcal{S}_{E}^{\bot }=\emptyset $. Nevertheless,
$\pi _{S}(\vdash E(x))=U$ and $\pi _{S}(N\vdash E(x))=U$ iff $S\notin
\mathcal{S}_{E}\cup \mathcal{S}_{E}^{\bot }$,
which shows that a *tertium non datur* principle does not hold for the pragmati
| 468
| 1,047
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ed a nonprincipal ultrafilter.
[^2]: Our terminology should not be confused with that of a hypergraph—an entirely different concept [@be].
[^3]: If $G$ were a finite graph, then every hypernode (resp. hyperbranch) could be identified with a node (resp. branch)in $G$, and $^{*}\!G$ would be identified with $G$.
[^4]: For examples of when a 0-walk is needed because a 0-path won’t do, see Figures 3.1 and 3.2 of [@tgen] and Figures 4.1, 5.1, 5.2, and 5.3 of [@gn].
[^5]: We write “wdistance” to distinguish this walk-based idea from a distance based on paths.
[^6]: Note that a 0-section in a locally 1-finite 1-graph may have infinitely many incident 1-nodes that are not boundary 1-nodes. Also, this definition of locally 1-finiteness does not prohibit 0-nodes of infinite degree.
---
abstract: 'Due to its interaction with the virtual electron-positron field in vacuum, the photon exhibits a nonzero anomalous magnetic moment whenever it has a nonzero transverse momentum component to an external constant magnetic field. At low and high frequencies this anomalous magnetic moment behaves as paramagnetic, and at energies near the first threshold of pair creation it has a maximum value greater than twice the electron anomalous magnetic moment. These results might be interesting in an astrophysical and cosmological context.'
author:
- 'S. Villalba-Chávez$^{\dag\ddag}$ and H. Pérez-Rojas$^{\ddag}$'
date: 'July, $21 \ \ 2006$'
title: 'Has the Photon an Anomalous Magnetic Moment?'
---
It was shown by Schwinger[@Schwinger] in 1951 that electrons get an anomalous magnetic moment $\mu^\prime=\alpha/2\pi\mu_B$ (being $\mu_B=e\hbar/2m_0c$ the Bohr magneton) due to radiative corrections in quantum electrodynamics (QED), that is, due to the interaction of the electron with the background virtual photons and electron-positron pairs. We want to show that also, due to the interaction with the virtual quanta of vacuum, an anomalous photon magnetic moment arises. It is obtained from the expression for the photon self-energy i
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scription of an element of $\underline{M}(R)$. Note that $$\left \{ \begin{array}{l}
\delta_{i-1}v_{i-1}\cdot (m_{i-1, i}m_{i,i}')+\delta_{i+1}v_{i+1}\cdot (m_{i+1, i}m_{i,i}')=\pi m_{i,i}^{\ast}\cdot m_{i,i}';\\
\delta_{i-1}v_{i-1}\cdot (m_{i-1, i-1}m_{i-1,i}')+\delta_{i+1}v_{i+1}\cdot (m_{i+1, i+1}m_{i+1,i}')
=\pi (m_{i,i}^{\ast})'+\pi \tilde{z}_i''^{\dag\dag}
\end{array} \right.$$ for some formal expansion $\tilde{z}_i''^{\dag\dag}$. Therefore, $$\delta_{i-1}v_{i-1}\cdot \tilde{m}_{i-1, i}''+\delta_{i+1}v_{i+1}\cdot \tilde{m}_{i+1, i}''=
\pi\left(m_{i,i}^{\ast}\cdot m_{i,i}'+(m_{i,i}^{\ast})'+ \tilde{z}_i''^{\dag\dag}+\tilde{z}_i''^{\dag} \right).$$ Then $$(m_{i,i}^{\ast})''=m_{i,i}^{\ast}\cdot m_{i,i}'+(m_{i,i}^{\ast})'+ \tilde{z}_i''^{\dag\dag}+\tilde{z}_i''^{\dag}$$ as an equation in $B\otimes_AR$.\
7. Assume that $i$ is odd and $L_i$ is *bound of type I*. Then the following formal sum $$\delta_{i-1}v_{i-1}\cdot {}^t\tilde{m}_{i, i-1}''+\delta_{i+1}v_{i+1}\cdot {}^t\tilde{m}_{i, i+1}''$$ equals $$\delta_{i-1}v_{i-1}\cdot ({}^tm_{i,i-1}'\cdot {}^tm_{i, i} +{}^tm_{i-1,i-1}'\cdot {}^tm_{i, i-1})+
\delta_{i+1}v_{i+1}\cdot ({}^tm_{i,i+1}'\cdot {}^tm_{i, i}+ {}^tm_{i+1,i+1}'\cdot {}^tm_{i, i+1})+\pi \tilde{z}_i''^{\dag}=$$ $$\left(\delta_{i-1}v_{i-1}\cdot ({}^tm_{i,i-1}'\cdot {}^tm_{i, i})+\delta_{i+1}v_{i+1}\cdot ({}^tm_{i,i+1}'\cdot {}^tm_{i, i})\right)+$$ $$\left(\delta_{i-1}v_{i-1}\cdot ({}^tm_{i-1,i-1}'\cdot {}^tm_{i, i-1})+\delta_{i+1}v_{i+1}\cdot ({}^tm_{i+1,i+1}'\cdot {}^tm_{i, i+1})\right)
+\pi \tilde{z}_i''^{\dag}$$ for some formal expansion $\tilde{z}_i''^{\dag}$. Here, $\delta_{j}v_{j}$ is as explained in Step (e) of the above description of an element of $\underline{M}(R)$. Note that $$\left \{ \begin{array}{l}
\delta_{i-1}v_{i-1}\cdot ({}^tm_{i,i-1}'\cdot {}^tm_{i, i})+\delta_{i+1}v_{i+1}\cdot ({}^tm_{i,i+1}'\cdot {}^tm_{i, i})
=\pi (m_{i,i}^{\ast\ast})'\cdot {}^tm_{i, i};\\
\delta_{i-1}v_{i-1}\cdot ({}^tm_{i-1,i-1}'\cdot {}^tm_{i, i-1})+\delta_{i+1}v
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X/I(Z)$ as an ${{\mathcal O}}_V$-module then $r_i\in {{\mathcal O}}_X$ and $I(Z)$ generate ${{\mathcal O}}_X$ as a $q^{-1}({{\mathcal O}}_V)$-module. Since $I(Z)\subset q^{-1}(S)$, we obtain that $r_i\in {{\mathcal O}}_X$ and $1\in {{\mathcal O}}_X$ generate ${{\mathcal O}}_X$ as a $q^{-1}(S)$-module. Applying (\[eak-nag\]) to $R_1={{\mathcal O}}_X$ and $R_2=q^{-1}({{\mathcal O}}_V)$ gives the rest.
For the proof of the following result, see [@mats-cr Thm.3.7] and the proof of (\[inv.of.fin.gps\]).
\[eak-nag\] Let $R_1\supset R_2$ be $A$-algebras with $A$ Noetherian. Assume that $R_1$ is finite over $R_2$.
1. If $R_1$ is Noetherian then so is $R_2$.
2. If $R_1$ is a finitely generated $A$-algebra then so is $R_2$.
Gluing for algebraic spaces, following [@raoult], is easier than the quasi projective case.
\[pf.of.glue.thm.asp\] For every $p\in V$ we construct a commutative diagram $$\begin{array}{ccccc}
V_p & \stackrel{g_p}{\leftarrow} & Z_p & \to & X_p\\
\tau_V\downarrow\hphantom{\tau_V} &&
\hphantom{\tau_Z}\downarrow\tau_Z &&\hphantom{\tau_X}\downarrow\tau_X \\
V & \stackrel{g}{\leftarrow} & Z & \to & X
\end{array}$$ where
1. $V_p, Z_p, X_p$ are affine,
2. $g_p$ is finite and $Z_p \to X_p$ is a closed embedding,
3. $V_p$ (resp. $Z_p, X_p$) is an étale neighborhood of $p$ (resp. $g^{-1}(p)$) and
4. both squares are fiber products.
Affine gluing (\[glue.lem.affine\]) then gives $Y_p:=X_p/(Z_p\to V_p)$ and (\[glue.etloc.lem\]) shows that the $Y_p$ are étale charts on $Y=X/(Z\to V)$.
Start with affine, étale neighborhoods $V_1\to V$ of $p$ and $X_1\to X$ of $g^{-1}(p)$. Set $Z_1:=Z\times_XX_1\subset X_1$. By (\[et.nbhds.say\]) we may assume that there is a (necessarily étale) morphism $Z\times_VV_1\to Z_1$. In general there is no étale neighborhood $X'\to X_1$ extending $Z\times_VV_1\to Z_1$, but there is an affine, étale neighborhood $X_2\to X_1$ extending $Z\times_VV_1\to Z_1$ over a Zariski neighborhood of $g^{-1}(p)$ (\[et.nbhds.say\]).
Thus we have affine, étale neighborhoods $V_
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|
�Yes 312 85 (27.2)
No 227 (72.8)
Secondhand smoke exposure
No 225 (70.3)
In-house 320 70 (21.9)
Out-house 25 (7.8)
SD: standard deviation.
Numbers vary due to missing data
median with interquartile range.
A total of 383 infants were followed up, and 124 infants dropped out during follow-up. The differences among these infants were in the maternal vitamin A level (*p*=0.01) and caregiver (mother or other individual) (*p*\<0.0001) ([Table 3](#T0003){ref-type="table"}).
######
Comparison of followed-up and non-followed-up population[a](#TF0004){ref-type="table-fn"}
Total Follow-up loss (*n*=124) Followed up (*n*=383)
------------------------------------------------------ ------- -------------------------- -----------------------
Mothers
Vitamin A (µg/dL)[\*](#TF0005){ref-type="table-fn"}
Low 135 44 (37.3) 91 (24.9)
High 349 74 (62.7) 275 (75.1)
Vitamin C (µg/mL)
Low 340 75 (69.4) 265 (75.1)
High 121 33 (30.6) 88 (24.9)
Vitamin E (µg/dL)
Low 367 93 (7
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closed. I cannot change any code on the PLC.
But when I stop the VisualStudio debugger (Shift+F5) while the connection is active, it is closed correctly. What is VisualStudio doing differently?
Edit:
These 2 lines are captured by wireshark additionally when I stop the program by Shift+F5
Edit 2:
I have a thread that reads data:
while (m_runListener)
{
int cnt = m_reader.Read(buffer, 0, 1024);
if (cnt > 0)
{
// handle data
}
}
When I close the program, I cannot stop the thread without calling Thread.Abort();
If I delete the blocking call m_reader.Read(buffer, 0, 1024); just for testing, the disconnect works.
A:
I finally found the solution to my problem here:
http://sysperf.yingyuhsieh.com/2007/08/force-tcp-closed-by-sending-rst-c.html
Normally the TCP connection is closed as follows:
The client sends FIN to the server and the server responds with ACK
The server sends FIN to the client and the client responds with ACK
In my case the second step was missing.
I needed to force that a RST packet was sent. This can be done by the following code:
m_socket.Send(new byte[1]);
m_socket.Shutdown(SocketShutdown.Receive);
Q:
Access private method or Variable in Test Class
I want to access Private Method or Variable in Test class.??
A:
Read about and use the @TestVisble annotation.
From the documentation:
Use the TestVisible annotation to allow test methods to access private
or protected members of another class outside the test class. These
members include methods, member variables, and inner classes. This
annotation enables a more permissive access level for running tests
only. This annotation doesn’t change the visibility of members if
accessed by non-test classes.
Q:
Insert removes backslash
With Entity Framework I'm inserting a json string with all quotes escaped.
For example: "{\"PDFName\":\"Test \",\"PDFDesc\":\"test desc\"}"
Somehow the backslashes are getting removed from my string before the insert and the value in the database is:
"{"PDFName":"Test ","PDFD
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|
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|
llowing two formal equations: $$\left\{
\begin{array}{l}
(\tilde{z}_i)_1+ \delta_{i-2}(\tilde{k}_{i-2, i})_1+\delta_{i+2}(\tilde{k}_{i+2, i})_1=2 (\tilde{z}_i^{\ast})_2;\\
(\tilde{z}_i)_2+ \delta_{i-2}(\tilde{k}_{i-2, i})_2+\delta_{i+2}(\tilde{k}_{i+2, i})_2= (\tilde{z}_i^{\ast})_1.
\end{array} \right.$$ Using these, the sum of $\mathcal{F}_{j-2l}(\tilde{m})$ is the following: $$\begin{gathered}
\label{ea31}
\sum_{l=0}^{m_j}\mathcal{F}_{j-2l}(\tilde{m})=\sum_{l=0}^{m_j}\left((\tilde{z}_{j-2l}^{\ast})_1+(\tilde{z}_{j-2l}^{\ast})_1^2 \right)+\\
\left({}^t(\tilde{m}_{j-2m_j-1, j-2m_j}')_1\cdot h_{j-2m_j-1}\cdot (\tilde{m}_{j-2m_j-1, j-2m_j}')_2+{}^t(\tilde{m}_{j+1, j}')_1\cdot h_{j+1}\cdot (\tilde{m}_{j+1, j}')_2\right)+\\
\frac{1}{2}\left({}^t(\tilde{m}_{j-2m_j-2, j-2m_j})_1'\cdot a_{j-2m_j-2}\cdot (\tilde{m}_{j-2m_j-2, j-2m_j})_1'+{}^t(\tilde{m}_{j+2, j})_1'\cdot a_{j+2}\cdot (\tilde{m}_{j+2, j})_1'\right)\\
+ \left(\delta_{j-2m_j-3}'(\tilde{k}_{j-2m_j-3, j-2m_j})_1^2+ \delta_{j+3}'(\tilde{k}_{j+3, j})_1^2\right)+
\left(\delta_{j-2m_j-4}(\tilde{k}_{j-2m_j-4, j-2m_j})_1^2+ \delta_{j+4}(\tilde{k}_{j+4, j})_1^2\right)+\\
\sum_{\textit{$L_{j-2l}$ : of type $I^e$,
$l=0$}}^{m_j}\bar{\gamma}_{j-2l}\left((\tilde{x}_i)_1^2+1/2\cdot{}^t(\tilde{r}_i)_1a_i(\tilde{r}_i)_1+
\left(\delta_{i-2}(\tilde{m}_{i-2, i}^{\natural})_1^2+\delta_{i+2}(\tilde{m}_{i+2, i}^{\natural})_1^2\right)\right).\end{gathered}$$ Here, $(\tilde{m}_{i\pm 2, i}^{\natural})_1$ is as explained in the above Step (5). Note that both $(\tilde{m}_{j-2m_j-1, j-2m_j}')_1$ and $(\tilde{m}_{j+1, j}')_1$ are zero in $R$ because of Condition (f) of the description of an element of $\tilde{M}(R)$ given at the paragraph following Lemma \[la1\] since $L_{j-2m_j-2}$ and $L_{j+2}$ are *of type II*.
The proof of the above $\sum_{l=0}^{m_j}\mathcal{F}_{j-2l}$ is basically similar to that of Lemma A.7 of [@C2] and we skip it. It is mainly based on Equation (\[ea2\]), especially when $j-i=1\textit{
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|
lative to the plane, that is above the plane.
What I tried was taking a simple two dimensional matrix:
a =
1 1 1
1 1 1
and tried replacing the ones in the second column with zeros, which I did by typing a(:,2)=0, and matlab gave me
a =
1 0 1
1 0 1
I then tried to generalize this to a 3 dimensional matrix, but ran into some difficulty. Could someone help me?
A:
I assume you want to set the 2nd component of a 3 dimensional matrix to zero.
You can do this in the same way as you do for 2 dimensional case.
A = ones(3,3,3) % Never use For Loops the way you did for operating on matrices.
A(:,2,:) = 0
Q:
python sort 2D dictionary by index
I have a 2D dictionary as follows
dict = {'182.12.17.50': {'185.23.15.69': 30, '175.12.13.14': 14}, '182.15.12.30': {'175.12.13.15': 10, '145.33.34.56': 230}}
I want to sort that based on the value such that the out put looks like
[{IP1: '182.15.12.30', IP2: '175.12.13.15', val:10}, {IP1: '182.12.17.50', IP2: '175.12.13.14', val:14}, ...]
I am a newbie in python. I have written an ugly code for that. Is there any nice way to implement that?
Thanks,
A:
You can use a generator expression and the built-in sorted:
sorted(({'IP1': ip1, 'IP2': k, 'val':v}
for ip1,subdct in dct.items()
for k,v in subdct.items()),
key=lambda newd: newd['val'])
By the way, it's a bad idea to use dict as the name of a variable, as doing so overshadows the built-in dict. Therefore, I renamed the variable to dct.
Q:
SQL return optimal value if
I'm working with a database in which a table like the one below appears.
StudentNum | Coin
-------------+------------
1 | Heads
1 | Tails
3 | Tails
3 | Tails
2 | Heads
3 | Tails
I do not have permissions to add or adjust the table, and need to know if it's possible to control the conditions on which rows are populated when I join this to another table.
Specifically, I am tryin
| 475
| 6,335
| 105
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| 1,166
| 0.793306
|
github_plus_top10pct_by_avg
|
and *uidA* integration. Sample sizes used exceeded the minimum required to statistically represent the population at 95% confidence with an acquired precision error of ≤3%. The PMTF frequencies obtained from analyzing GUS expression in seedlings were 2.86% in 2005 and 1.39% in 2006 ([Table 3](#pone-0025810-t003){ref-type="table"}). Moreover, PCR analyses confirmed, at the molecular level, the transgenic nature of all GUS-positive seedlings and dismissed the presence of transgene-silencing in GUS-negative seedlings without exception ([Table 3](#pone-0025810-t003){ref-type="table"}). When comparing these results with those obtained previously for GUS expression in seeds in the same years ([Table 1](#pone-0025810-t001){ref-type="table"}), a χ^2^-test showed no statistically significant differences between the frequencies for either of the two years at the 95% confidence level, indicating that the hybrid seed identification system used during the seven years of assessment to determine PMTF frequency was reliable.
10.1371/journal.pone.0025810.t003
###### Molecular validation of the pollen-mediated transgene flow (PMTF) assessment method by testing seedlings from a subset of open-pollinated recipient trees during two years (2005 and 2006).
{#pone-0025810-t003-3}
Year clementine number Number of seedlings PMTF (%)[2](#nt102){ref-type="table-fn"} χ^2^ value[3](#nt103){ref-type="table-fn"}
---------- ------------------- --------------------- ------------------------------------------ -------------------------------------------- ---------- -----------
**2005** 2 21 0 13
8 21 1 0
14 3 0
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| 1,703
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|
bel{13}
\pi b_i'=-\pi^2 \cdot{}^tv_i'+\pi^2\cdot a_iy_i'.$$ By letting $b_i'=b_i=0$, we have $$-\pi \cdot{}^tv_i'+\pi \cdot a_iy_i'=0$$ as an equation in $B\otimes_AR$. Thus there are exactly $(n_i-1)$ independent linear equations among the entries of $v_i'$ and $y_i'$ and the entries of $v_i'$ determine all entries of $y_i'$.
3. We postpone to consider the $(2, 2)$-block later in Step (vi).\
By combining two cases (a) and (b), there are exactly $((n_i-1)^2-(n_i-1))/2+(n_i-1)=n_i(n_i-1)/2$ independent linear equations. Thus $n_i^2-1-n_i(n_i-1)/2=n_i(n_i+1)/2-1$ entries of $m_{i,i}'$ determine all entries of $m_{i,i}'$ except for $z_i'$ and $(z_i^{\ast})'$.\
5. Assume that $i$ is even and that $L_i$ is *of type $I^e$*. Then
$\pi^ih_i=\xi^{i/2}\begin{pmatrix} a_i&{}^tb_i&\pi e_i\\ \sigma(b_i) &1+2f_i&1+\pi d_i \\ \sigma(\pi \cdot {}^te_i) &\sigma(1+\pi d_i) &2\bar{\gamma}_i+4c_i \end{pmatrix}$ as explained in Section \[h\] and thus we have $$\begin{gathered}
\label{ea13}
\begin{pmatrix} a_i'&{}^tb_i'&\pi e_i'\\ \sigma(b_i') &1+2f_i'&1+\pi d_i' \\
\sigma(\pi \cdot {}^te_i') &\sigma(1+\pi d_i') &2\bar{\gamma}_i+4c_i' \end{pmatrix}=\\
\sigma(1+\pi\cdot {}^tm_{i,i}')\cdot
\begin{pmatrix} a_i&{}^tb_i&\pi e_i\\ \sigma(b_i) &1+2f_i&1+\pi d_i \\ \sigma(\pi \cdot {}^te_i) &\sigma(1+\pi d_i) &2\bar{\gamma}_i+4c_i \end{pmatrix}
\cdot(1+\pi m_{i,i}')+\pi^3(\ast).\end{gathered}$$ Here, the nondiagonal entries of $a_i'$ as well as the entries of $b_i', e_i', d_i'$ are considered in $B\otimes_AR$, each diagonal entry of $a_i'$ is of the form $2 x_i$ with $x_i\in R$, and $c_i', f_i'$ are in $R$. In addition, $b_i=0, d_i=0, e_i=0, f_i=0, c_i=0$ as explained in Remark \[r33\].(2) and $a_i$ is the diagonal matrix with $\begin{pmatrix} 0&1\\1&0\end{pmatrix}$ on the diagonal.
Note that in this case, $m_{i,i}'=\begin{pmatrix} s_i^{\prime}& r_i^{\prime}&\pi t_i^{\prime}\\ \pi y_i^{\prime}&\pi x_i^{\prime}&\pi z_i^{\prime}\\ v_i^{\prime}& u_i^{\prime}&\pi w_i^{\prime} \end{pmatrix}
| 477
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|
* = 23; 50% of CU participants). Itch-related sleep disturbances were regarded by 18 patients (39% of the group). Ten of them reported more than 3 awakenings during one night.
The quality of life results (expressed as converted scores) are presented in [Table 1](#t0001){ref-type="table"}. Of note, subscales itching and embarrassment were the most severely affected.
######
Quality of life in the study group (CU-Q2oL subscales)
CU-Q2oL Mean Median 25--75% values
------------------------ ------- -------- ----------------
Itching 60.22 60.00 40.00--70.00
Swelling/mental status 49.39 48.00 36.00--60.00
Functioning 41.45 33.34 20.00--56.67
Sleep 51.63 52.50 30.00--70.00
Eating/limits 49.67 47.50 30.00--60.00
Embarrassment 62.61 70.00 40.00--80.00
Disease severity positively correlated with global itch score (*r* = 0.35, *p* \< 0.05), itch intensity (*r* = 0.33, *p* \< 0.05) and range (*r* = 0.33, *p* \< 0.05). Regarding psychological parameters, higher CU activity was associated with a higher stress level (VAS scale -- *r* = 0.31, *p* \< 0.05; SRRS -- *r* = 0.33, *p* \< 0.05) and worse QoL (all dimensions). The strongest correlations were observed between disease severity and subscales itching (*r* = 0.61, *p* \< 0.001) and functioning (*r* = 0.48, *p* \< 0.05).
Any further relations, thus between age, disease duration and psychological variables were not revealed (*p* \> 0.05).
Stress, itch and quality of life -- correlations {#sec4.3}
------------------------------------------------
We did not note any statistically significant correlations between stress (both scales) and itch (and its features). Regarding the global itch score, all CU-Q2oL dimensions were affected, except for subscale swelling/mental status (results shown in [Table 2](#t0002){ref-type="table"}).
######
The correlations between itch and CU-Q2oL
CU-Q2oL Itch characteristics
| 478
| 859
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| 579
| null | null |
github_plus_top10pct_by_avg
|
j-k_j+1},$ $L_{j-k_j-1},$ $L_{j-k_j-2},$ $L_{j-k_j-3}$) are *of type II* if $j-k_j$ is even (resp. odd).
We denote $\mathcal{X}_{i,2,2}-\bar{\gamma}_i$ by $\mathcal{F}_{i}$ when $i$ is odd and $L_i$ is *free of type I* (cf. Equation (\[24’\])), and denote $\mathcal{X}_{i,2,2}$ by $\mathcal{E}_{i}$ when $i$ is even and $L_i$ is *of type $I^e$* (cf. Equation (\[ea27\])). Then, based on Equations (\[24’\]) and (\[ea32\]) and $\mathcal{X}_{i,2,2}$ in Equation (\[ea27\]), the sum of equations $$\sum_{l=0}^{k_j}\mathcal{F}_{j-l}(m)+
\sum_{\textit{ $L_{j-l}$ : type $\textit{I}^e$, }l=0}^{k_j}
\bar{\gamma}_{j-l} \cdot \mathcal{E}_{j-l}(m)$$ equals $$\begin{gathered}
\label{32'}
\sum_{l=0}^{k_j}\left(z_{j-l}^{\ast}+(z_{j-2l}^{\ast})^2 \right)+
\sum_{l=0}^{k_j}
\left(\bar{\gamma}_{j-l}u_{j-l}^{\ast}+(\bar{\gamma}_{j-l}u_{j-l}^{\ast})^2\right)=\\
\left(\sum_{l=0}^{k_j}z_{j-l}^{\ast}+\sum_{l=0}^{k_j}
\bar{\gamma}_{j-l}u_{j-l}^{\ast} \right)
\left(\left(\sum_{l=0}^{k_j}z_{j-l}^{\ast}+\sum_{l=0}^{k_j}
\bar{\gamma}_{j-l}u_{j-l}^{\ast}\right)+1\right)=0.\end{gathered}$$
Here, $$z_{j-l}^{\ast} = \left\{
\begin{array}{l l}
z_{j-l}^{\ast} & \quad \textit{if $j-l$ is even and $L_{j-l}$ is \textit{of type I}};\\
z_{j-l} & \quad \textit{if $j-l$ is odd and $L_{j-l}$ is \textit{free of type I}};\\
0 & \quad \textit{otherwise},
\end{array} \right.$$ and $$u_{j-l}^{\ast} = \left\{
\begin{array}{l l}
u_{j-l} & \quad \textit{if $j-l$ is even and $L_{j-l}$ is \textit{of type $I^e$}};\\
0 & \quad \textit{otherwise}.
\end{array} \right.$$
The proof of the above is also basically similar to that of Lemma A.7 in [@C2] and we skip it. It is mainly based on Equation (\[ea20\]), especially when $j-i=2\textit{ or }3$.\
Let $G^{\ddag}$ be the subfunctor of $ \mathrm{Ker~}\tilde{\varphi}/\tilde{M}^1$ consisting of those $m$ satisfying Equations (\[ea20\]), (\[ea22\]), (\[24\]), (\[24’\]),
| 479
| 3,391
| 734
| 378
| null | null |
github_plus_top10pct_by_avg
|
.33 −32.61
**B2‐A2** −36.66 −4.98 −14.36 −5.39 −50.99 −4.84 −12.86 −5.35
**B3** −100.00 −28.68 −61.86 −24.74 −100.00 −17.42 −81.05 −48.75
**C1** −100.00 −16.72 −39.54 −14.38 n/a n/a n/a n/a
**C2** −100.00 −16.86 −40.56 −15.94 n/a n/a n/a n/a
**D1** −100.00 −19.20 −66.97 −24.63 −100.00 −33.67 −99.98 −62.07
**D2** −100.00 −11.65 −30.04 −11.79 −100.00 −10.50 −37.84 −22.19
See Table [1](#sim7930-tbl-0001){ref-type="table"} for full data generation details relating to each scenario. True value for is 7.79, except scenarios D1 and D2 where is equal to 3.9 and 15.6, respectively.
n/a = not applicable, since there is no τ ~β~ ^2^ to vary when a beta distribution is used for the intercept data generating mechanism. Options: ML, maximum likelihood estimation; REML, restricted maximum likelihood estimation.
{ref-type="fig"}A) and beta distributions (Figure [2](#sim7930-fig-0002){ref-type="fig"}B) for the intercept data generating mechanisms, for stratified (left) and random (right) intercept models, under each of th
| 480
| 1,202
| 1,289
| 630
| 1,667
| 0.78702
|
github_plus_top10pct_by_avg
|
mber of hypermultiplets is 27. Clearly $n_H - n_V \neq 244$, so this model is anomalous in six dimensions.
Potential refinements of anomaly cancellation {#sect:possible-anomcanc}
---------------------------------------------
So far we have described some consistent (0,2) SCFT’s of the class III form, and also illustrated in detail how theories of this form cannot be consistently used in supersymmetric heterotic string compactifications. This begs the question of whether there exists a criterion, perhaps a generalization of anomaly cancellation, that can be used to distinguish theories of this form. In this section, we will examine one such possibility.
In appendix \[app:chern-reps\] we describe a modified notion of Chern classes and characters, labelled $c^{\rm rep}$ and ${\rm ch}^{\rm rep}$, that contain extra information in twisted sectors. It is tempting to speculate that one might be able to use these to obtain additional finite-group anomaly constraints on theories by demanding matching ${\rm ch}_2^{\rm rep}$’s. Let us check this by studying GLSM’s, for which anomaly cancellation conditions are more or less well understood. We will argue that although ${\rm ch}^{\rm rep}$’s play a vital role in index theory, confusingly they do not seem to define any new anomaly-cancellation conditions.
Consider a (0,2) theory over the hypersurface $\mathfrak{X} = {\mathbb P}^n_{[k,k,\cdots,k]}[d]$, with gauge bundle ${\cal E}$: $$0 \: \longrightarrow \: {\cal E} \: \longrightarrow \:
\oplus_a {\cal O}(n_a) \: \longrightarrow \: {\cal O}(m)
\: \longrightarrow \: 0.$$
It is straightforward to compute that $$c_1^{\rm rep}(T\mathfrak{X})|_{\alpha} \: = \:
(n+1) \frac{k}{k} J \: - \: \frac{d}{k} \alpha^{-d} J,$$ $$\begin{aligned}
{\rm ch}_2^{\rm rep}(T\mathfrak{X})|_{\alpha} & = &
{\rm ch}_2^{\rm rep}( \oplus_{n+1} {\cal O}(k) )|_{\alpha} \: - \:
{\rm ch}_2^{\rm rep}( {\cal O}(d) )|_{\alpha}, \\
& = &
\frac{1}{2} (n+1) \left( \frac{k}{k} J \right)^2
\: - \: \frac{1}{2} \left( \frac{d}{k} J \right)^2 \alpha^{-d},
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calculated separately for each unit with a non-uniform response. For both measures and all examined layers, the average across the layer was positive (significant in half of the calculations (Table \[illusory\_table\])).
Source Layer $IC_A$ $IC_R$ Layer $IC_A$ $IC_R$ Layer $IC_A$ $IC_R$ Layer $IC_A$ $IC_R$
---------- ------- -------- ---------- ------- ---------- -------- ------- ---------- -------- ------- ---------- --------
Monkey A V1S $0.19$ $0.31$ V2S $0.21$ $0.11$ V1D $0.09$ $0.11$ V2D $0.28$ $0.24$
Monkey B V1S $0.10$ $0.16$ V2S $0.08$ $0.12$ V1D $0.04$ $0.13$ V2D $0.07$ $0.20$
PredNet $E_1$ $0.09$ $0.14$\* $E_2$ $0.15$\* $0.09$ $R_1$ $0.11$\* $0.04$ $R_2$ $0.12$\* $0.03$
PredNet $A_1$ $0.03$ $0.10$\* $A_2$ $0.15$\* $0.09$
: Illusory responsiveness measures for the units in Lee et al. [@Lee_2001] and the PredNet. $IC_a$ and $IC_r$ compare the response of the illusion to the amodal and rotated stimuli, respectively. Positive measures indicate a preference to the illusion. \*$p<0.05$ (T-test)[]{data-label="illusory_table"}
Flash-Lag Effect
----------------
The flash-lag stimulus was created with a rotation speed of $6$per time step, with a flash every $6$ time steps for $3$ full rotations. Angles of the predictions were quantified over the last two rotations. The angles of the predicted bars were estimated by calculating the mean-squared error (MSE) between the prediction and a probe bar generated at $0.1$increments and a range of centers, and taking the angle with the minimum mean-squared error. Fig. \[flash\_lag\_post\_flashes\] contains additional predictions by the model after four consecutive flashes.
![Four consecutive post-flash predictions by the PredNet model following training on the KITTI dataset.[]{data-label="flash_lag_post_flashes"}](flash_lag_post_flashes-4nt_kitti_keras
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- a proof of the judgment $0 {\:|\!\!\!=\!\!\!\!=\:}C(L_1),C(L_1),{\rm Id}_{C,1}\leadsto
(\varepsilon,\varepsilon) {\:|\!\!\!=\!\!\!\!=\:}{\rm SUCC}$ in the formal system ${\cal J}(C(L_1),C(L_1),{\rm Id}_{C,1},{\cal B})$ (see $\pi_4$).
- a proof of the judgment $0 {\:|\!\!\!=\!\!\!\!=\:}D(L_1),D(L_1),{\rm Id}_{D,2}\leadsto (\varepsilon,\varepsilon) {\:|\!\!\!=\!\!\!\!=\:}{\rm SUCC}$ in the formal system ${\cal J}(D(L_1),D(L_1),{\rm Id}_{D,2},{\cal B})$ (see $\pi_5$).
- a proof of the judgment $0 {\:|\!\!\!=\!\!\!\!=\:}E(L_1),E(L_1),{\rm Id}_{E,2}\leadsto (\varepsilon,\varepsilon) {\:|\!\!\!=\!\!\!\!=\:}{\rm SUCC}$ in the formal system ${\cal J}(E(L_1),E(L_1),{\rm Id}_{D,2},{\cal B})$ (see $\pi_6$).
{width="14cm"}
where $H(A,B)$ stands for $0 {\:|\!\!\!=\!\!\!\!=\:}A(\bot),B(\bot), S$.\
Proof $\pi_2$:
{width="10cm"}
{width="10cm"}
{width="16cm"}
where $H(C,C)$ stands for $0 {\:|\!\!\!=\!\!\!\!=\:}C(L1),C(L1),{\rm Id}_{C,1}$.\
{width="10cm"}
{width="14cm"}
In the above proofs the following defender strategies (or prefix of strategies) were used (in fact, they can be deduced from the proofs):\
Let $${\cal S} := \{(yx,xy),(yy,xx),(xxx,yxx)\}.$$ For every subset $Z$ of $({\cal A} \times {\cal A})^* $, by ${{\rm PREF}}(Z)$ we denote its set of prefixes.\
We define $${\cal P} := {{\rm PREF}}({\cal S})$$ namely: $${\cal P} = \{(\varepsilon,\varepsilon),(y,x),(yx,xy),(x,y),(xx,yx),(xxx,yxx)\}$$ Finally, we define $S$ as the subset of $({\cal R} \times {\cal R})^* $ obtained by replacing, in ${\cal P}$, every 2-tuple $(u,v) \in ({\cal A} \times {\cal A})^* $ by the unique 2-tuple $(r_u,r_v) \in ({\cal R} \times {\cal R})^*$, such that $r_u$ (resp. $r_v$) is applicable on $A$ (resp. on $B$), ${{\rm LAB}_{\cal T}}(r_u) = u$ and ${{\rm LAB}_{\cal T}}(r_v) = v$. Namely: $$S = \{ (\varepsilon,\
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n-1} \xi(w_0,\eta_i)\\
w_{n\delta} =& w_0 + \sum_{i=0}^{n-1} \delta \nabla U(w_{i\delta}) + {\sqrt{\delta}} \sum_{i=0}^{n-1} \xi(w_{i\delta},\eta_i)
\end{aligned}$$ Note that conditioned on the randomness up to time $0$, $\E{\sum_{i=0}^{n-1} \xi(w_0,\eta_i)} = \E{\sum_{i=0}^{n-1} \xi(w_{i\delta},\eta_i)} = 0$, so that $$\begin{aligned}
& \E{\circled{1}}\\
=& \E{\lin{\nabla f(x_0 - v_0), v_T - w_T}}\\
=& \delta \E{\lin{\nabla f(x_0 - v_0), \sum_{i=0}^{n-1} \nabla U(w_{0}) - \nabla U(w_{i\delta})}} + \sqrt{\delta} \E{\lin{\nabla f(x_0 - v_0), \sum_{i=0}^{n-1} \xi(w_{0},\eta_i) - \sum_{i=0}^{n-1} \xi(w_{i\delta},\eta_i)}}\\
=& \delta \E{\lin{\nabla f(x_0 - v_0), \sum_{i=0}^{n-1} \nabla U(w_{0}) - \nabla U(w_{i\delta})}}\\
\leq& \delta \sum_{i=0}^{n-1} L \E{\lrn{w_0 - w_{i\delta}}_2}\\
\leq& T L \sqrt{32 T\beta^2} \leq 8 T^{3/2} L \beta
\end{aligned}$$
where the third equality is becayse $\xi(\cdot, \eta_i)$ has $0$ mean conditioned on the randomness at time $0$, and the second inequality is by Lemma \[l:divergence\_wt\].
Next, $$\begin{aligned}
& \E{\circled{2}}\\
=& \E{\lin{\nabla f(x_T - v_T) - \nabla f(x_0 - v_0), v_T - w_T}}\\
\leq& \E{\lrn{\nabla f(x_T - v_T) - \nabla f(x_0 - v_0)}_2 \lrn{v_T - w_T}}\\
\leq& \frac{4}{\epsilon} \sqrt{\E{\lrn{x_T - x_0}_2^2 + \lrn{v_T - v_0}_2^2}} \cdot \sqrt{\E{\lrn{v_T - w_T}_2^2}}\\
\leq& \frac{4}{\epsilon} \sqrt{16T\beta^2 + 2T\beta^2} \cdot \sqrt{32 \lrp{T^2 L^2 + TL_\xi^2} T\beta^2}\\
\leq& \frac{128}{\epsilon} T \beta^2 \lrp{\sqrt{T} L_\xi + TL}
\end{aligned}$$ where the second inequality is because $\lrn{\nabla^2 f}_2 \leq \frac{2}{\epsilon}$ from item 2(c) of Lemma \[l:fproperties\] and by Young’s inequality. The third inequality is by Lemma \[l:divergence\_xt\], Lemma \[l:divergence\_vt\] and Lemma \[l:vt-wt\].
Finally, $$\begin{aligned}
& \E{\circled{3}}\\
=& \E{\int_0^1\int_0^s \lin{\nabla^2 f(x_T - v_T + s(v_T-w_T)), (v_
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n define $A_{n}(Q)$ more rigorously in terms of the set partitions (See P. P. Maritin’s paper [@Ma2]).
Next we define special elements $s_i, f_i$ ($1\leq i \leq n-1$) and $e_i$ ($1\leq i\leq n$) of $\Sigma_n^1$ by $$\begin{aligned}
s_i &=& \{\{1,1'\},\ldots, \{i-1,(i-1)'\},
\{i+2, (i+2)'\},\ldots, \{n, n'\},\\
& &\quad \{i, (i+1)'\}, \{i+1, i'\}\}\\
f_i &=& \{\{1,1'\},\ldots, \{i-1,(i-1)'\},
\{i+2, (i+2)'\},\ldots, \{n, n'\},\\
& &\quad \{i, i+1, i', (i+1)'\}\}\\
e_i &=& \{\{1,1'\},\ldots, \{i-1,(i-1)'\}, \{i\}, \{i'\}
\{i+1, (i+1)'\},\ldots, \{n, n'\}\}.\end{aligned}$$ The diagrams of these special elements are illustrated by the figures in Figure \[fig:gen\]. Note that in the picture of $e_i$, there exist “a male” only part and “a female” only part. We call such a part “defective” (see Section 3.1).
![Special elements[]{data-label="fig:gen"}](3.eps)
We easily find that they satisfy the following basic relations. $$\begin{array}{rcl}\tag{$R0$}
f_{i+1} &=& s_is_{i+1}f_is_{i+1}s_i \quad (i = 1, 2, \ldots, n-2),\\
e_{i+1} &=& s_ie_{i}s_i \quad (i = 1, 2, \cdots, n-1)
\end{array}$$ $$\begin{array}{rcl}\tag{$R1$}
s_i^2 &=& 1 \quad (i = 1, 2, \ldots, n-1),\\
s_is_{i+1}s_i &=& s_{i+1}s_is_{i+1} \quad (i = 1, 2, \ldots, n-2),\\
s_is_j &=& s_js_i \quad (|i-j|\geq 2),
\end{array}$$ $$f_i^2 = f_i,\ f_if_j = f_jf_i,\tag{$R2$}$$ $$f_is_i = s_if_i=f_i,\tag{$R3$}$$ $$f_is_j = s_jf_i \quad (|i -j|\geq 2),\tag{$R4$}$$ $$e_{i}^2 = Qe_i ,\tag{$E1$}$$ $$s_ie_{i}e_{i+1}
= e_ie_{i+1}s_i
= e_ie_{i+1}
\quad (i = 1, 2, \ldots, n-1),\tag{$E2$}$$ $$e_is_j = s_je_i
\quad(j-i\geq1,\ i-j\geq 2),
\quad e_ie_j
= e_je_i,\tag{$E3$}$$ $$\begin{array}{rcl}\tag{$E4$}
e_if_ie_i = e_i
& e_{i+1}f_{i}e_{i+1} = e_{i+1}
& (i = 1, 2, \ldots, n-1),\\
f_ie_{i}f_i = f_{i},
&f_{i}e_{i+1}f_{i} = f_{i}
&(i = 1, 2, \ldots, n-1),
\end{array}$$ $$e_if_j = f_je_i
\quad(j-i\geq1,\ i-j\geq 2).\tag{$E5$}$$ Here we m
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building blocks for the assembly of nanostructured materials.
This research was supported by a PhD grant of the Vietnamese Government Scholarship Program (Project 911).
[^1]: Peak 1
[^2]: Peak 2
[^3]: Undefined value
---
abstract: 'The ability of a robot to detect and respond to changes in its environment is potentially very useful, as it draws attention to new and potentially important features. We describe an algorithm for learning to filter out previously experienced stimuli to allow further concentration on novel features. The algorithm uses a model of habituation, a biological process which causes a decrement in response with repeated presentation. Experiments with a mobile robot are presented in which the robot detects the most novel stimulus and turns towards it (‘neotaxis’).'
author:
- |
Stephen Marsland, Ulrich Nehmzow and Jonathan Shapiro\
Department of Computer Science\
University of Manchester\
Oxford Road\
Manchester M13 9PL\
`{smarsland, ulrich, jls}@cs.man.ac.uk`
bibliography:
- 'thebib.bib'
- 'Manbib.bib'
title: 'Novelty Detection for Robot Neotaxis [^1]'
---
Introduction
============
Many animals have the ability to detect novelty, that is to recognise new features or changes within their environment. This paper describes an algorithm which learns to ignore stimuli which are presented repeatedly, so that novel stimuli stand out. A simple demonstration of the algorithm on an autonomous mobile robot is given. We term the robot’s behaviour of following the most novel stimulus [*neotaxis*]{}, meaning ‘turn towards new things’, taken from the Greek ([*neo*]{} = new, [*taxis*]{} = follow). A number of different versions of the novelty filter are described and compared to find the best for the particular data used.
Attending to more novel stimuli is a useful ability for a mobile robot as it can limit the amount of data which the robot has to process in order to deal with its environment. It can be used to recognise when perceptions are new and must therefore be
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yed a crucial role in combinatorics and representation theory; see, for example, [@BEGfd; @BEGqi; @gordc]. A good way to think of the functor $S_d$ is as the analogue of the translation functor [@BG] from Lie theory.
In order to have control over $B$ we need to know that the $Q_{d}^{d+1}$ are progenerators for all $d\in c+{\mathbb{N}}$; equivalently that the $S_d$ are Morita equivalences. This is a conjecture from [@GGOR Remark 5.17] which we answer with:
Theorem {#morrat-intro}
-------
\[Corollary \[morrat-cor\]\] [*The shift functor $S_d$ is a Morita equivalence for all $d\in c+{\mathbb{N}}$.* ]{}
The significance of this result is that $B$ now has rather pleasant properties; in particular Theorem \[mainthm-intro\](1) is an easy consequence. For the second assertion of Theorem \[mainthm-intro\], we note that it is easy to obtain a ${\mathbb{Z}}$-algebra $\widehat{A} =\bigoplus_{i\geq
j\geq 0} A_{ij}$ from the graded algebra $A=\bigoplus_{k\geq 0}I^k$ for which $A{\text{-}{\textsf}{qgr}}\simeq \widehat{A}{\text{-}{\textsf}{qgr}}$. One simply takes $A_{ij}=I^{i-j}$ for each $i,j$. Thus the main step in the proof of Theorem \[mainthm-intro\] is given by:
Proposition {#pre-cohh-intro}
-----------
\[Theorem \[main\]\] [*Under the filtration induced from the order filtration of differential operators, $\operatorname{gr}B_{ij} \cong A_{i-j} = I^{i-j}$ and so $\operatorname{gr}B\cong \widehat{A}$ as ${\mathbb{Z}}$-algebras.* ]{}
In this result the inclusion $ I^{i-j}\subseteq \operatorname{gr}B_{ij}$ is straightforward. The opposite inclusion is much more subtle as it is difficult to keep close control of the filtration on $B_{ij}$. Our proof leans heavily on the work of Haiman in [@hai3] and [@hai1] surrounding the $n!$ and polygraph theorems and the strategy is outlined in more detail in за.
Applications {#intro-1.10}
------------
Theorem \[mainthm-intro\] gives a powerful technique for relating $H_c$- or $U_c$-modules to sheaves on $\operatorname{Hilb(n)}$: given a $U_c$-module $M$ with a good
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ed here.
The paper ends with some brief final remarks.
Stochastic approach to the 1PI EA
=================================
The goal of this Section is to provide an heuristic introduction to stochastic equations derived from the 1PI EA. For a deeper discussion see [@CH08; @GRLE98].
From Langevin equations to effective actions
--------------------------------------------
To see why it is natural to translate a problem described in terms of an effective action into an equivalent Langevin equation framework, let us first traverse the opposite road, that is, how to associate a generating functional to a problem whose primary description is in terms of a stochastic equation of motion.
We therefore assume we have a string of c-number fields $\Phi_s^a$ obeying a system of equations of the form [@MaSiRo73; @CooRos01; @ZanCal02; @ChaDem01a; @ChaDem01b]
\_a=-q\_[b]{}F\^b\_a\[ne1\] where $\mathbf{D}_a$ and $F^b_a$ are possibly nonlinear functionals and the $q_{b}$ are stochastic Gaussian variables with zero mean and self-correlation $\left\langle q_{b}q_{c}\right\rangle =Q_{bc}$. To avoid the complexities associated to nonlinear Langevin equations, we take this equation to mean that it is possible to write $\Phi_s^a=\phi^a+\varphi^a$, where $\phi^a$ is a solution of the homogeneous equation
\_a=0 \[ne2\] and
\_[a,c]{}\^c=-q\_[b]{}F\^b\_a\[ne3\] where here and henceforth a comma denotes a functional derivative
\_[a,c]{} \[ne4\] If there are no zero modes, this implies that the expectation value $\left\langle \varphi^a\right\rangle=0$, so within this approximation we may say that $\phi^a$ is the expectation value of $\Phi_s^a$.
The generating functional for expectation values of the $\Phi_s^a$ fields is
Ze\^[iW]{}=D\_sDq(\_s\^a-\^a-G\_[ret]{}\^[ab]{}q\_[c]{}F\^c\_b)e\^[iJ\_d\_s\^d]{} \[ne5\] where $G_{ret}^{ab}$ is the causal Green function for the operator $\mathbf{D}_{a,c}$, namely
\_[a,c]{}G\_[ret]{}\^[cb]{}=-\^b\_a \[ne6\] and $\mathcal{Q}$ is the Gaussian probability density functional of the $q$ sources. Th
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60.5±27.7 (142) 75.2±25.9 (124)
Head circumference percentile 56.7±25.7 (382) 66.5±27.2 (80) 65.5±26.8 (128) 65.7±25.4 (67) 64.2±28.7 (83) 69.0±23.3 (118)
Units: mean±standard deviation (*N*).
Numbers vary due to missing data.
######
General characteristics of the study population[a](#TF0002){ref-type="table-fn"}
Characteristics *N* Mean±SD or *N* (%)
----------------------------------------------------------- ----- --------------------
Mothers
Vitamin A (µg/dL) 366 100.02±34.54
Vitamin C (µg/mL) 353 7.49±2.46
Vitamin E (µg/dL) 365 1654.96±463.84
MDA (µmol/g creatinine) 136 2.33±1.11
8-OHdG (µg/g creatinine) 133 0.12±0.04
Age at delivery (years) 382 31.2±3.5
Weight (kg) 329 54.3±6.9
Height (cm) 331 161.1±5.0
Employment status
Employed 315 113 (35.9)
Unemployed 202 (64.1)
Education period
\<12 years 63 (24.9)
13--16 years 253 156 (61.7)
\>17 years 34 (13.4)
Fathers
Weight (kg) 329 72.6±9.3
Height (cm) 330 174.1±5.0
E
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n every degree. Assume furthermore, that there are derivations $d\in \mathrm{Der} (F_{\mathcal P}\,A)$, and $g\in \mathrm{Der}_d (F_{\mathcal P,A}M)$ over $d$. The maps $d$ and $g$ are determined by maps $$\begin{aligned}
d_n:\,A&\to& \bigoplus_n \mathcal P (n)\otimes A^{\otimes n},\\ g_n:\,M&\to& \bigoplus_{k+l=n-2} \mathcal P (k+l+1)\otimes
A^{\otimes k} \otimes \,M \otimes A^{\otimes l}.\end{aligned}$$ Then there is an induced derivation on $M^*$ over $d$ in the following way. Define $h\in \mathrm{Der}_d (F_{\mathcal P,A}M^*)$ by maps $h_n:\,M^* \to \bigoplus_{k+l=n-2} \mathcal P(k+l+1)\otimes
A^{\otimes k} \otimes M^* \otimes A^{\otimes l}
$, which are given by its application to $a^\ast_1,\dots,a^\ast_{k+l} \in \,A^\ast$, $m^*_1\in \,M^*$, $m_2\in \,M$ as $$\begin{gathered}
h_n(m^*_1) (a^*_1,\dots,a^*_{k},m_2,a^*_{k+1},\dots,a^*_{k+l}) \\ :=(-1)^\epsilon
\cdot \tau_{k+l+2}^{l+1}(g_n(m_2)(a^*_{k+1},\dots,a^*_{k+l},m^*_1,a^*_1,\dots,
a^*_{k})) \in\mathcal P(k+l+1).\end{gathered}$$ $$\begin{pspicture}(0,-1)(5,2.5)
\psline(2,1)(0.8,0)
\psline(2,1)(1.2,0)
\psline(2,1)(1.6,0)
\psline(2,1)(2.4,0)
\psline(2,1)(2.8,0)
\psline(2,1)(3.2,0)
\psline[arrowsize=0.2, arrowinset=0, linestyle=dashed](2,2)(2,1)
\rput[l](2.5,1.35){$h$} \rput[m](2,2.2){$m^*_1$}
\psline[linestyle=dashed](2,0)(2,1)
\rput(2,-0.4){$a^*_{k+l}\dots a^*_{k+1}$ $m_2$ $a^*_{k} \dots a^*_{1}$\quad}
\psline[linearc=0.3, arrowsize=0.15]{->}(1.6,1.2)(1.9,1.5)(2.4,1)(1.9,0.5)(1.5,0.9)
\rput(4.5,1.5){$:=(-1)^\epsilon \cdot$}
\end{pspicture}
\begin{pspicture}(0,-1)(4,2.5)
\psline(2,1)(0.8,0)
\psline(2,1)(1.2,0)
\psline(2,1)(1.6,0)
\psline(2,1)(2.4,0)
\psline(2,1)(2.8,0)
\psline(2,1)(3.2,0)
\psline[arrowsize=0.2, arrowinset=0, linestyle=dashed](2,2)(2,1)
\rput[l](2.5,1.35){$\left(\tau_{k+l+2}^{l+1}\otimes
id\right) (g)$} \rput[m](2,2.2){$m_2$}
\psline[linestyle=dashed](2,0)(2,1)
\rput(2,-0.4){\quad $a^*_{k} \dots a^*_{1}$ $m^*_1$ $a^*_{k+l} \dots a^*_{k+1}$}
\psline[linearc=0.3, arrowsize=0.15]{->}(1.6,1.2)(1.9,1.5)(
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\,\,z=\frac{t}{h^{1/\beta\delta}}.
\label{chiralsuscept}$$
The singular function $f_G$ is well studied in spin models and has been parametrized for $O(2)$ and $O(4)$ groups. For the regular part we consider leading-order (linear) dependence in $H$ and quadratic in $T$: $$f_{M,reg}(T,H) = \left( a_0 + a_1 \frac{T-T_c^0}{T_c^0} +
a_2 \left(\frac{T-T_c^0}{T_c^0} \right)^2 \right) H.
\label{eq:freg}$$ Then we are left with 6 parameters to be determined from fitting the data, $T_c^0$, $t_0$, $h_0$, $a_0$, $a_1$ and $a_2$.
We perform simultaneous fits to $M_b$ and $\chi_{m,l}$ for the asqtad action on $N_\tau=8$, 12 and the HISQ/tree action on $N_\tau=6$, 8 and 12. An example of such a fit for HISQ/tree, $N_\tau=8$ is shown in Fig. \[pbp\_and\_chi\].
![ An example of a simultaneous fit to the chiral condensate (left) and susceptibility (right) for HISQ/tree on $N_\tau=8$ lattices. Open symbols indicate the range included in the fit. Dotted black line is an extrapolation to the physical light quark mass. []{data-label="pbp_and_chi"}](hisq_pbpO4_Nt8.eps "fig:"){width="48.00000%"} ![ An example of a simultaneous fit to the chiral condensate (left) and susceptibility (right) for HISQ/tree on $N_\tau=8$ lattices. Open symbols indicate the range included in the fit. Dotted black line is an extrapolation to the physical light quark mass. []{data-label="pbp_and_chi"}](hisq_chiO4_Nt8.eps "fig:"){width="48.00000%"}
Then, performing a combined $1/N_{\tau}^2$ extrapolation of $T_c$ values obtained with the asqtad and HISQ/tree action as shown in Fig. \[tc\_comb\] we obtain $$T_c=( 154 \pm 8 \pm 1)\mbox{ MeV},$$ where the first error is from the fit and the second is the overall error on the lattice scale determination. The fits for asqtad and HISQ/tree are constrained to have a common intercept. (See Ref. [@hotqcd2] for more details on the fitting procedure and analysis of systematic errors.) To present a combined error we add the two errors giving our final value $T_c=154\pm9$ MeV.
{width
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)^2$ vertices. [Now assume that $k < (\log n)^2$. Combining (\[in:cyc\]) and (\[new\]),]{} and taking the union bound over all choices for a set of $p$ edges, we find that the probability that a $c$-loaded $k$-vertex tree contains $p$ cycle-producing edges is at most $$\begin{aligned}
\label{ineq:cycle}
k^{2p}\cdot \left(\frac{{4}}{ n^{\varepsilon}}\right)^p\cdot n\cdot 2^{-k}=
\left(\frac{{4\cdot k^{2}}}{ n^{\varepsilon}}\right)^p\cdot n\cdot 2^{-k}{\leqslant}n^{-\varepsilon p/2} \cdot n\cdot 2^{-k},
\end{aligned}$$ where the inequality holds as $k<(\log n)^2$. Therefore the probability that $p= \lceil 2(c+1)/\varepsilon\rceil$ cycle-producing edges are present is at most $n^{-c}$. We conclude that $p < 2(c+1)/\varepsilon$ with probability at least $1-n^{-c}$.
Combining the Lemmas \[lem:tree\] and \[lem:treecycle\] establishes the proposition.
[^1]: UNSW Sydney, Australia, `c.greenhill@unsw.edu.au`
[^2]: Macquarie University, Sydney, Australia, `bernard.mans@mq.edu.au`
[^3]: Macquarie University, Sydney, Australia, `ali.pourmiri@mq.edu.au`
[^4]: The first author is supported by the Australian Research Council Discovery Project DP190100977. The second and third authors are supported by the Australian Research Council Discovery Project DP170102794.
---
abstract: |
In the past years, analyzers have been introduced to detect classes of non-terminating queries for definite logic programs. Although these non-termination analyzers have shown to be rather precise, their applicability on real-life Prolog programs is limited because most Prolog programs use non-logical features. As a first step towards the analysis of Prolog programs, this paper presents a non-termination condition for Logic Programs containing integer arithmetics. The analyzer is based on our non-termination analyzer presented at ICLP 2009. The analysis starts from a class of queries and infers a subclass of non-terminating ones. In a first phase, we ignore the outcome (success or failure) of the arithmetic operations,
| 492
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| 0.784793
|
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|
) indicates that all coefficients are significant, not equal to 0 under the nominal level 5%. Our method is consistent to the traditional Logistic regression. Compared with $K=150$ and $K=50$, $K=100$ is better since each block sample contains enough data points. For $\beta_{3}$, the average proportion of rejecting the null hypothesis by mVC, mMSE, BLB and SDB are much lower than 1 while ours are 1. It implies that our proposed method works in cases where others don’t work.
[cccc ccc]{}\
Method & $\beta_{1}$ & $\beta_{2}$ & $\beta_{3}$ & $\beta_{4}$ & $\beta_{5}$ & $\beta_{6}$\
\
TLR & -1.514 & 0.630 & 0.063 & 0.877 & 0.226 & 0.521\
\
K=50 & -1.525 & 0.637 & 0.063 & 0.885 & 0.229 & 0.529\
K=100 & -1.537 & 0.644 & 0.063 & 0.896 & 0.231 & 0.538\
K=150 & -1.549 & 0.651 & 0.062 & 0.905 & 0.234 & 0.547\
mVC & -1.510 & 0.627 & 0.066 & 0.876 & 0.225 & 0.527\
mMSE & -1.514 & 0.634 & 0.059 & 0.876 & 0.229 & 0.518\
\
TLR & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000\
\
K=50 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000\
K=100 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000\
K=150 & 1.000 & 1.000 & 1.000 & 1.000 & 0.990 & 1.000\
mVC & 1.000 & 1.000 & 0.860 & 1.000 & 1.000 & 1.000\
mMSE & 1.000 & 1.000 & 0.770 & 1.000 & 1.000 & 1.000\
BLB($n^{0.6}$) & 1.000 & 1.000 & 0.000 & 1.000 & 0.910 & 1.000\
BLB($n^{0.8}$) & 1.000 & 1.000 & 0.750 & 1.000 & 1.000 & 1.000\
SDB($n^{0.6}$) & 1.000 & 1.000 & 0.000 & 1.000 & 1.000 & 1.000\
SDB($n^{0.8}$) & 1.000 & 1.000 & 0.010 & 1.000 & 1.000 & 1.000\
\[table10\]
Appendix {#appendix .unnumbered}
========
[**Proof of Theorem \[theorem1\]**]{}.
From Assumption \[assumption1\], we can get $$\sqrt{m} ({\widehat}{\theta}_{km}-\theta )=\frac{1}{\sqrt{m}}\sum_{i=1}^{m}\eta_{ki}+R_{km}.$$ Hence, $$\begin{aligned}
\label{eqA1}
\sqrt{n}(\widetilde{\theta} - \theta ) & = \sqrt{n} \Big{(}\frac{1}{K}\sum_{k=1}^{K} {\widehat}{\theta}_{km} -\theta \Big{)} \notag \\
&= \frac{\sqrt{n}}{K}\sum_{k=1}^{K} ({\widehat}{\theta}_{km} -\theta ) \notag \\
&= \frac{1}{\sqrt{K}}\sum_{k=1}^{K}
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matrix}.$$ As in the case (ii) of the above step (1), the Dickson invariant of $T_1$ is the same as that of $\begin{pmatrix} 1 & 1/\sqrt{(a+a')/2}(z_j^{\ast})_1\\ 0 & 1 \end{pmatrix}$, which turns to be $(z_j^{\ast})_1$.
In conclusion, $(z_j^{\ast})_1$ 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.\
3. Assume that $M_1=A(4b'', 2\delta, \pi) \oplus (\oplus H(1))$ with $b''\in A$. Let $(e_3, e_4)$ be a basis for $A(4b'', 2\delta, \pi)$. Recall that $e_2$ is a basis for the direct summand $(a')$ of $M_0$. Then choose a basis $(e_2-e_3, e_3-\frac{2b''\pi}{\delta}e_4, e_4+\pi e_2)$, denoted by $(e_2', e_3', e_4')$, for the lattice spanned by $(e_2, e_3, e_4)$ such that the associated Gram matrix is $$\begin{pmatrix} a'(1+4a'b'')&0&0\\ 0 & -4b''(1+4b'')&-\pi(1+4b'')\\ 0&\pi(1+4b'') &2\delta(1-a') \end{pmatrix}$$ (cf. Lemma 2.9 and the following paragraph of loc. cit. in [@C2]). Note that this lattice is the same as $(a')\oplus A(4b'', 2\delta, \pi)$. Since the lattice spanned by $(e_3', e_4')$ is $\pi^1$-modular with the norm $(4)$, it is isometric to $H(1)$ by Theorem 2.2 of [@C2]. Now choose another basis $(e_1, e_1+e_2', e_3', e_4')$ for the lattice $(a)\oplus (a')\oplus A(4b'', 2\delta, \pi)$ such that the associated Gram matrix is $$\begin{pmatrix} a&a&0&0\\ a&a+a'(1+4a'b'')& 0&0 \\ 0&0 & -4b''(1+4b'')&-\pi(1+4b'')\\0&0&\pi(1+4b'') &2\delta(1-a') \end{pmatrix}.$$
Let $$\left\{
\begin{array}{l}
\tilde{M}_0=(\oplus_{\lambda}H_{\lambda})\oplus \left( Be_1\oplus B(e_1+e_2') \right);\\
\tilde{M}_1=Be_3'\oplus Be_4' \oplus (\oplus H(1)).
\end{array}\right.$$ 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 $\
| 494
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| 0.77837
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ic. By the way, some elucidations of the standard concept of quantum truth are also obtained.
**Key words:** pragmatics, quantum logic, quantum mechanics, justifiability, decidability, global pluralism.
author:
- |
Claudio Garola\
Dipartimento di Fisica, Università di Lecce e Sezione INFN\
73100 Lecce, Italy\
E-mail: Garola@le.infn.it
title: A Pragmatic Interpretation of Quantum Logic
---
Introduction
============
The formal structure called *quantum logic* (QL) springs out in a natural way from the formalism of quantum mechanics (QM). Scholars have debated for a long time on it, wondering whether it subtends a concept of quantum truth which is typical of QM, and a huge literature exists on this topic. We limit ourselves here to quote the classical book by Jammer,$^{(1)}$ which provides a general review of QL from its birth to the early seventies, and the recent books by Rèdei$^{(2)}$ and Dalla Chiara *et al.*,$^{(3)}$ which contain updated bibliographies.
Whenever the existence of a quantum concept of truth is accepted, one sees at once that it has to be radically different from the classical (Tarskian) concept, since the set of propositions of QL has an algebraic structure which is different from the structure of classical propositional logic. Thus, a new problem arises, *i.e*. the problem of the “correct” logic to be adopted when reasoning in QM.
We want to show in the present paper that the above problem can be avoided by adopting an *integrated perspective*, which preserves both the globality of logic (in the sense of *global pluralism*, which admits the existence of a plurality of mutually compatible logical systems, but not of systems which are mutually incompatible$^{(4)}$) and the classical notion of *truth as correspondence*, which we consider as explicated rigorously by Tarski’s semantic theory.$^{(5,6)}$ This perspective reconciliates non-Tarskian theories of truth with Tarski’s theory by reinterpreting them as theories of metalinguistic concepts that are different f
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hentication and checks the Drupal Database for a valid username and password.
If you have any problems with PHP CLI, Drush or cron, you can add following code in the hook:
// Allow cron through
if (basename($_SERVER['PHP_SELF']) == 'cron.php') {
return;
}
// Allow PHP CLI/Drush through
if (isset($_SERVER['argc'])) {
if (php_sapi_name() == 'cli' || (is_numeric($_SERVER['argc']) && $_SERVER['argc'] > 0)) {
return;
}
}
A:
If you're using Drupal 7 the Shield module is available for this purpose. It authenticates a single, shared user and password.
PHP Authentication shield. It creates a simple shield for the site with Apache authentication. It hides the sites, if the user does not know a simple username/password. It handles Drupal as a "walled garden".
This module helps you to protect your (dev) site with HTTP authentication.
Q:
Использование memoryDC WINAPI, обновление окна только при изменении размера
Я новачок в WINAPI и пытаюсь зделать мини игру, мне надо чтобы изображение выводилось на екран целиком, а не каждый блок по очереди, смог найти только то что сначало нужно всё записовать в memoryDC, а потом выводить его, только как это реализовать доконца не понял.
Также окно почему-то перерисовуется только при изменении размера окна, как это исправить?
Мои попытки что-то сделать:
#ifndef UNICODE
#define UNICODE
#endif
#include <windows.h>
HBITMAP hBmp_red = (HBITMAP)LoadImage(NULL, L"C:\\Red.bmp", IMAGE_BITMAP, 0, 0, LR_LOADFROMFILE);
HDC bmpdc = NULL;
HDC memdc = NULL;
HBITMAP membmp = NULL;
LRESULT CALLBACK WindowProc(HWND hwnd, UINT uMsg, WPARAM wParam, LPARAM lParam);
int WINAPI wWinMain(HINSTANCE hInstance, HINSTANCE, PWS
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|
ed Einstein equations.
#### Future work. {#future-work. .unnumbered}
Although we have shown that bases in global coordinates are orthogonal, we did not mention completeness. There are clues that, in global coordinates, combining the highest- and lowest-weight modules will give a complete set of states. We leave a rigorous treatment of completeness to future work. However, many problems can already be attacked without worrying about completeness—for example, if the source term lives in exactly one irrep.
Since the near-horizon near-extremal geometry exhibits the same isometry as NHEK, we expect all discussions in this paper can be applied to understanding metric perturbations in near-NHEK, which is more astrophysically relevant. With the knowledge of isometry-adapted bases in NHEK, we hope to enhance our understanding of the Kerr/CFT conjecture [@Guica:2008mu] from the gravity side.
The authors would like to thank Yanbei Chen, Alex Lupsasca, Zachary Mark, and Peter Zimmerman for useful conversations. LCS acknowledges the support of NSF grant PHY–1404569, and both authors acknowledge the support of the Brinson Foundation. Some calculations used the computer algebra system <span style="font-variant:small-caps;">Mathematica</span>, in combination with the <span style="font-variant:small-caps;">xAct/xTensor</span> suite [@JMM:xAct; @MARTINGARCIA2008597].
Scalar, vector, and symmetric tensor bases {#app:S-V-T-Basis}
==========================================
In this section we present the expressions of scalar, vector, and symmetric tensor bases both in Poincaré coordinates and global coordinates, up to constant factors. All the basis functions are defined on the three-dimensional hypersurface $\Sigma_u$. To promote these basis functions to the full four-dimensional manifold $\mathcal{M}$, one promotes all constant coefficients $c_{\beta}$ to become unknown functions of the (cosine) polar angle, $c_{\beta}(u)$. The basis functions given here are (mostly) obtained using the highest-weight method introduced
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|
he elements $g_i$, $i\in I$, and $y_l$, $l\in L$. Let $$R^\chi =R^\chi _+\cup -R^\chi _+.$$
[@p-Heck07b Thm.3.13] \[th:rschi\] Let $\chi \in {\mathcal{X}}$ such that $\chi '$ is $p$-finite for all $p\in
I$. $\chi '\in {\mathcal{G}}(\chi )$. Then ${\mathcal{R}}(\chi )={\mathcal{R}}({\mathcal{C}}(\chi ), (R^{\chi '})_{\chi
'\in {\mathcal{G}}(\chi )})$ is a root system of type ${\mathcal{C}}(\chi )$.
Roots with finite bounds often play a distinguished role. For all $\chi \in {\mathcal{X}}$ let $$\begin{aligned}
R^\chi _{+{\mathrm{fin}}}=\{\beta \in R^\chi _+\,|\,
{b^{\chi}} (\beta )<\infty \},\quad
R^\chi _{+\infty }=R^\chi _+\setminus R^\chi _{+{\mathrm{fin}}}.
\label{eq:R+fin}\end{aligned}$$
We will use several finiteness properties of bicharacters. $$\begin{aligned}
\label{eq:X1}
{\mathcal{X}}_1=\{\chi \in {\mathcal{X}}\,|\,&
\text{$\chi $ is $p$-finite for all $p\in I$}\},\\
{\mathcal{X}}_2=\{\chi \in {\mathcal{X}}\,|\,&
\text{$\chi '$ is $p$-finite for all $\chi '\in {\mathcal{G}}(\chi )$, $p\in I$}\},\\
{\mathcal{X}}_3=\{\chi \in {\mathcal{X}}\,|\,&
\text{$R^\chi $ is finite}\},\\
{\mathcal{X}}_4=\{\chi \in {\mathcal{X}}\,|\,&
\text{$R^\chi $ is finite, $R^\chi _+=R^\chi _{+{\mathrm{fin}}}$}\},\\
\label{eq:X5}
{\mathcal{X}}_5=\{\chi \in {\mathcal{X}}_4\,|\,&
\text{$\chi ({\alpha },{\alpha })\not=1$ for all ${\alpha }\in R^\chi _+$}\}.\end{aligned}$$ Clearly, ${\mathcal{X}}_i\supset {\mathcal{X}}_j$ for $1\le i<j\le 5$. By Eq. , $\chi \in {\mathcal{X}}_5$ if and only if $R^\chi $ is finite and $\chi ({\alpha },{\alpha })$ is a root of $1$ different from $1$ for all ${\alpha }\in R^\chi _+$.
\[le:equalrs\] Let $\chi ,\chi '\in {\mathcal{X}}_2$.
\(i) If $R^\chi _+=R^{\chi '}_+$, then $C^{w^*\chi }=C^{w^*\chi '}$ for all $w\in {\mathrm{Hom}}(\chi ,\underline{\,\,})
\subset {\mathrm{Hom}}({\mathcal{W}}(\chi ))$.
\(ii) Assume that $\chi ,\chi '\in {\mathcal{X}}_3$. If $C^{w^*\chi }=C^{w^*\chi '}$ for all $w\in {\mathrm{Hom}}(\chi ,\underline{\,\,})
\subset {\mathrm{Hom}
| 498
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|
tude of the inferred activations, which was measured as $\frac{\mathbb{E}_{u\in{\bf U}}[a_{u}]}{\mathbb{E}_{v\in{\bf V}}[a_{v}]}$. Fig. \[fig:energyCurve\](right) shows the ratio of the latent patterns being strongly activated. We used a threshold $\tau=\mathbb{E}_{v\in{\bf V}}[a_{v}]$ to identify strong activations, *i.e.* computing the activation ratio as $\mathbb{E}_{u\in{\bf U}}[{\bf 1}(a_{u}>\tau)]$. Curves in Fig. \[fig:energyCurve\] were reported as the average performance using images in the CUB200-2011 dataset.
Fig. \[fig:visualization\] visualizes latent patterns in the AOG based on the technique of [@FeaVisual]. More specifically, Fig. \[fig:patches\] lists images patches inferred by different latent patterns in the AOG with high inference scores. It shows that each latent pattern corresponds to a specific part shape through different images.
Fig. \[fig:results\] shows part localization results based on AOGs. Tables \[tab:imgnet\], \[tab:VOC\], and \[tab:cub200\] compare the part-localization performance of different baselines on different benchmark datasets using the evaluation metric of the normalized distance. Tables \[tab:VOC\], and \[tab:cub200\] show both the number of part annotations and the number of questions. Fig. \[fig:curve\] shows the performance of localizing the head part on objects in the PASCAL VOC Part Dataset, when people annotated different numbers of parts for training. Table \[tab:pcp\] lists part-localization performance, which was evaluated by the PCP metric. In particular, the method of *Ours+fastRCNN* combined our method and the fast-RCNN to refine part-localization results[^5]. Our method learned AOGs with about $1/6$–$1/2$ part annotations, but exhibited superior performance to the second best baseline.
![Part localization performance on the Pascal VOC Part dataset.[]{data-label="fig:curve"}](curve.pdf){width="\linewidth"}
Justification of the methodology
--------------------------------
We have three reasons to explain the good performance of our method. Fi
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| 1,419
| 0.789807
|
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|
C14---P6---C20 103.7 (2) C61---C62---H62 120.1
C14---P6---C13 107.2 (2) P2---C63---P3 112.0 (2)
C20---P6---C13 103.2 (2) P2---C63---H63A 109.2
C14---P6---Ag4 121.93 (15) P3---C63---H63A 109.2
C20---P6---Ag4 108.08 (14) P2---C63---H63B 109.2
C13---P6---Ag4 110.97 (15) P3---C63---H63B 109.2
C6---C1---C2 119.4 (5) H63A---C63---H63B 107.9
C6---C1---P1 123.9 (4) C69---C64---C65 118.7 (4)
C2---C1---P1 116.7 (4) C69---C64---P2 118.9 (4)
C3---C2---C1 119.9 (6) C65---C64---P2 122.4 (4)
C3---C2---H2 120.1 C64---C65---C66 120.7 (5)
C1---C2---H2 120.1 C64---C65---H65 119.6
C2---C3---C4 119.8 (6) C66---C65---H65 119.6
C2---C3---H3 120.1 C67---C66---C65 120.0 (5)
C4---C3---H3 120.1 C67---C66---H66 120.0
C5---C4---C3 120.6 (6) C65---C66---H66 120.0
C5---C4---H4 119.7 C66---C67---C68 120.3 (5)
C3---C4---H4 119.7 C66---C67---H67 119.9
C4---C5---C6 120.1 (6) C68---C67---H67 119.9
C4---C5---H5 120.0 C67---C68---C69 119.6 (5)
C6---C5---H5 120.0 C67---C68---H68 120.2
C1---C6---C5 120.2 (6) C69---C68---H68 120.2
C1---C6---H6 119.9 C64---C69---C68 120.7 (5)
C5---C6---H6 119.9 C64---C69---H69 119.7
C12---C7---C8 119.3 (4) C68---C69---H69 119.7
C12---C7---P1 123.2 (4) C71---C70---C75 119.5 (4)
C8---C7---P1 117.6 (4) C71---C70---P2 123.7 (4)
C9---C8---C7 120.7 (5) C75---C70---P2 116.8 (3)
C9---C8---H8 119.6 C70---C71---C72 120.0 (4)
C7---C8---H8 119.6 C70---C71---H71 120.0
C8---C9---C10 119.4 (5) C72---C71---H71 120.0
C8---C9---H9 120.3 C73---C
| 500
| 3,158
| 1,663
| 699
| null | null |
github_plus_top10pct_by_avg
|
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