text large_stringlengths 384 2.05k | rank_avg float64 1 4.19k ⌀ | rank_max float64 1 8.21k ⌀ | rank_min float64 1 5.03k ⌀ | rank_median float64 1 4.21k ⌀ | rank_by_avgsim float64 1 4.19k ⌀ | avgsim_to_github float32 0.77 0.85 ⌀ | dataset large_stringclasses 1
value |
|---|---|---|---|---|---|---|---|
ch $z_i$. Therefore $P=\widetilde{P}$.
Another module {#C}
==============
{#app-c-1}
Fix $c\in {\mathbb{C}}$ that satisfies Hypothesis \[main-hyp\] and an integer $k\geq 0$. For applications in [@GS2] we will need an analogue of Proposition \[pre-cohh\] for the left $H_{c+k}$-module $M(k) = H_{c+k}eB_{k0}\subseteq ... | 901 | 487 | 779 | 945 | 2,055 | 0.783176 | github_plus_top10pct_by_avg |
specifically, $(w_0 ... w_{n\delta})$ in and $(v_0...v_{n\delta})$ in are coupled through the shared $(\eta_0...\eta_{n-1})$ variables.
For convenience, we will let $v_t := v_{i \delta}$ and $w_t := w_{i\delta}$, where $i$ is the unique integer satisfying $t\in[i\delta, (i+1)\delta)$.
We can verify that, marginally,... | 902 | 1,576 | 1,064 | 877 | null | null | github_plus_top10pct_by_avg |
2(GS)]{}\^2\
=&-C\_0\_[L\^2(GS)]{}\^2, and hence $${\left\langle}(A_0(E)-CI)\phi,\phi{\right\rangle}_{L^2(G\times S)}
={}&{\left\langle}A_0(E)\phi,\phi{\right\rangle}_{L^2(G\times S)}-C{\left\Vert \phi\right\Vert}^2_{L^2(G\times S)} \\
\leq{}&(C_0-C){\left\Vert \phi\right\Vert}^2_{L^2(G\times S)}.$$ Choosing $C\geq C_0... | 903 | 392 | 1,123 | 1,012 | 3,993 | 0.768739 | github_plus_top10pct_by_avg |
472.5 ± 13.9 260.7 ± 2.8 277.9 ± 3.3 314.7 ± 4.4 292.7 ± 8.2 264.2 ± 0.9 266.9 ± 17.3 77.3 ± 1.0 62.2 ± 2.8 101.4 ± 0.8 95.9 ± 5.3
Sac 2 436.3 ± 14.8 456.4 ± 17.5 285.0 ± 3.6 279.3 ± 7.9 322.7... | 904 | 4,965 | 441 | 358 | null | null | github_plus_top10pct_by_avg |
j_1}} \Bigg(\frac{\exp(\ltheta_{j_2})}{\lW-\exp(\ltheta_{j_1})}\cdots \Bigg( \sum_{\substack{j_{\ell-1} \in S \\ j_{\ell-1} \neq i, \\ j_1,\cdots,j_{\ell-2}}} \frac{\exp(\ltheta_{j_{\ell-1}})}{\lW-\sum_{k=j_1}^{j_{\ell-2}}\exp(\ltheta_{k})}\Bigg)\Bigg)\Bigg) \frac{e^{2b}}{\kappa-\ell+1} \nonumber\\
&\leq & e^{4b} \sum_... | 905 | 1,122 | 1,069 | 929 | null | null | github_plus_top10pct_by_avg |
del $\mathcal{C}_{\alpha \beta}$ is bounded from above and below as [@Fong:2016yyh] $$\frac{1}{N}
\biggl( 1 - \sum_{j=1}^3 |U_{\alpha j}|^2 \biggr)
\biggl( 1 - \sum_{j=1}^3 |U_{\beta j}|^2 \biggr)
\leq
\mathcal{C}_{\alpha \beta}
\leq
\biggl( 1 - \sum_{j=1}^3 |U_{\alpha j}|^2 \biggr)
\biggl( 1 - \sum_{j=1}^3 |U_{\beta... | 906 | 1,628 | 1,147 | 1,046 | 1,956 | 0.784162 | github_plus_top10pct_by_avg |
phisms from $S^\la$ to $S^{\mu'}$ is one-dimensional, spanned by the homomorphism $\sigma=\sum_{T\in{\calu}}{\hat\Theta_{T}}$. On the other hand, the space of homomorphisms from $S^\mu$ to $S^\la$ has dimension one or two, each homomorphism being a linear combination of the homomorphisms ${\hat\Theta_{A}}$ and ${\hat\T... | 907 | 612 | 973 | 879 | 2,494 | 0.779344 | github_plus_top10pct_by_avg |
ma_{\textrm{d}} > \sigma_{i}$, the colloid-droplet adsorption energy is [@Ingmar2011] $$\Phi_{i\textrm{d}}(r)= \left \{
\begin{array}{ll}
- \gamma_{i} \pi \sigma_{\textrm{d}} h & \dfrac{\sigma_{\textrm{d}}-\sigma_{i}}{2}<r< \dfrac{\sigma_{\textrm{d}}+\sigma_{i} }{2}\\
0 & \textrm{otherwise},
\end{array} \rig... | 908 | 4,016 | 964 | 788 | null | null | github_plus_top10pct_by_avg |
es of the quantum numbers, super-inflationary phase takes place in this semi-classical region.
Our goal is to describe the production of the gravitational waves during the super-inflation. This problem was preliminary analysed in Ref. [@Mielczarek:2007zy], but quantum corrections to the equation for tensor modes was n... | 909 | 1,283 | 926 | 925 | null | null | github_plus_top10pct_by_avg |
302 180.9 449.5 3.24X10^-4^/5.25X10^-7^ *p*=0.227
3 107 250 159.8 416.6 1.17X10^-2^/2.27X10^-5^ *p*=0.0295^\*\*^
1 267 506 345.7 698.5 0.200/0.702
Women 2 72 ... | 910 | 2,819 | 1,469 | 952 | null | null | github_plus_top10pct_by_avg |
s is a larger literature than can be addressed completely here, it includes early work on model selection [@hurvich1990impact] and model averaging interpretations [@hjort2003frequentist]; the impossibility results of [@leeb2008can], [@buja2015models] on random $X$ and model misspecification; methods based on resampling... | 911 | 772 | 1,714 | 1,117 | null | null | github_plus_top10pct_by_avg |
nerated by assigning to each $p_{ij}$ ($i\neq j$) a random number between $0$ and $ \frac{1}{m}$ and $p_{ii}= 1-\sum_{j\neq i} p_{ij}$. The mean KSE is plotted versus the mixing time (Fig. \[fig:KS1\]) by working out $h_{KS}$ and $t(\epsilon)$ for each random matrix. (Fig. \[fig:KS1\]) shows that KSE is on average a de... | 912 | 2,723 | 2,358 | 926 | 1,372 | 0.790365 | github_plus_top10pct_by_avg |
\rm out\to inn}) \sigma^m_{k'}({\rm out}){\cal V}_{N_R+1},\end{aligned}$$ $$\begin{aligned}
\label{eq:Theta_out}
\Theta^m_k({\rm out}) &= \sum_{i'=1}^{N_R} {\cal G}^m_{k,i'}({\rm top\to out}) \sigma^m_{i'}({\rm top}){\cal V}_{i'} + \sum_{i'=1}^{N_R} {\cal G}^m_{k,i'}({\rm bot\to out}) \sigma^m_{i'}({\rm bot}){\cal V}... | 913 | 2,056 | 1,108 | 926 | null | null | github_plus_top10pct_by_avg |
in $\cup_{j=1}^{k} D_{t_j}$ is allocated at least $c$ balls (that is, the tree $T$ is $c$-loaded) is at most $$\binom{m}{cy} \left(\frac{\alpha y}{n}\right)^{cy}{\leqslant}\left(\frac{{\mathrm{e}}m}{cy}\right)^{cy} \left(\frac{\alpha y}{n}\right)^{cy}{\leqslant}\left(\frac{{\mathrm{e}}\alpha}{c}\right)^{cy}{\leqslant}... | 914 | 975 | 1,422 | 933 | 3,025 | 0.775375 | github_plus_top10pct_by_avg |
e{z}_i&1+\pi \tilde{w}_i \end{pmatrix}$$ such that $\tilde{s}_i=\mathrm{id}$ mod $\pi \otimes 1$. Then $$\begin{gathered}
\label{ea23}
\sigma({}^t\tilde{m}_{i,i})h_i\tilde{m}_{i,i}=(-1)^{(i-1)/2}
\begin{pmatrix}\sigma({}^t\tilde{s}_i)&\sigma( {}^t \tilde{y}_i)&\sigma(\pi\cdot {}^t \tilde{v}_i)\\
\sigma(... | 915 | 2,918 | 623 | 900 | null | null | github_plus_top10pct_by_avg |
\to \beta \in R$, implying that the same step can be performed in $G$ as $\gamma_1 \alpha_1 \underline{\alpha} \alpha_2 \gamma_2 {\Rightarrow}_{G,1}
\gamma_1 \alpha_1 \underline{\beta} \alpha_2 \gamma_2.$ Thus $L(G')\subseteq L(G)$ holds as well. Moreover, any derivation step in $G$, $\gamma_1 \alpha_1 \underline{\al... | 916 | 3,312 | 1,038 | 702 | 2,599 | 0.778542 | github_plus_top10pct_by_avg |
dealloc
{
[super dealloc];
}
@end
Calling code:
{
self.userInteractionEnabled = NO;
mathKeyboardAccess = [[MathKeyboardKey alloc] initWithImage:[UIImage imageNamed:@"mathKey.png"]];
CGRect frm = mathKeyboardAccess.frame;
frm.origin = CGPointMake(80, 171);
mathKeyboardAccess.frame = frm;
... | 917 | 3,031 | 412 | 601 | null | null | github_plus_top10pct_by_avg |
chi_2}}} \end{bmatrix}
+ o(1).$$ From here the argument is completed as in the proof of Theorem \[T:circular-law-correlated\].
Suppose now that $p > 0$. Given $\chi_1 \in \widehat{G}$, by Lemma \[T:extensions\] there are exactly $\frac{1}{p_2}$ values of $\chi_2 \in \widehat{G}$ with $\chi_1\vert_A = \chi_2\vert_A$.... | 918 | 1,785 | 790 | 868 | null | null | github_plus_top10pct_by_avg |
, in which $k_{\parallel}\gg 4m^2$.
![\[fig:mb1\] Photon magnetic moment behavior with regard to external magnetic field strength for the second mode.](prl2.eps){width="3in"}
We conclude, thus, that for photons in a strong magnetic field a nonzero magnetic moment arises, which is paramagnetic, and has a maximum near ... | 919 | 512 | 499 | 872 | 3,006 | 0.775487 | github_plus_top10pct_by_avg |
3rd, 4th and 5th order polynomial terms respectively with each polynomial having evenly spaced roots between $t=0$ and $t=t_f$. As with the simple parametrization $t_f$ specifies the end of the ramps in time.
In each of the three ramps being optimized, the parameters $y_{i}$, $y_{f}$, $A_{1}$, $A_{2}$, $A_{3}$ are ind... | 920 | 1,184 | 1,761 | 1,059 | null | null | github_plus_top10pct_by_avg |
we altered the final step of the data generating mechanism in Equation [(8)](#sim7930-disp-0008){ref-type="disp-formula"}, so that the final outcome was calculated by $$\begin{matrix}
Y_{\mathit{Fij}} & {= \beta_{i} + \left( {\theta + u_{2i}} \right)\textit{treat}_{\mathit{ij}} + e_{\mathit{ij}}} \\
& {\beta_{i} \sim ... | 921 | 900 | 1,998 | 912 | 458 | 0.809316 | github_plus_top10pct_by_avg |
\[prop-ex\]) $$(L_-g)(y,\omega,E):=g(y-\tau_+(y,\omega)\omega,\omega,E),\quad g\in T^2_{\tau_-}(\Gamma_-).$$ From [@dautraylionsv6 p. 253] (or [@cessenat85]) it follows that for $g\in T^2_{\tau}(\Gamma)$, where $\tau|_{\Gamma_-}=\tau_-$, $\tau|_{\Gamma_+}=\tau_+$ and $\tau|_{\Gamma_0}=0$, there exists an element $\tild... | 922 | 592 | 1,089 | 919 | null | null | github_plus_top10pct_by_avg |
_i(r_p(\chi ^{-1}))^{-1} E ^-_{i,-c_{pi}},\\
{T}_p^-(F_p)=&E _p L _p^{-1},&
{T}_p^-(F_i)=&(-1)^{c_{p i}} F ^-_{i,-c_{p i}}.
\end{aligned}$$
\(ii) The maps ${T}_p$, ${T}_p^-$ satisfy ${T}_p {T}_p^-={T}_p^-{T}_p={\operatorname{id}}_{U(\chi )}$.
\(iii) There exists a unique ${\underline{a}}\in ({{\Bbbk }^\tim... | 923 | 1,269 | 1,045 | 892 | null | null | github_plus_top10pct_by_avg |
r this study. However, the scale needs to be validated using a larger representative sample. Tension-reduction motivations seemed to be the most important social-cognitive factor in young Sri Lankan males' drinking behavior. These findings have several implications for public health research and interventions. There is... | 924 | 4,669 | 667 | 468 | null | null | github_plus_top10pct_by_avg |
nonzero elements is nonzero. This is a contradiction, and so Eq. \[eq-identity\] does not hold.
Concluding remarks {#sec-conclude}
==================
In this work we presented the first 2-server PIR scheme (information theoretic) with sub-polynomial cost. It is unclear what is the optimal communication cost of 2-ser... | 925 | 1,070 | 2,121 | 1,045 | 1,915 | 0.784412 | github_plus_top10pct_by_avg |
riangle;
- each side of triangle intersect one outgoing edge of corresponding vertex.
$$\begin{picture}(260,60) \qbezier[25](0,30)(0,50)(20,50)
\qbezier[25](0,30)(0,10)(20,10) \qbezier[25](20,10)(40,10)(40,30)
\qbezier[20](60,30)(60,45)(75,45)
\qbezier[20](60,30)(60,15)(75,15)
\qbezier[20](75,45)(90,45)(90,30)
\qbe... | 926 | 3,225 | 1,387 | 701 | null | null | github_plus_top10pct_by_avg |
{\Delta_{c}(\lambda)^{\text{reg}}}\not=0.$$
If $c\not\in \mathcal{C}$, we are done. Indeed, in this case [@BEGqi Corollary 2.11] implies that $\Delta_{c+1}(\lambda)$, $\Delta_{c}(\lambda)$ and hence $\widetilde{S}_c(\Delta_{c}(\lambda))$ are all simple modules. The isomorphism implies that $\widetilde{S}_c(\Delta_{c}(... | 927 | 367 | 1,229 | 968 | 3,922 | 0.769286 | github_plus_top10pct_by_avg |
(\pi)\cdot {}^tm_{i,i}'a_i+ \pi\cdot a_i m_{i,i}'=\pi\begin{pmatrix} 2z&-x+w\\-x+w&-2y\end{pmatrix}.$$ Thus there are three linear equations $-x+w=0, ~~~ z=0, ~~~ y=0$ and $x$ determines every other entry of $m_{i,i}'$.\
2. Assume that $i$ is odd and that $L_i$ is *free of type $I$*. Then
$\pi^ih_i=\xi^{(i-1)/2}... | 928 | 2,934 | 1,123 | 884 | null | null | github_plus_top10pct_by_avg |
$m_\pi=138$ MeV and $m_K=495$ MeV, $q_0\equiv
\frac12(M_\Lambda-M_N)$, $g_{NN\pi}\equiv \frac{g_A M_N}{f_\pi}$, $g_{\Lambda N
K}\equiv-\frac{D_s+3F_s}{2\sqrt3f_\pi}$, ${\overline{M}}\equiv\frac12(M_N+M_\Lambda)$, and $$\begin{aligned}
{\hat A} &=\left( \frac{ C^{PV}_{K}}{2} +
D^{PV}_{K} + \frac{
C^{PV}_{K}}{2} {\vec... | 929 | 1,322 | 1,428 | 955 | null | null | github_plus_top10pct_by_avg |
er analysis indicated that the genetic heterogeneity has certain unique properties. First, a majority of the genetic heterogeneity sites were detected in unique genomic areas. Many of them have non-synonymous mutations, leading to amino acid alterations in target proteins (Table [2](#T2){ref-type="table"}). For example... | 930 | 1,806 | 2,186 | 1,003 | null | null | github_plus_top10pct_by_avg |
16) 0.0040 (16)
C27 0.018 (2) 0.016 (2) 0.019 (2) −0.0002 (18) 0.0084 (19) 0.0023 (18)
C28 0.019 (3) 0.020 (2) 0.037 (3) 0.005 (2) 0.012 (2) 0.000 (2)
C29 0.011 (2) 0.033 (3) 0.022 (3) −0.002 (2) 0.0048 (19) 0.002 (2)
C30 0.018 (2)... | 931 | 4,789 | 453 | 540 | null | null | github_plus_top10pct_by_avg |
1}.\end{aligned}$$ As before, the coefficient of the principal chiral model term is $1/f^2$ and the Wess-Zumino term has coefficient $k$. The Maurer-Cartan equation $d (dg g^{-1} ) = dg g^{-1} \wedge dg g^{-1}$ is: $$\begin{aligned}
- \frac{1}{2} ( \frac{1}{f^2} - k) \bar{\partial} j^a_z + \frac{1}{2} ( \frac{1}{f^2}... | 932 | 2,634 | 1,210 | 946 | null | null | github_plus_top10pct_by_avg |
follows: $$\begin{aligned}
{\bf 45} & = & {\bf 8}_{-2} \oplus {\bf 28}_0 \oplus {\bf 1}_0 \oplus
{\bf 8}_2, \\
{\bf 16} & = & {\bf 8}_{-1} \oplus {\bf 8}_{+1}, \\
{\bf 10} & = & {\bf 1}_{-2} \oplus {\bf 8}_0 \oplus {\bf 1}_{2}, \\
{\bf 1} & = & {\bf 1}_0,\end{aligned}$$ where the subscript indicates the $q_-$ charge.
... | 933 | 1,097 | 1,373 | 865 | 3,480 | 0.772065 | github_plus_top10pct_by_avg |
{aligned}$$ where $\w\in\Rbb^L$, and $\bsG$ is defined in with $\h$ being nonnegative ordered. Also, let $\floor{\w}_\ell$ and $\ceil{\w}_\ell$ be the vectors generated from $\w$ by applying the floor and the ceiling operations on the $\ell$-th element only, respectively.
${{\bar{\a}}^\diamond}_k\leftarrow {{\bar{\a}}... | 934 | 511 | 1,353 | 951 | null | null | github_plus_top10pct_by_avg |
$\bar{A} = (a_1, \dotsc, a_n)$ and $\bar{B} = (b_1, \dotsc, b_n)$. Inductively and by symmetry, it suffices to show for each $\ell$ that $(\bar{A}-\{a_\ell\},\bar{B}-\{b_{\ell}\})$ is upper-triangular in $N = M \con a_\ell \del b_\ell$. Indeed, for each $k < \ell$ we have $\cl_N(\{a_1,\dotsc, a_k\}) \supseteq \cl_M(\{a... | 935 | 933 | 1,198 | 908 | null | null | github_plus_top10pct_by_avg |
thcal O(n) \otimes A^{\otimes r}\otimes M\otimes A^{\otimes s}\to M$, and since $\widehat{\mathcal O}(\vec X;\varnothing) =\mathcal O(n-1)$ for $|\vec X|=n$, we also have “inner product maps” $ \mathcal O(n-1) \to Hom(A^{\otimes i-1} \otimes M
\otimes A ^{\otimes j-i-1} \otimes M \otimes A^{\otimes n-j} ,k)$. Notice th... | 936 | 765 | 833 | 873 | 2,566 | 0.778813 | github_plus_top10pct_by_avg |
\sum_{t=1}^{m} q_i(t,\text{blue})\right)
\, \left( { \prod_{i\in {\text{col}}^{-1}(\text{red})}} \,
\sum_{t=1}^{m} q_i(t, \text{red})\right)
\nonumber\\
&{\leqslant}\frac{n}{\binom{{s}}{d}} \left({\beta d^3}\right)^{|{\text{col}}^{-1}({\text{blue}})|} \left({\frac{2\beta kd^4}{n^{\varepsilon}}}\ri... | 937 | 1,098 | 858 | 964 | null | null | github_plus_top10pct_by_avg |
-1$ instead of $\mu $). We obtain that $$\begin{aligned}
F_{\beta '_{n+\nu +1-\mu }} F_{\beta '_{n+2-\mu }}^{{b^{\chi}} (\beta '_{n+2-\mu })-1}
F_{\beta '_{n+3-\mu }}^{{b^{\chi}} (\beta '_{n+3-\mu })-1}\cdots
F_{\beta '_n}^{{b^{\chi}} (\beta '_n)-1} F_{i_\mu }^t v_{\Lambda _\mu }=0
\end{aligned}$$ for all... | 938 | 890 | 1,226 | 1,034 | null | null | github_plus_top10pct_by_avg |
lo variability and the size of the numerical lattice required for accurate numerical integration also increase as with the true number of MUs. This demonstrates the challenge of MUNE for large neuromuscular systems that possess complex features resulting from alternation. Of the $19$ datasets where the MAP estimate $\h... | 939 | 41 | 1,300 | 804 | null | null | github_plus_top10pct_by_avg |
1
, R., [van Dokkum]{}, P. G., [Tal]{}, T., [Marchesini]{}, D., [Kriek]{}, M., [Franx]{}, M., & [Coppi]{}, P. 2009, , 697, 1290
, M. R., [Eisenstein]{}, D., [Hogg]{}, D. W., [Schlegel]{}, D. J., & [Brinkmann]{}, J. 2005, , 629, 143
, M. [et al.]{} 2010, , 524, A76+
, F., [Jog]{}, C. J., & [Combes]{}, F. 2007, , 476... | 940 | 317 | 2,485 | 1,129 | null | null | github_plus_top10pct_by_avg |
triplet probability for that class is computed.[]{data-label="triplet_detector"}](figures/classification_with_triplet.pdf){width="80.00000%"}
where $p_c(y | x)$ and $p_t(y | x)$ are the probability distributions from the classifier and triplet network respectively, $k$ is the most probable class output by the classif... | 941 | 79 | 2,241 | 938 | 2,252 | 0.781421 | github_plus_top10pct_by_avg |
`atcttatttatt`
2481059 NONSYN T:5 G:148 G:37 `ttagattggttg` response regulator protein
... | 942 | 1,339 | 2,605 | 1,055 | null | null | github_plus_top10pct_by_avg |
riaxone daily (3.26 ± 6.9 days) (p = 0.034). The odds ratio for ICU utilization was 0.11 (95% CI 0.02--0.65). However, this difference was no longer significant after controlling for MELD score - odds ratio 0.21 (95% CI 0.04--1.07). Finally, we examined one-year survival for patients treated with 1 versus 2 g ceftriaxo... | 943 | 818 | 1,282 | 1,055 | null | null | github_plus_top10pct_by_avg |
\[TKMeqn\] and \[TKMupdate\] below). This is similar to a short-term memory, allowing previous inputs to have some effect on the processing of the current input, so that the neurons which have won recently are more likely to win again. In the experiments reported here the value $\gamma = 0.4$ was used, meaning that on... | 944 | 4,849 | 1,206 | 903 | 607 | 0.804457 | github_plus_top10pct_by_avg |
} - u_{m,n}^{(i+\ell_2)} = v^{(i)}_{m+1,n} - v^{(i+\ell_1)}_{m,n} , \label{eq:dLP-ex-cc-2}\end{gathered}$$
for $i \in {\mathbb{Z}}_N$.
Quotient potentials {#sect:coprime-quotient}
-------------------
Equations (\[eq:dLP-ex-cc-1\]) hold identically if we set $$\begin{gathered}
\label{eq:dLP-gen-ph-1}
u^{(i)}_{m,n} =... | 945 | 467 | 1,439 | 1,069 | null | null | github_plus_top10pct_by_avg |
frac{2k}{\lambda_n}\tau\right)d\tau,\quad s \in [0,t),\end{aligned}$$
which leads to $$\begin{aligned}
e_{n,2}(s)&=c_1\sin\left(\frac{2k}{\lambda_n}s\right)-c_2\cos\left(\frac{2k}{\lambda_n}s\right)\\*
&\hspace{4mm}+c_2\left(\cos\left(\frac{2k}{\lambda_n}t\right)+1\right)-c_1\sin\left(\frac{2k}{\lambda_n}t\right),\qua... | 946 | 3,563 | 1,561 | 897 | null | null | github_plus_top10pct_by_avg |
based on desired tolerance of $10^{-4}$. From top left to bottom right, we see the standard deviation of the estimator, the sample variance, the absolute error (using a quadrature approximation for for the reference value), and the amount work (number of samples $\times$ mean number of steps).[]{data-label="fig:test5"}... | 947 | 140 | 1,028 | 913 | 2,558 | 0.778876 | github_plus_top10pct_by_avg |
\hat{\mathcal{H}}^{[2]}_{-},$$ where $$\label{hblocks-}
\begin{aligned}
& \hat{\mathcal{H}}^{[1]}_{-} =
\bigoplus_{n = 0}^{m - 1} \langle n , e |\hat{\mathcal{H}}^{(m)}_{+} | n , e \rangle
= \hbar
\bigoplus_{n = 0}^{m - 1} \left( \nu n + \tfrac{\omega_0}{2} \right), \\
& \hat{\mathcal{H}}^... | 948 | 3,685 | 821 | 694 | null | null | github_plus_top10pct_by_avg |
d in $\hat H_{\rm e-ph}$ since it captures the fact that a vibrational excitation of the adsorbed molecule may couple to electrons in the substrate when parts of the molecule periodically beat onto the substrate surface. In particular, we will show below that this unconventional Holstein coupling can reduce the Kondo t... | 949 | 118 | 2,004 | 1,111 | null | null | github_plus_top10pct_by_avg |
}{n}} \cdot \frac{\binom{{s}-2}{d-2}}{\binom{{s}}{d}} \cdot {\ensuremath{\operatorname{\mathbf{Pr}}\left[A(p_J,t)\right]}}
= {\frac{2\beta d(d-1)}{({s}-1)n}}\, {\ensuremath{\operatorname{\mathbf{Pr}}\left[A(p_J,t)\right]}},
\end{aligned}$$ as $\binom{{s}-2}{d-2}$ is the number of $d$-element subsets of $H_t$ wh... | 950 | 2,750 | 1,065 | 923 | 3,946 | 0.769077 | github_plus_top10pct_by_avg |
in of precursor events should actually lead to a different conclusion.
Transduced values potentially control the status of any safety concern. Tests simply pass or fail, but evaluation of why a test passes or fails can become nontrivial, requiring collaboration between mechanical, software, and system safety engineers... | 951 | 3,956 | 1,933 | 727 | 2,229 | 0.781644 | github_plus_top10pct_by_avg |
iscoveryCNN_1; @ObjectDiscoveryCNN_2; @ObjectDiscoveryCNN_3] and co-segmentation [@InteractiveCoseg] only require image-level labels without object bounding boxes. Object discovery is mainly implemented by identifying common foreground patterns from the noisy background. People usually consider closed boundaries and co... | 952 | 316 | 1,087 | 1,036 | 765 | 0.800575 | github_plus_top10pct_by_avg |
1.375 (8)
C10---H10 0.9500 C66---H66 0.9500
C11---C12 1.381 (7) C67---C68 1.380 (8)
C11---H11 0.9500 C67---H67 0.9500
C12---H12 0.9500 C68---C69 1.395 (7)
C13---H13A 0.9900 C68---... | 953 | 4,096 | 987 | 707 | null | null | github_plus_top10pct_by_avg |
Q}$*, then* $\delta _{1}A$* *$\delta _{2}$* may belong or not to* $\psi _{AD}^{Q}$*. To be precise, it belongs to* $\psi _{AD}^{Q}$* iff* $S_{\delta _{1}}\subset S_{\delta _{2}}$* or* $S_{\delta _{2}}\subset S_{\delta _{1}}$
Indeed, $S_{\delta _{1}}\cup S_{\delta _{2}}\in \mathcal{L(S)}$ or, equivalently, $S_{\delta _... | 954 | 2,890 | 1,545 | 991 | null | null | github_plus_top10pct_by_avg |
r>
<td>
@Html.TextBoxFor(model => model.AllFeatures[i].Id)
</td>
<td>
@Html.TextBoxFor(model => model.AllFeatures[i].Name)
</td>
<td>
@Html.EditorFor(model => model.AllFeatures[i].IsActive)
</td>
</tr>
}
Q:
Add class to td with ... | 955 | 1,314 | 57 | 837 | 829 | 0.799194 | github_plus_top10pct_by_avg |
mulation if no signal were present. []{data-label="tab:lim"}
Table \[tab:MSSM\_lim\] shows the preliminary 95% C.L. lower limits on ${M_{\mathrm{h}}}$ and ${M_{\mathrm{A}}}$ for the four LEP experiments [@felcini; @al_moriond; @del_moriond; @l3_moriond; @op_moriond], as well as the derived excluded ranges of $\tan\bet... | 956 | 864 | 1,627 | 1,112 | null | null | github_plus_top10pct_by_avg |
--0.2
PM25 --0.34 --0.23 0.31 --0.18 1 0.73 0.65 0.81 0.29 0.29
SO~2~ --0.33 0.03 0.09 --0.27 0.73 1 0.35 0.66 0.43 0.22
CO --0.26 --0... | 957 | 5,631 | 326 | 263 | null | null | github_plus_top10pct_by_avg |
ackrel{\eta}{\to} (u\times\id)_!(\id\times v)_\ast (u\times\id)^\ast(u\times\id)_!\\
&\toiso (u\times\id)_!(u\times\id)^\ast(\id\times v)_\ast (u\times\id)_!\\
& \stackrel{\varepsilon}{\to} (\id\times v)_\ast (u\times\id)_!\end{aligned}$$ is an isomorphism in . This is to say that the morphism $u_!\colon{\sD}^A\to{\sD}... | 958 | 1,101 | 871 | 948 | 1,102 | 0.7944 | github_plus_top10pct_by_avg |
= 2k+1, \ldots, 3k$, $\{a_n, \ldots, a_{n+k}\}$ contains one point in every row.
From now on, $a_n$ refers to the points defined in the above proof. This proposition is the motivation for choosing the value $6k$ in the proof of Lemma \[otherlemma\].
We can now prove Theorem \[generalk\]. We will need 3 distinct parti... | 959 | 750 | 1,070 | 881 | 3,126 | 0.774711 | github_plus_top10pct_by_avg |
h} x} (UX)^{\dagger} A W e^{ - i {\bf \Delta_{s} } x} \\
e^{ i {\bf \Delta_{s} } x} W^{\dagger} A (UX) e^{ - i {\bf h} x} & e^{ i {\bf \Delta_{s} } x} W^{\dagger} A W e^{ - i {\bf \Delta_{s} } x} \\
\end{array}
\right].
\label{H1-matrix}\end{aligned}$$ That is, $(H_{1})_{i j} = 0$ in the whole active neutrino subsp... | 960 | 2,944 | 1,331 | 999 | null | null | github_plus_top10pct_by_avg |
\in {{\mathbb R}}^2 : x_1\cos \theta + x_2\sin\theta = r \}$, where $\theta\in[0,\pi)$ is the angle and $r\in{{\mathbb R}}$ is the distance of $L$ from the origin as shown in Figure \[Radon transform\].
(100,80) (0,-65)[![An illustration of the Radon transform. It maps the object $f$ on the $(x_1,x_2)$-domain into $f$... | 961 | 4,137 | 581 | 707 | 1,961 | 0.784131 | github_plus_top10pct_by_avg |
mperature-dependent coupling that runs into a three-dimensional fixed point $\alpha_{*,3d}k_{\rm phys}/T$ for low cut-off scales $k_{\rm phys}/T\ll 1$. This choice carries some uncertainty as the running coupling in Yang-Mills theory is not universal beyond two loop order. Here we have chosen the Landau gauge couplings... | 962 | 1,168 | 1,571 | 1,057 | 2,591 | 0.778643 | github_plus_top10pct_by_avg |
with frequency separations of $4.7-4.8\,\mu$Hz. However, the low amplitude central peak of this triplet at $f_6=5569.6\,\mu$Hz do not reach the 4S/N significance limit in the test 30s data. Still, to make the discussion of the triplet structures clear, we added $f_6$ to the list of Table \[table:lp133freq\] in parenth... | 963 | 90 | 1,387 | 991 | 2,024 | 0.783401 | github_plus_top10pct_by_avg |
om the introduction. Indeed we will prove more generally that a version of that theorem holds for all values of $c\in {\mathbb{C}}$ that satisfy Hypothesis \[morrat-hyp\]. As was true with Corollary \[morrat-cor\] and Proposition \[shiftonO\], the theorem will take slightly different forms depending on whether $c\in \m... | 964 | 778 | 788 | 905 | 2,051 | 0.783179 | github_plus_top10pct_by_avg |
3 for $b=2$, and 0.0211 for $b=3$ fractal, equal to $D^*$ for the corresponding cases $v<v_c(u_\theta)$ of the ASAWs model.
- When $w=w_c(u_\theta,t)$, the RG parameters tend to the fixed point $$\label{fpt2}
(A_\theta,B_\theta,C^*,A_1^*,A_2^*,A_3^*,A_4^*,B_1^*,
B_2^*)\>,$$ which corresponds to the phase ... | 965 | 1,716 | 1,937 | 1,040 | 2,017 | 0.783489 | github_plus_top10pct_by_avg |
oot>
So in short, I have a node in which I can have some text, and various different nodes (or none) in any order. There is no way of knowing before hand if the content is only text, text and one of the nodes, only one of the nodes, text and both nodes in any order, etc.
Here's what I need to have:
Wanted XML output
<... | 966 | 696 | 197 | 549 | 466 | 0.808808 | github_plus_top10pct_by_avg |
vq-\MW\,\vln\,\vu+const_1+\vln\,\softmax(\MW\,\vln\,\vu+\vb)) \\
&=\softmax(\MW\,\vln\,\vq-\MW\,\vln\,\vu+const_1+\MW\,\vln\,\vu+\vb+const_2) \\
&=\softmax(\MW\,\vln\,\vq+\vb+const_1+const_2)
=\softmax(\MW\,\vln\,\vq+\vb)=\muh_{DirLin}(\vq; \MW,\vb)\\
&=\muh(\vq)\end{aligned}$$
#### 3.
Consider a function $\muh(\vq)=... | 967 | 1,800 | 1,470 | 960 | 3,044 | 0.775238 | github_plus_top10pct_by_avg |
nd §\[details\]. We will show that a germ $\alpha(t)$ as above leads to a rank-2 limit (and hence does not contribute a component to the PNC) unless $\alpha(t)$ and certain formal branches (cf. [@MR88a:14001] and [@MR1836037], Chapter 6 and 7) of the curve are closely related. More precisely, we will prove the followin... | 968 | 1,833 | 1,853 | 950 | null | null | github_plus_top10pct_by_avg |
the polar angle $\phi$ is shown in Fig. \[Fig::occl1\]. Besides a change of the absolute hit rate, analogous distributions can be observed for the remaining layers. The $\phi$ distribution shows a significant increase of the number of hits in the region $|\phi|<50^\circ$, due to the particles with large hit time which... | 969 | 3,925 | 1,544 | 924 | null | null | github_plus_top10pct_by_avg |
l{final}
&& F^{(1)}=\frac{\alpha}{3\pi}\left[\frac{(Z\alpha)^2}{\gamma}x^2+
\frac{\kappa(\gamma+\kappa)}{\gamma^2}x+\frac{\kappa}{2\gamma^2}+a
\right]\nonumber\\
&& G^{(1)}=\frac{\alpha}{3\pi}\left[\frac{(Z\alpha)^2}{\gamma}x^2-
\frac{\kappa(\gamma-\kappa)}{\gamma^2}x-\frac{\kappa}{2\gamma^2}+a\right],\end{aligned}... | 970 | 1,024 | 1,489 | 1,114 | null | null | github_plus_top10pct_by_avg |
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------... | 971 | 598 | 542 | 1,245 | null | null | github_plus_top10pct_by_avg |
we present a collective detection technique based on statistical divergence. The technique extracts distribution similarities among data collections, and then uses the statistical divergence to detect collective anomalies. Our technique continuously evaluates metrics as evolving features and calculates adaptive thresho... | 972 | 1,247 | 591 | 963 | 1,839 | 0.785175 | github_plus_top10pct_by_avg |
el{\otimes}{\to}{\sV}(A\times B\op\times B\times C\op)\stackrel{\int^B}{\to}{\sV}(A\times C\op),$$ and also this operation enjoys associativity and unitality properties.
\[thm:bicategory\] If is a monoidal left derivator, then there is a bicategory $\cProf({\sV})$ described as follows:
- Its objects are small categ... | 973 | 503 | 1,262 | 986 | 2,823 | 0.776752 | github_plus_top10pct_by_avg |
ic kinds of navigational patterns. To explicitly rule this possibility out, we would need to investigate the underlying link networks in greater detail, which we leave open for future work. We also plan on looking at data capturing navigational paths over distinct platforms of the Web (e.g., from toolbar data) which ma... | 974 | 781 | 2,309 | 880 | null | null | github_plus_top10pct_by_avg |
^{\iota}(X,t)\rangle&=&
\overrightarrow{\cal U}_{{\mbox{\tiny\boldmath$\cal B$}},[\hat{\rho}]}(t)
\vert\psi^{\iota}(X)\rangle
\\
\langle\psi^{\iota}(X,t)\vert&=&
\langle\psi^{\iota}(X,)\vert
\overleftarrow{\cal U}_{{\mbox{\tiny\boldmath$\cal B$}},[\hat{\rho}]}(t)
\;.\end{aligned}$$ Quantum classical averages can be wri... | 975 | 883 | 1,698 | 1,084 | 3,680 | 0.770754 | github_plus_top10pct_by_avg |
his type of differential operator. This is the underlying reason why the method of finding the unitary irreps of NHEK’s isometry introduced in Sec. \[sec:high-lowest-weight\] will lead to separation of variables in many physical systems.
Scalar Laplacian {#sec:sep-scalar}
----------------
As the first example, we loo... | 976 | 3,948 | 781 | 751 | null | null | github_plus_top10pct_by_avg |
tic). Of course the proofs can be rewritten with prefixes $\alpha \in ({\cal R} \times {\cal R})^*$.
#### Strategies
$\;\;$\
The formal systems ${\cal J}(T_0,T'_0,S_0,{\cal B})$ described in subsection \[subsec\_formal\_systems\] were devised so that their set of judgments is recursive. Let us consider now the formal... | 977 | 466 | 973 | 1,098 | 1,536 | 0.788525 | github_plus_top10pct_by_avg |
he right hand side of is precisely $$\mu_1\left\|\sum_p\nu^p\right\|^2-n\sum_p\left\|\nu^p\right\|^2,$$ which by Lemma \[ineq-1\] is bounded above by $\mu_1n^2-n\left\|\mu\right\|^2$ with equality only where either $\rho^p=(1^{\mu_p})$ (case (ii)) or all $\rho^p$ are equal and $\mu=(t^{n/t})$ for some $t$ (case (i)).
... | 978 | 1,412 | 836 | 1,071 | null | null | github_plus_top10pct_by_avg |
rate (FDR) are presented in [Table [2](#tbl2){ref-type="other"}](#tbl2){ref-type="other"}. Interestingly, the metabolites were predominantly increased following freezing at −80 °C prior to preparation of fecal water ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}). The sample stored on ice for 24 h had the... | 979 | 146 | 2,163 | 1,311 | null | null | github_plus_top10pct_by_avg |
$R$ (see \[eqn:R\]) of the neutron frequency to the frequency of the cohabiting mercury magnetometer, which samples the volume uniformly. The measured EDM signals as a function of this ratio are shown in 13 of [@pendlebury04], and are fitted to the straight lines anticipated from \[eqn:DeltaR\] above. However, the fre... | 980 | 310 | 1,514 | 981 | null | null | github_plus_top10pct_by_avg |
{\label{eq:2nddec-bd:n=0}}
&\bigg(\sup_y\sum_{v,b}|v|^2P_{\Lambda;o}^{\prime{{\scriptscriptstyle}(0)}}(v,{\underline{b}})\,
\tau_b\big(\delta_{{\overline{b}},y}+\tilde G_\Lambda({\overline{b}},y)\big)\bigg)\bigg(
\sup_z\sum_{y,v}\tilde Q''_{\Lambda;v,o}(y,z)\bigg)^{j-1}\bigg(
\sum_{z,x}P'_{\Lambda;o}(z,x)\bigg){\non... | 981 | 396 | 1,389 | 1,115 | null | null | github_plus_top10pct_by_avg |
\frac{a^2 k_{max}^2}{2}\right) - I_1\left(\frac{a^2 k_{max}^2}{2}\right) \right]
\label{eq:forcegamma0}$$ in terms of the modified Bessel functions of the first kind $I_n(x)$ and where $k_{max} =2\sqrt{V_p^2 -1}$. For vanishing $a$ the dominant term is proportional to $(V_p^2-1)/V_p$ [@astrakharchik2004motion]. Th... | 982 | 2,229 | 2,296 | 1,041 | 2,364 | 0.780512 | github_plus_top10pct_by_avg |
PSs and RCTs. In the sensitivity analysis excluding studies stopped for harm, benefit, or futility the difference between NPSs and RCTs was no longer statistically significant (p = 0.057, missing excluded, see [Table 3](#pone.0165605.t003){ref-type="table"}). Poor recruitment was the most frequent reason for discontinu... | 983 | 193 | 1,233 | 1,301 | null | null | github_plus_top10pct_by_avg |
law of the projection parameter cannot be consistently estimated without sample splitting.
We want to emphasize that we do not claim that the LOCO parameter is optimal in any sense. We just aim to show that there exist alternatives to the usual parameters that, when the linear model is not true, (i) are more interpre... | 984 | 2,929 | 1,101 | 949 | 2,432 | 0.779797 | github_plus_top10pct_by_avg |
. Perhaps a moderator, admin or dev happens to have a mentally challenged family member, or just has enough common sense to know that there are probably countless users on Stack Overflow who do. Would you call your boss that name, to his/her face? Would you feel good if your boss called you that name (to your face or b... | 985 | 4,501 | 447 | 789 | 93 | 0.826766 | github_plus_top10pct_by_avg |
ean and 95% confidence interval from @Hal04.[]{data-label="fig:RealParam"}](figures/R10_Fest.pdf "fig:"){width="33.00000%"} ![Estimated excitability curves from the eight MU hypotheses for data sets R10 (left) and R50 (centre) with corresponding expected MUTF mean estimates. Right: median and 95% credible interval for ... | 986 | 4,765 | 2,530 | 819 | null | null | github_plus_top10pct_by_avg |
\left(\frac{2}{n}\right)^{k-1}.
\end{aligned}$$ On the other hand, ball $t$ is allocated to a given bin with probability at most $\Delta_t/(n\Delta_t/2)=2/n$. Therefore, the probability that $T$ [is $c_1$-loaded]{} is at most $$\begin{aligned}
\label{up:2}
\binom{n}{ck}\left(\frac{2k}{n}\right)^{c_1k... | 987 | 1,382 | 1,223 | 1,038 | null | null | github_plus_top10pct_by_avg |
}^{{b^{\chi}} (\beta _2)-1}
F_{\beta _1}^{{b^{\chi}} (\beta _1)-1}v_\Lambda \,|&\\
0\le l_k<{b^{\chi}} (\beta _k)\quad
\text{for all $k\in \{m+1,m+2,\dots ,m+n\}$}&
\end{aligned}$$ forms a vector space basis of $M^\chi (\Lambda )$.
For all $k\in \{1,2,\dots ,m\}$ let $\Lambda _k={t}_{i_{k-1}}\cdo... | 988 | 1,879 | 1,007 | 1,008 | null | null | github_plus_top10pct_by_avg |
random vectors in $\mathbb{R}^p$. Let $S^X_n = \frac{1}{\sqrt{n}} \sum_{i=1}^n X_i$ and, similarly, let $S^Y_n
= \frac{1}{n} \sum_{i=1}^n Y_i$, where $Y_1,\ldots, Y_n$ are independent vectors with $Y_i \sim N_p(0,\mathbb{E}[X_i X_i^\top])$. Let $\mathcal{A}$ be the collection of polyhedra $A$ in $\mathbb{R}^p$ of the f... | 989 | 2,052 | 670 | 920 | null | null | github_plus_top10pct_by_avg |
t path (i.e., $o\to v_1\to
b_2\to v_3\to\cdots\to x$) and a middle zigzag path. We use the lowermost path to bound $|x|^2$ as $$\begin{aligned}
{\label{eq:x2-bd}}
|x|^2=\sum_{n=0}^j|a_n|^2+2\sum_{0\leq m<n\leq j}a_m\cdot a_n
\leq(j+1)\sum_{n=0}^j|a_n|^2,\end{aligned}$$ where $a_0=v_1$, $a_1={\underline{b}}_2-v_1$ ,$a_... | 990 | 1,512 | 989 | 1,080 | 3,564 | 0.771524 | github_plus_top10pct_by_avg |
though it is dynamical. It “anchors” the construction, setting a reference scale by fixing an observable dimensionful dynamical variable. (In closed worlds $K$ is like a “time” variable, in that it may “locate” the thin sandwich. In cosmology, $K$ is essentially the inverse mean “Hubble time.”) There is no underlying g... | 991 | 3,834 | 767 | 790 | 2,899 | 0.776237 | github_plus_top10pct_by_avg |
pmod4)\\[5pt]
\hbox to \frt{\hfil$\mfrac a2$\hfil}&(a\equiv0\ppmod4).
\end{cases}$$ Then $n',a'$ satisfy the conditions of the proposition, and $n'<n$. So by induction there is a pair $u',v'$ such that $$v'\equiv1\pmod4,\qquad u-v\equiv-1\pmod{2^{l(v'-2)}},\qquad\mbinom{u'-v'}{u'-a'}\equiv1\pmod2.$$ Again, beca... | 992 | 1,474 | 1,135 | 918 | 1,298 | 0.791413 | github_plus_top10pct_by_avg |
the point $w$: :j\^a\_[L,z]{}(z) j\^b\_[L,z]{}(w): = \_[n,|n=0]{}\^ :(\^n |\^[|n]{} j\^a\_[L,z]{}) j\^b\_[L,z]{}:(w). Let us now consider the OPE of one of these composite operators with the current $j^c_{L,z}(x)$: $$\begin{aligned}
j^c_{L,z}(x) & :(\p^n \bar \p ^{\bar n} j^a_{L,z}) j^b_{L,z}:(w) =
j^c_{L,z}(x) \lim_... | 993 | 3,122 | 1,226 | 857 | null | null | github_plus_top10pct_by_avg |
t $L_i=\bigoplus_{\lambda}H_{\lambda}\oplus A(2\delta, 2b_i, 1)$ for certain $b_i\in A$ and $\delta (\in A) \equiv 1 \mathrm{~mod~}2$. Thus the orthogonal group $\mathrm{O}(B_i/Z_i, \bar{q}_i) ~(=\mathrm{O}(n_i, \bar{q}_i))$ is split if and only if the quadratic space $A(2\delta, 2b_i, 1)/\pi A(2\delta, 2b_i, 1)$ is is... | 994 | 1,296 | 1,197 | 962 | 3,382 | 0.772754 | github_plus_top10pct_by_avg |
ight).[]{data-label="fig:topology"}](Plot11_0b-eps-converted-to.pdf "fig:"){width=".3\textwidth"} (-95,-5)[graph size ]{} (-95,100)[Worst-case $\theta^*$]{}
The Role of the Position of the Separators
------------------------------------------
As predicted by theorem \[thm:main2\], rank-breaking fails when $\gamma$ is... | 995 | 549 | 299 | 1,066 | null | null | github_plus_top10pct_by_avg |
etermine factors associated with changes in percentage plasma choline concentration
**Simple regression** **Regression coefficient** **r** **r**^**2**^ ***P***
----------------------------------- ---------------------------- ------- -------------- ---------
Age \[months\] ... | 996 | 4,517 | 528 | 533 | null | null | github_plus_top10pct_by_avg |
(Q)\subset \cdots$.
First we define a graph $\Gamma_n$ \[resp. $\Gamma_{n+\frac{1}{2}}$\] for a non-negative integer $n\in\mathbb{Z}_{\geq 0}$. Then we define the sets of [*tableaux*]{} as sets of paths on this graph. Figure \[fig:brad\] will help the reader to understand the recipe.
![$\Gamma_4$[]{data-label="fig:br... | 997 | 1,376 | 748 | 1,025 | 3,652 | 0.770892 | github_plus_top10pct_by_avg |
since the proof of Theorem \[thm:mrdeterm\] is constructive, the states which can be transformed into $y$ by catalyst-assisted transformation while cannot by multiple-copy transformation can also be constructed.
We have proved that $T(y)\not = M(y)$ in some cases. Moreover, witness vectors which are in $T(y)$ but not... | 998 | 122 | 1,287 | 1,009 | 2,968 | 0.775765 | github_plus_top10pct_by_avg |
rtex states already found in §\[sec:3D\_InstOpt\_E0to0\] and §\[sec:3D\_InstOpt\_E\], and to the Poincaré limit. Another interesting possibility is to replace the energy $\K({\mathbf{u}})$ with the helicity [$\H({\mathbf{u}}) :=
\int_{\Omega} {\mathbf{u}}\cdot(\bnabla\times{\mathbf{u}})\,d\Omega$]{} in the multiobjec... | 999 | 442 | 1,576 | 1,103 | null | null | github_plus_top10pct_by_avg |
symbol meaning
${\mathbf{X}}^T$ transpose of ${\mathbf{X}}$
${\mathbf{X}}^H$ conjugate transpose of ${\mathbf{X}}$
${\mathbf{X}}\left(m,n\right)$ entry of ${\mathbf{X}}$ in $m$-th row and $n$-th column
$... | 1,000 | 1,215 | 1,849 | 1,148 | null | null | github_plus_top10pct_by_avg |
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