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 |
|---|---|---|---|---|---|---|---|
0 1
Marital status^[e](#table-fn1-0192513X17710773){ref-type="table-fn"}^ 0.16 0.37 0 1
Education 7.21 2.18 0 11
Years in the Netherlands 14.31 4.4... | 1,401 | 192 | 1,699 | 1,691 | 939 | 0.797256 | github_plus_top10pct_by_avg |
$\alpha\in L$ and that $\bar{s}$ is on a level above $\delta$. Similarly we may assume that for all $\xi,\rho<\delta$, $\bar{s}$ has decided the statement $$\dot{U}(\eta,0)\cap\dot{Z}(\xi,\rho)\neq\emptyset\quad
\text{ for all }\xi,\rho<\delta.$$ Now choose any $\alpha\in L$ (e.g.the least one), and then choose an infi... | 1,402 | 1,775 | 1,678 | 1,266 | null | null | github_plus_top10pct_by_avg |
oint union $$\begin{aligned}
{\label{eq:fin-ind}}
&{\mathop{\Dot{\bigcup}}}_{T\ge j}\,{\mathop{\Dot{\bigcup}}}_{\vec b_T}{\mathop{\Dot{\bigcup}}}_{\{s_it_i\}_{i=1}^j\in
{{\cal L}}_{[0,T]}^{{\scriptscriptstyle}(j)}}\bigg\{H_{{{\bf n}};\vec b_T}(y,x)\cap\bigcap_{i=1}^j
\big\{z_i\in{{\cal D}}_{{{\bf n}};s_i},\,z'_i\in{{... | 1,403 | 485 | 1,430 | 1,494 | 3,856 | 0.769678 | github_plus_top10pct_by_avg |
K \sqrt{p}$ and $\mathbb{E}\left[ \| X_i \|^2
\right] \leq U p$ for all $i = 1,\ldots,n$, Proposition 1.2 in [@hsu12] yields that $$\label{eq:vector.bernstein}
\mathbb{P}\left( \frac{1}{n} \left\| \sum_{i=1}^n X_i \right\| \leq \sqrt{\frac{U p}{n}} + \sqrt{ 8 \frac{U p}{n} \log n} +
\frac{4 K \sqrt{p}}{3 n} ... | 1,404 | 3,841 | 1,371 | 1,074 | null | null | github_plus_top10pct_by_avg |
and $U'\subset Y$ the “same” open subset of $Y$ then $U'$ is also affine by Chevalley’s theorem and so $Y$ has the Chevalley-Kleiman property.
Let $E$ be an elliptic curve and set $S:=E\times {{\mathbb P}}^1$. Pick a general $p\in E$ and $g:E\times \{0,1\}\to E$ be the identity on $E_0:=E\times \{0\}$ and translation ... | 1,405 | 627 | 1,295 | 1,358 | 4,147 | 0.767764 | github_plus_top10pct_by_avg |
lity, it suffices to show this for contraction. If $M \con X = N \con X$ then $M \dcon X = N \dcon X$, so $\dist(M,N) \le \dist(M,M \dcon X) + \dist(N \dcon X,N) \le 2|X|.$
We now consider an operation that turns various elements of a matroid into loops, and moves other elements into parallel with existing elements. L... | 1,406 | 867 | 905 | 1,378 | null | null | github_plus_top10pct_by_avg |
$-module via the ${\mathbb{K}}$-module structure of the second tensor factor.
Let $\Lambda \in {{\mathrm{Hom}}({\mathcal{U}}^0,{{\mathbb{K}}^\times })}$. Triangular decomposition of $U (\chi )$ gives the following standard fact.
The map $U ^-(\chi ){\otimes }_{\Bbbk }{\mathbb{K}}\to M^\chi (\Lambda )$, $u{\otimes }x\... | 1,407 | 1,357 | 1,254 | 1,318 | null | null | github_plus_top10pct_by_avg |
t( \det {\cal E}_0^{\alpha *} \right) \otimes \left( \det T_0^{\alpha }
\right) \otimes {\cal L},$$ which, by symmetry, should also be the same as ${\cal L}^*$. In other words, $$\left( \det {\cal E}_0^{\alpha *} \right) \otimes \left( \det T_0^{\alpha }
\right) \otimes {\cal L}
\: \cong \: {\cal L}^*$$ or more simply ... | 1,408 | 868 | 1,288 | 1,326 | null | null | github_plus_top10pct_by_avg |
%
\mathfrak{m}+q+2d/p_{\ast }}}+\overline{\Phi }_{n}^{\mathfrak{m}}(\delta
_{\ast })\Big)^{1+\varepsilon _{\ast }} \label{TR6''}\end{aligned}$$
**C**. Let $p>2d.$ Set $\bar{%
\mathfrak{m}}=1+\frac{q+1+2d/p_{\ast }}{\delta _{\ast }}$. There exist $%
C\geq 1,\eta \geq 0$ (depending on $q,p,\varepsilon _{\ast },\del... | 1,409 | 533 | 1,383 | 1,414 | null | null | github_plus_top10pct_by_avg |
gg > = \alpha{\pi \over 2}
\sum_{m=1}^{\bar{K}}\sum_{n=1}^{K} d_{\bar{K}m} d_{Kn}\ n \
\Delta_{\bar{\nu}-\nu} (\Delta_{m-n+1}-\Delta_{n-m+1}) \eqno(A9)$$
$$\bigg < \bar{K}^- \bar{\nu} \bigg | {\alpha^2 \over
F^2}{\partial^2 \over \partial^2 \phi} \bigg | K^- \nu \bigg > =
{\alpha^2 \pi \over \sqrt{1-\alpha^2}}
\su... | 1,410 | 2,823 | 925 | 1,382 | null | null | github_plus_top10pct_by_avg |
ch is different from the result of Ref. [@konno] for $DY_\hbar(sl_2)_k$. The reason for this difference is that, first, the Yangian double $DY_\hbar(sl_2)_k$ of Ref. [@konno] is realized in an asymmetric way which differs from the symmetric one which we are using by a shift of parameter [@KL]; Second, as we have remark... | 1,411 | 613 | 1,129 | 1,430 | 1,201 | 0.792829 | github_plus_top10pct_by_avg |
FloorCondition2\] With Lemma \[lemma:FloorCondition\], the inequality condition $f\left(\floor{{{\bar{\a}}^\dagger}_k}_\ell\right) < f\left(\ceil{{{\bar{\a}}^\dagger}_k}_\ell\right)$ in line \[line:FloorCondition\] of Algorithm \[agorithm:SuccessiveQuantization\] can be simplified as $$\begin{aligned}
2\floor{{{\bar{\a... | 1,412 | 432 | 720 | 1,462 | 2,827 | 0.776743 | github_plus_top10pct_by_avg |
rsity of Zurich
*Colin C. Venters*, University of Huddersfield
*Coral Calero*, University of Castilla-La Mancha
*Sedef Akinli Kocak*, Ryerson University
*Stefanie Betz*, Karlsruhe Institute of Technology\
---
abstract: |
Multi-dimensional data classification is an important and challenging problem in many ast... | 1,413 | 144 | 1,654 | 1,411 | null | null | github_plus_top10pct_by_avg |
ar2005].
In our case, firstly, we took the improved parameters, such as the radial velocity curve amplitudes of the F hotter ($K_{1}$) and the K cooler ($K_{2}$) components, the inclination of the orbital axis ($i$), the conjunction time ($T_{0}$; the hotter component is behind) and the orbital period ($P$), from the ... | 1,414 | 2,019 | 2,947 | 1,651 | 1,263 | 0.791921 | github_plus_top10pct_by_avg |
r reasoning establishes that the other restriction $\phi$ is a member of ${\prod{\Phi}}$. The unique $\psi \in {\prod{\Psi}}$ and $\phi \in {\prod{\Psi}}$ such that $\upsilon = \psi\phi$ are expressed by the restrictions $\psi = {{\upsilon}\negmedspace\mid\negmedspace{{{\operatorname{dom}{\Psi}}}}}$ and $\phi = {{\upsi... | 1,415 | 222 | 2,177 | 1,547 | 2,102 | 0.782717 | github_plus_top10pct_by_avg |
\]) with $s=0$. By using Theorem \[th:1\], we obtain the following propositions. It should be noted that $T(0,a,b \,; -y,x-y) = T(0,a,b \,; y, y-x)$ when $(x,y) = (1,1)$, $(1,1/2)$, $(1/2,1)$ or $(1/2, 1/2)$. In this case, the next proposition coincides with [@NakamuraT Proposition 2.8] or [@Zhou Proposition 1].
For a... | 1,416 | 630 | 1,001 | 1,450 | 3,644 | 0.770962 | github_plus_top10pct_by_avg |
\mathcal{F}_n^c \right).$$ Thus, $$\begin{aligned}
\mathbb{P}\left( |Z_{n,j}| \leq z_{\alpha/(2s)} \hat{\gamma}_j, \forall j\right)
& \geq (1-\alpha)- \mathbb{P}\left( \mathcal{F}_n^c \right)+ \mathbb{P}\left(
|Z_{n,j}| \leq z_{\alpha/(2s)} (\gamma_j - \Xi_n), \forall
j \right) -\mathbb{P}\left( |Z_{n,j}| \leq z_{\alph... | 1,417 | 1,955 | 1,328 | 1,323 | null | null | github_plus_top10pct_by_avg |
same truncation must in fact be identical, hence they cannot differ at $y^C$, hence $C$ is not characteristic. Since the set of exponents of any branch is discrete, the first assertion follows.
The second assertion follows from Lemma \[quadconics\]: if $C>\lambda_0$ and $B=\frac{C-\lambda_0}2+1$, then the limit is a u... | 1,418 | 556 | 1,421 | 1,464 | 4,029 | 0.76857 | github_plus_top10pct_by_avg |
}={\left\langle}d\psi,\psi{\right\rangle}_{L^2(G\times S\times I)},$$ where $$d:=-\mathrm{div}_{\tilde{\omega}}(F),$$ and $\mathrm{div}_{\tilde{\omega}}$ is the divergence operator on $S$ with respect to its Riemannian metric.
The equation (\[add1\]) in velocity coordinates $(x,v)\in{\mathbb{R}}^3\times{\mathbb{R}}^3$... | 1,419 | 496 | 1,411 | 1,472 | null | null | github_plus_top10pct_by_avg |
$, $U_c$ and $U_c^-$ are simple, Morita equivalent rings (see the introduction to [@BEG3] for the details). Since this also applies to $H_{c+1}$ the conditions are trivially satisfied and the result follows.
Thus we may assume that $c\in \mathcal{C}$. If $c\geq -1$, then necessarily $c\geq 0$ and so the result follows... | 1,420 | 593 | 638 | 1,473 | 2,553 | 0.778921 | github_plus_top10pct_by_avg |
t 11/17/2001 at 1:00:00 PM CT thru Sat 11/17/2001 at 5:00:00 PM CT
Sat 11/17/2001 at 11:00:00 AM PT thru Sat 11/17/2001 at 3:00:00 PM PT
Sat 11/17/2001 at 7:00:00 PM London thru Sat 11/17/2001 at 11:00:00 PM London
Outage: Migrate VMS objects from Enpower test to production
Environments Impacted: Corp
Purpo... | 1,421 | 504 | 1,262 | 1,961 | null | null | github_plus_top10pct_by_avg |
}$ with this highest weight. Given an arbitrary finite-dimensional (complex) $G$-representation $V$, we can always decompose it into irreducible sub-representations $
V \cong \bigoplus_{\lambda \in \Lambda^*_{G,+}} m_{G,V}(\lambda) \, V_{G,\lambda}
$. We shall call the function $m_{G,V}$ thus defined the *highest wei... | 1,422 | 4,206 | 1,720 | 1,131 | 3,536 | 0.771701 | github_plus_top10pct_by_avg |
ll-studied in the $O(1)$ model which is in the same universality class as $SU(2)$ Yang-Mills theory. Moreover, in Polyakov gauge the effective action $\Gamma[A_0]$ after integrating-out the spatial gauge field is close to that of an $O(1)$-model. Studies using the FRG in local potential approximation with an optimised ... | 1,423 | 490 | 1,080 | 1,516 | null | null | github_plus_top10pct_by_avg |
8,34)$$ 1 It is a simple exercise to show that $\la{^{\operatorname{reg}}}$ is a $2$-regular partition, and we have the following result.
[ ]{}\[jreg\] Suppose $\la$ and $\mu$ are partitions of $n$, with $\mu$ $2$-regular. Then $[S^\la:D^{\la{^{\operatorname{reg}}}}]=1$, while $[S^\la:D^\mu]=0$ if $\mu\ndom\la{^{\oper... | 1,424 | 606 | 443 | 1,398 | 882 | 0.798369 | github_plus_top10pct_by_avg |
$\bigcirc$ indicate the boundary of the chiral phases characterized by long-range ordered chirality-chirality correlations $\left<\kappa_i\kappa_j\right>$; $\square$ indicate the boundary of the SF-phases indicated by the critical Luttinger parameter $K=2$. Note that narrow CMI and CHI phases may occur as well. For $U... | 1,425 | 398 | 1,078 | 1,445 | null | null | github_plus_top10pct_by_avg |
Positive emotions 8.85 3.50 3--16 9.11 3.30 2--18 7.56 3.36 0--15 4.56 2.26 0--9
Quality of life 69.94 13.76 35--95 12.62 6.56 2--34 10.88 6.04 0--30 73.44 14.99 35--95
... | 1,426 | 407 | 1,187 | 1,426 | null | null | github_plus_top10pct_by_avg |
next case, we will describe $\psi_j|_{F_j} : F_j \rightarrow \mathbb{Z}/2\mathbb{Z}$ explicitly in terms of a formal matrix. To do that, we will first describe a morphism from $F_j$ to the special fiber of the smooth integral model associated to $L^j$. Then we will describe a morphism from $F_j$ to the even orthogonal ... | 1,427 | 695 | 1,729 | 1,408 | null | null | github_plus_top10pct_by_avg |
tikzpicture}}},;{\hat\imath},;{{\begin{tikzpicture}[baseline=0cm]\draw[thick,densely dotted](0,.13-1*.125)--++(0,1*.25);\end{tikzpicture}}},;{b\!\!+\!\!2})$}}.\end{aligned}$$ So, modulo homomorphisms labelled by tableaux not dominated by $S$, we have $\sigma=\sum_i{\hat\Theta_{T'[i]}}+\sum_{i,j}{\hat\Theta_{T'[i,j]}}$.... | 1,428 | 1,510 | 1,209 | 1,461 | 2,837 | 0.776669 | github_plus_top10pct_by_avg |
of interest in this work.
![CT and MRI of the pelvic area.\
**Notes:** (**A**) Bone destruction of the right sacroiliac joint with perifocal abscess formation in the right iliac muscle (white arrows); (**B**) MRI of the pelvic area, axial short-TI inversion recovery, which shows diffuse thickening and increased signa... | 1,429 | 600 | 935 | 1,945 | null | null | github_plus_top10pct_by_avg |
$C=0$) \[csda27a\] B\_0(,v)=& ,S\_0[E]{}\_[L\^2(GSI)]{} -,\_x v\_[L\^2(GSI)]{} +,(\^\* -K\^\*)v\_[L\^2(GSI)]{}\
&+\_+(), \_+(v)\_[T\^2(\_+)]{} +(,,0),S\_0(,0) v(,,0)\_[L\^2(GS)]{}. The linear form $F_0:C^1(\ol G\times S\times I)\to{\mathbb{R}}$ is given by $$F_0(v)=
{\left\langle}{f},v{\right\rangle}_{L^2(G\times S\tim... | 1,430 | 522 | 1,616 | 1,520 | null | null | github_plus_top10pct_by_avg |
}}^b (0) \sim \ \kappa^{ab} c_3 \frac{1}{\bar{z}^2}
+ {f^{ab}}_c \left[ \frac{c_4}{\bar{z}} j_{L,\bar{z}}^c(0) + \frac{(c_4-g)z}{\bar{z}^2} j_{L,z}^c(0)\right] \cr
& + {f^{ab}}_c \left[\frac{g}{4}\frac{z}{\bar z}(\partial_z j_{\bar z}^c(0)-\partial_{\bar z}j_z^c(0)) + \frac{c_4}{2} \partial_{\bar z} j_{L,\bar z}^... | 1,431 | 1,387 | 1,627 | 1,304 | null | null | github_plus_top10pct_by_avg |
gives a suboptimal coefficient vector.
Proposed Method {#section:ProposedMethod}
===============
In this section, we will first derive our method for the real-valued channel model, and then extend the method for the complex-valued channel model.
Preliminaries
-------------
We start with investigating some propertie... | 1,432 | 243 | 1,059 | 1,521 | null | null | github_plus_top10pct_by_avg |
as observed in [@Meckes].
\[T:C-Ginibre-eigenvalues\] Let $G$ be a finite abelian group and let $\{Y_a \mid a \in G\}$ be independent, standard complex Gaussian random variables. Then the eigenvalues $\bigl\{ \lambda_\chi \mid \chi \in \widehat{G} \bigr\}$ of $M$ given by are independent, standard complex Gaussian ran... | 1,433 | 1,230 | 1,563 | 1,256 | null | null | github_plus_top10pct_by_avg |
eft\{ (UX)^{\dagger} A W \right\}_{m K}
\left\{ W^{\dagger} A (UX) \right\}_{K k}
\biggr\}.
\label{P-beta-alpha-W4-H3-Second} \end{aligned}$$
$$\begin{aligned}
&& P(\nu_\beta \rightarrow \nu_\alpha)^{(4)}_{6th}
\equiv
2 \mbox{Re} \left[ \left(
S^{(0)}_{\alpha \beta} \right)^{*}
S_{\alpha \beta}^{(4)} [2]
\righ... | 1,434 | 1,727 | 1,700 | 1,537 | null | null | github_plus_top10pct_by_avg |
tive map $\theta :
J^{k-1}\delta^ke\hookrightarrow M(k)$ of left $\mathbb C[{\mathfrak{h}}]$-modules such that:
1. $\theta$ is an ${\mathbf{E}}$-graded homomorphism and is a filtered homomorphism under the order filtration.
2. The associated graded map $\operatorname{{\textsf}{ogr}}\theta: J^{k-1}\delta^ke \to \ope... | 1,435 | 902 | 557 | 1,447 | 4,089 | 0.76818 | github_plus_top10pct_by_avg |
n_i & \quad \textit{if $L_i$ is \textit{of type} $\textit{I}^o$ or \textit{free of type II}};\\
n_i+1 & \quad \textit{if $L_i$ is \textit{bound of type II}}.
\end{array} \right.$$ **
We next assume that $i=2m-1$ is odd. Recall that $Y_i$ is the sublattice $B_i$ such that $Y_i/\pi A_i$ is the radical of the al... | 1,436 | 926 | 1,628 | 1,388 | null | null | github_plus_top10pct_by_avg |
e most dangerous area---the main tunnel, is mostly determined (besides smokiness level) by evacuees' familiarity with the situation, scenario and layout of the tunnel.
4.4 Movement speed {#sec011}
------------------
We calculated movement speed for experiments 1-3. Movement speed in the main tunnel and the evacuation... | 1,437 | 702 | 2,561 | 1,599 | null | null | github_plus_top10pct_by_avg |
ubscales) and quality of life (PedsQL scores and MMQ scores) per family member are presented in [Table 5](#T5){ref-type="table"}. Mean scores for mother, father, sibling and patients were compared.
######
Mean scores for cancer appraisal (PSS scores), family functioning (FES subscale scores), cancer related emotions... | 1,438 | 3,486 | 1,743 | 1,097 | null | null | github_plus_top10pct_by_avg |
el obtained by forcing with a Souslin tree, if $X$ is locally compact normal, $D$ is a closed discrete subspace of $X$ of size $\aleph_1$ and $\{U_\alpha:\alpha\in\omega_1\}$ are open sets with compact closures, then for any countable $T\subseteq\omega_1$, $\stackrel{}{\overline{\bigcup\{U_\alpha:\alpha\in T\}}}\cap\; ... | 1,439 | 730 | 1,357 | 1,491 | null | null | github_plus_top10pct_by_avg |
omology concentrated in degree zero.
We now state our main theorem.
\[O\_hat\_Koszul\] If $\mathcal O$ is cyclic quadratic and Koszul, then $\widehat{\mathcal O}$ has a resolution, which for a given sequence $\vec X$ of colors, with $|\vec X|=n$, is given by the quasi-isomorphisms $$\begin{aligned}
\textbf{D}(\wideha... | 1,440 | 1,012 | 1,093 | 1,321 | 519 | 0.807201 | github_plus_top10pct_by_avg |
ta} \, G \cong H\, {}_{\alpha'}\!\! \bowtie_{\beta'}
\, G'$ between two arbitrary bicrossed product of groups is obtained in a unique way by the above deformation method. As applications two Schreier type classification theorems for bicrossed product of groups are given.
address: 'Faculty of Mathematics and Compute... | 1,441 | 345 | 1,257 | 1,242 | null | null | github_plus_top10pct_by_avg |
on of the dimensionless detuning $\delta$ (full line). The dashed line corresponds to the asymptotic behavior $\epsilon_b \simeq -mg_1^2/4$ and the dotted line to the asymptotic behavior $\epsilon_b \simeq \nu$.](BFRMboundstate.eps "fig:"){height="6cm"} \[BFRMboundstate\]
The bound state energy $\epsilon_b$ is plotted... | 1,442 | 275 | 1,701 | 1,502 | 2,354 | 0.780612 | github_plus_top10pct_by_avg |
sampled independently and are also independent of other iterations.
Intuitively, an $(s, \sigma, b_1, b_2)$-large-noise SGD should be considered as an SGD algorithm with step size $s$ and minibatch size $b_1$ and an additional noise term. The noise term computes the difference of two independent and unbiased estimates... | 1,443 | 1,225 | 1,059 | 1,302 | 1,181 | 0.793075 | github_plus_top10pct_by_avg |
e boundaries fully cover the region of gravitational waves creation. The energy density of gravitons is given by $$d\rho_{\text{gw}} = 2 \cdot \hslash \omega \cdot \frac{4 \pi \omega^2 d\omega}{(2\pi c)^3} \cdot |B_{-}(k)|^2.$$ where we used definition (\[particles\]). The expression for the parameter $\Omega_{\text... | 1,444 | 3,621 | 2,243 | 1,488 | null | null | github_plus_top10pct_by_avg |
the general case. In the Coulomb gauge the vector potential ${\mathbf
A}(\theta,\phi) = {1 \over 2} \mathbf{B} \times \mathbf{r} $ expressed in surface variables reduces to $$\notag \mathbf {A}(\theta,\phi) = {1\over 2}\big [ B_1 (W
{\rm sin\phi \cos \theta} +
a \ {\rm sin^2\theta sin}\phi){\bm \theta} +
(B_0... | 1,445 | 4,297 | 878 | 1,049 | null | null | github_plus_top10pct_by_avg |
}_g (c_2-g) {{B}^{gd}}_{xy} :j^{x}_{z} j^{y}_{\bar z}:
\nonumber \\ &
+ \mathcal{O}(f^2) %\mbox{higher order in $f^2$} \end{aligned}$$ We use current conservation and the Maurer-Cartan equation to write: $$\begin{aligned}
+i &(c_4-\frac{g}{2}) {f^{ac}}_g
{f^g}_{de} :j^e_z j^d_{\bar z}:
+c_- {B^{ac}}_{ed} : j_z^{e... | 1,446 | 2,015 | 1,617 | 1,412 | null | null | github_plus_top10pct_by_avg |
e have: $$i(h, g) \cdot i(h', g') = \bigl( h (g \rhd h'), (g \lhd h')
g'\bigl)\, \stackrel{g \in {\rm Fix}(G)} {=} \bigl( h(g \rhd h'),
gg'\bigl) = i\bigl((h, g) (h',g')\bigl)$$
Thus the two semidirect products constructed above, $H
{}_{\varphi_{\rhd}}\!\! \ltimes {\rm Fix}(G)$ and ${\rm Fix}(H)
\rtimes_{\psi_{\lhd}} ... | 1,447 | 1,250 | 1,297 | 1,373 | null | null | github_plus_top10pct_by_avg |
\muhat^*},$$ where the sum is over types $\omhat$ as above. Comparison with Euler’s formula $$\Log\left(\sum_{n\geq 0}p(n)\,T^n\right)=\sum_{n\geq1}T^n,$$ shows that $L$ reduces to $\sum_{t\geq 1}
\,m_{t\muhat^*}$. Hence the coefficient of the lowest power of $q$ in $\H_\muhat\left(\sqrt{q},1/\sqrt{q}\right)$ is also $... | 1,448 | 1,243 | 1,267 | 1,328 | 2,853 | 0.776532 | github_plus_top10pct_by_avg |
of . The Gaussian comparison yields that $A_2 \leq C \Delta_{n,3} + \frac{2}{n}$. To bound the term $A_3$, we repeat the arguments used in the first part of the proof of , applied to the larger class $\mathcal{P}_n^*$ and restricting to the event $\mathcal{E}_n$. As argued above, we will replace $\psi$ with $\hat\psi$ ... | 1,449 | 961 | 978 | 1,375 | null | null | github_plus_top10pct_by_avg |
at{\pi}^{'} &=& i [ \hat{H}_{\text{t}}, \hat{\pi} ]. \label{Ham2}\end{aligned}$$
The Hamilton operator have the form $$\begin{aligned}
\hat{H}_{\text{t}} &=& \frac{1}{2}\int d^3 {\bf x} [ \hat{\pi}^{2}+D \delta^{ij} \partial_i \hat{u} \partial_j \hat{u}
+m^2_{\text{eff}}\hat{u}^2 ] \nonumber \\
&=& \frac{1}{2... | 1,450 | 4,724 | 289 | 1,144 | null | null | github_plus_top10pct_by_avg |
r \[item:pc4b\] implies statement \[item:pc3\]. Moreover, since the empty functor is a sieve and a cosieve, statement \[item:pc3\] implies \[item:pc2\]. By duality, it remains to show that \[item:pc1\] implies \[item:pc4a\]. Given a functor $u\colon A\to B$, the morphism $u_\ast\colon{\sD}^A\to{\sD}^B$ is a right adjoi... | 1,451 | 996 | 1,395 | 1,353 | null | null | github_plus_top10pct_by_avg |
^\alpha}{\sum_j c_jk_j^\alpha},$$
where $c_i=\sum_j A_{ij}k_j^\alpha$,
Using Eqs. (\[eq:diff1\]) and (\[eq:diff2\]), we check that the transition matrix is reversible and then has $m$ real eigenvalues. From this stationary probability density, we can thus compute both the KSE and the second largest eigenvalue $\lambd... | 1,452 | 2,193 | 2,594 | 1,572 | 2,833 | 0.776695 | github_plus_top10pct_by_avg |
weinberg].
Once Weinberg’s formalism is expressed by means of the symplectic form in Eq. (\[eq:wein\_eqofm\]), it can be generalized very easily in order to obtain a non-Hamiltonian quantum algebra. To this end, one can substitute the antisymmetric matrix $\mbox{\boldmath$\cal B$}$ with another antisymmetric matrix $\... | 1,453 | 1,537 | 1,594 | 1,474 | null | null | github_plus_top10pct_by_avg |
d will be denoted by $L^{n-4k}_z$. The structure group of the framing of this component is $\I_{2,z}$. Lemma 1 is proved.
### The last part of the proof of the Theorem 1 {#the-last-part-of-the-proof-of-the-theorem-1 .unnumbered}
Let us construct a pair of polyhedra $(P',Q') \subset \R^n$, $dim(P') =2s-n=n-2k-q-2$, $d... | 1,454 | 683 | 1,256 | 1,408 | null | null | github_plus_top10pct_by_avg |
\alpha (t) \dot{\beta} (t) \dot{\gamma} (t)+\gamma (t)
\big(\dot{\alpha} (t) \dot{\beta} (t)+\alpha (t) \ddot{\beta} (t)\big)\bigg) +\beta (t)
\bigg(\alpha (t)^2 \dot{\beta} (t) \dot{\gamma} (t)^2
\\&
-\alpha (t)^2 \gamma (t) \big(\dot{\gamma} (t)
\ddot{\beta} (t)+\dot{\beta} (t) \ddot{\gamma} (t)\bigg) ... | 1,455 | 2,195 | 1,666 | 1,468 | null | null | github_plus_top10pct_by_avg |
nBufferEnd(void * pBufferContext);
void OnBufferStart(void * pBufferContext);
void OnLoopEnd(void * pBufferContext);
void OnVoiceError(void * pBufferContext, HRESULT Error);
};
Everything is fine until I try to figure out how to call back from an instance of my native callback class to the parent SoundSamp... | 1,456 | 4,493 | 247 | 1,282 | 234 | 0.816969 | github_plus_top10pct_by_avg |
Proj}{\mathbb{S}}$, where ${\mathbb{S}}={\mathbb{C}}[{\mathbb{C}}^{2n}][t{\mathbb{J}}^1],$ is the blowup of ${\mathbb{C}}^{2n}$ at ${\mathbb{J}}^1$ [@hai3 Proposition 3.4.2].
{#subsec-5.5}
Observe that ${\mathbb{J}}^d$ is generated by its ${{W}}$-alternating or ${{W}}$-invariant elements, respectively, depending on ... | 1,457 | 497 | 1,417 | 1,449 | null | null | github_plus_top10pct_by_avg |
\tilde{t}_1\right)^2 + \mathrm{Re}(\tilde{t}_2) &=
0.075\pm 0.018 \,. \label{eq:result-combi}\end{aligned}$$ Employing [@Tanabashi:2018oca] $$\begin{aligned}
\mathrm{Im}\left(\frac{\lambda_b}{\Sigma}\right) = (-6.3\pm 0.3)\cdot 10^{-4}\,,\end{aligned}$$ and inserting the measurement of $\Delta a_{CP}^{\... | 1,458 | 1,000 | 1,166 | 1,505 | 842 | 0.79905 | github_plus_top10pct_by_avg |
DI`
`SRR022865_49291` `-36` `tactagaaaaga`
1542366 NONSYN A:14 G:85 G:37 `tcatga... | 1,459 | 2,573 | 2,883 | 1,555 | null | null | github_plus_top10pct_by_avg |
the effective action. In turn, a local approximation such as requires $k_{0,\rm phys}=k_{\bot,\rm phys}$. In other word, a local approximation works best if the momentum transfer in the flow is minimised. More details about such a scale matching and its connection to optimisation [@Litim:2000ci; @Pawlowski:2005xe] can... | 1,460 | 723 | 2,434 | 1,407 | 1,925 | 0.784346 | github_plus_top10pct_by_avg |
extit{ together with } z_i^{\ast}, m_{i,i}^{\ast}, m_{i,i}^{\ast\ast}.$$ Here, if $i$ is odd and $L_i$ is *free of type I*, then $$m_{i,i}=\begin{pmatrix} s_i&\pi r_i&t_i\\ y_i&1+\pi x_i& u_i\\\pi v_i&\pi z_i&1+\pi w_i \end{pmatrix},$$ where $s_i\in M_{(n_i-2)\times (n_i-2)}(B\otimes_A\kappa_R)$, etc. If $i$ is odd a... | 1,461 | 2,846 | 1,453 | 1,261 | 1,893 | 0.784635 | github_plus_top10pct_by_avg |
| v
Stillwater & St. Paul | w
Winona & St. Peter | x
Winona, Mankato & New Ulm | y
=====================================================================
Road abbrev. | Termini. | Miles.
... | 1,462 | 4,677 | 426 | 947 | null | null | github_plus_top10pct_by_avg |
27 (100) 154 (97) 54 (96) 235 (98) 302 (99) 697 (98)
Median; IQR 30; 20--48 60; 30--238 115;50--300 60; 30--230 200; 81--449 240; 60--600
**Centre... | 1,463 | 4,781 | 652 | 840 | null | null | github_plus_top10pct_by_avg |
ment similar to the paragraph just before Equation (\[ea20\]) of Step (1), if we write the $(1, 2), (1,3), (2,3), (2,2)$-blocks of the $(i, i)$-block of the formal matrix product $\sigma({}^t\tilde{m})\cdot h\cdot \tilde{m}$ as $\xi^{i/2}\cdot \mathcal{X}_{i,1,2}(\tilde{m})$, $\xi^{i/2}\cdot \pi\mathcal{X}_{i,1,3}(\til... | 1,464 | 2,030 | 1,665 | 1,479 | null | null | github_plus_top10pct_by_avg |
q:hess_posl_5}\end{aligned}$$ where follows from the definition of $D _{\max}$ in Equation and follows from the definition of $\beta$ in . Observe that from Equation , ${\|M^{(j)}\|} \leq 2\delta_{j,1} \leq 2\sqrt{\delta}$. Applying matrix Bernstein inequality, we have, $$\begin{aligned}
\mathbb{P}\Big[\big\|M - \E[M]\... | 1,465 | 1,830 | 1,576 | 1,307 | null | null | github_plus_top10pct_by_avg |
000 1.000
K=150 1.000 1.000 1.000 1.000 1.000 1.000 1.000
mVC 1.000 1.000 1.000 1.000 1.000 1.000 1.000
mMSE 1.000 1.000 1.000 ... | 1,466 | 5,945 | 533 | 714 | null | null | github_plus_top10pct_by_avg |
le}{{\bf m}}+{{\bf n}}$}}
{\overset{}{\longleftrightarrow}}}v\}\setminus\{y{\underset{\raisebox{5pt}{${\scriptscriptstyle}{{\bf n}}$}}
{\overset{}{\longleftrightarrow}}}v\}}{\nonumber}\\
&~\leq\sum_{v_0}\big(\psi_\Lambda(v_0,v)-\delta_{v_0,v}\big)\sum_{u\in{{\cal A}}}
\,\sum_{{\partial}{{\bf n}}=y{\vartriangle}x}\fr... | 1,467 | 675 | 1,247 | 1,582 | null | null | github_plus_top10pct_by_avg |
s, E_{\tau^{-1}(s)})$. Then the following lemma holds.
\[lem:defect\] Let ${\mathbb M} = (M_1, \ldots, M_u)$ and ${\mathbb F} = (F_1, \ldots, F_v)$ be sequences of the upper and the lower (non-empty) parts of a seat-plan respectively. If $M_i$ \[resp. $F_i$\] is defective and $\sigma_i = (i,i+1)$, the $i$-th adjacent ... | 1,468 | 2,032 | 1,496 | 1,383 | null | null | github_plus_top10pct_by_avg |
-3\right)}{8 \left(u^2-1\right) \left(u^2+1\right)^3} \\
\mathcal{D}_{uu} & \frac{-\left(u^8+8 u^6+10 u^4-3\right) m^2+4 h \left(u^2-1\right) \left(u^2+1\right)^2+16 u^2 \left(u^2-1\right)}{8 \left(u^2-1\right)^2 \left(u^2+1\right)^3} & -\frac{(h+1) u}{u^4-1} \\
\mathcal{D}_{TR} & \frac{i m \left(u^4+6 u^2-3\right)... | 1,469 | 2,744 | 1,445 | 1,407 | null | null | github_plus_top10pct_by_avg |
his frame) for $V_p=1.6$ and $\gamma=0$. []{data-label="fig:BufferRegion"}](Figure_4.pdf){width="45.00000%"}
Numerical simulations of dGPE Eq. (\[eq:ComovingdGPE\]) are run for a system size of $128\times 256$ (in units of $\xi$) corresponding to the grid size $dx=0.25\xi$, and $dt=0.01\xi/c$. To simulate an infinite ... | 1,470 | 1,111 | 2,362 | 1,609 | 1,185 | 0.792978 | github_plus_top10pct_by_avg |
ng the lines of proof of Theorem 1.8 in [@hayes2005large].
### Proof of Lemma \[lem:hessian\_positionl\]
The Hessian $H(\theta)$ is given in . For all $j\in [n]$, define $M^{(j)} \in \cS^d$ as $$\begin{aligned}
\label{eq:posl_M_j_def}
M^{(j)} &\equiv& \sum_{a=1}^{\ell_j} \lambda_{j,a} \sum_{i<\i \in S_j} \I_{\big\... | 1,471 | 1,136 | 1,132 | 1,364 | null | null | github_plus_top10pct_by_avg |
Moreover, for the groups $N$ listed in Table 2, there exist a prime $s \in \pi(N) \setminus (\pi({{\operatorname}{\textup{Out}}({N})}) \cup \{t\})$ and a Sylow $s$-subgroup of order $s$ which is self-centralising in $N$.
If $N=L_2(q)$, $C_N(x)$ is a $t$-group for each $t$-element $x \in N$.
If $N=L_3(q)$, there exist... | 1,472 | 1,962 | 1,755 | 1,439 | null | null | github_plus_top10pct_by_avg |
as “T” here. This form of threshold can also be applied to other types of distributions even there is no intersection between these two.[]{data-label="fig:example-threshold"}](./ExampleThreshold.pdf){width="\linewidth"}
Moreover, as is verified in experiments, the meta-distribution of anomalous data collections lies i... | 1,473 | 6,009 | 1,759 | 624 | 2,716 | 0.777622 | github_plus_top10pct_by_avg |
pond to roots with zero and negative squared length respectively [@Kleinschmidt:2003mf]. In [@axel] it was shown that only the $E_{11}$ roots with positive squared length are associated to branes.
The constraint corresponding to $E_{9,3}$ is $$Q^{[ab}_e P^{c]e}_d+ P^{[ab}_e Q^{c]e}_d=0 \quad ,$$ and has already been p... | 1,474 | 523 | 1,794 | 1,533 | null | null | github_plus_top10pct_by_avg |
-------- ----------------------- ---------
Discharged patients
D2P AED 51 (37, 68) 29 (21, 41) \<0.01
CE... | 1,475 | 354 | 1,218 | 1,825 | null | null | github_plus_top10pct_by_avg |
ion $$\begin{aligned}
\label{eq:w*functor}
(ww')^*\chi =w^*(w'{}^*\chi )\end{aligned}$$ holds for all $w,w'\in {\mathrm{Aut}}_{{\mathbb{Z}}}({\mathbb{Z}}^I)$ and all $\chi \in {\mathcal{X}}$.
\[de:Cartan\] Let $\chi \in {\mathcal{X}}$, $p\in I$, and $q_{ij}=\chi ({\alpha }_i,{\alpha }_j)$ for all $i,j\in I$. W... | 1,476 | 2,267 | 1,650 | 1,394 | null | null | github_plus_top10pct_by_avg |
representation in a probability space.
The rest of this paper is organized as follows. In Section 2, we present our results on the law of large numbers. Section 3 contains the results related to the CLT. A new representation of the $G$-normal distribution is derived in Section 4. Most of the proofs are deferred to Se... | 1,477 | 546 | 595 | 1,637 | null | null | github_plus_top10pct_by_avg |
\hat{\mathbf{\tau}}}^{2}$
-------------------------------------------------- -- ------------------------------------------------------- -------- -- -------- -------- -- --------- -------- -- --------- --------
Scenario [\*](#sim7930-note-0003){ref-... | 1,478 | 4,929 | 1,745 | 911 | null | null | github_plus_top10pct_by_avg |
the direction of the root edge of the cubic graph. The cubic graph itself and its “simplification” are presented in the figure below. $$\begin{picture}(300,100) \linethickness{0.6mm} \put(0,30){\line(1,0){80}}
\put(60,30){\line(0,1){10}} \thinlines \put(20,30){\line(0,1){10}}
\put(20,30){\oval(40,40)[b]} \put(50,30){\o... | 1,479 | 4,333 | 866 | 1,088 | 1,991 | 0.783777 | github_plus_top10pct_by_avg |
-------------------------------------------------------------------------
The third order in $H_{1}$ contribution to order $W^4$ $\hat{S}$ matrix elements $\hat{S}_{i j}^{(4)} \vert_{i \neq j}$ is given by $$\begin{aligned}
&& \hat{S}_{ij}^{(4)} \vert_{i \neq j} [3]
\nonumber \\
&=&
- \sum_{K}
(ix) e^{- i \Delta_{K... | 1,480 | 3,229 | 2,051 | 1,515 | null | null | github_plus_top10pct_by_avg |
}$ and $\bar{\beta}^i$ do not appear in the one-hypersurface IVP for $(\Sigma, \bar{\mbox{\bf g}}, \bar{\mbox{\bf K}})$.
Turning now to the conformal metrics in the IVP, we recall that two metrics $g_{i j}$ and $\bar{g}_{i j}$ are conformally equivalent if and only if there is a scalar $\psi > 0$ such that $\bar{g}_{i... | 1,481 | 2,612 | 1,784 | 1,510 | null | null | github_plus_top10pct_by_avg |
in [@dress].
\[Dress\] A bivariant functor $M~=~(M^{*},M_{*})$ from $G$-$\rm{set}$ to $R$-$\rm{Mod}$ is a pair of functors from $G$-$\rm{set}\to$ $R$-$\rm{Mod}$ such that $M^{*}$ is a contravariant functor, and $M_{*}$ is a covariant functor. If $X$ is a $G$-set, then the image by the covariant and by the contravarian... | 1,482 | 4,021 | 1,907 | 1,133 | null | null | github_plus_top10pct_by_avg |
0.001 (2) −0.001 (2)
C48 0.030 (3) 0.018 (2) 0.019 (3) −0.006 (2) −0.003 (2) 0.002 (2)
C49 0.027 (3) 0.030 (3) 0.017 (2) −0.006 (2) 0.007 (2) 0.009 (2)
C50 0.024 (3) 0.024 (2) 0.015 (2) 0.001 (2) 0.007 (2) 0.0054 (19)
C51 ... | 1,483 | 5,379 | 849 | 763 | null | null | github_plus_top10pct_by_avg |
of the leaves of the tree using the $S_2$-action on $E$, and the composition maps are given by attaching trees. This definition can readily be seen to define a colored operad.
An ideal $\mathcal I$ of a colored operad $\mathcal P$ is a collection of $S_n$-sub-modules $\mathcal I(\vec X;z)\subset
\mathcal P(\vec X;z)$ ... | 1,484 | 892 | 1,392 | 1,421 | 948 | 0.79706 | github_plus_top10pct_by_avg |
ogarithmic factor larger than the number of parameters to be estimated. Such a logarithmic gap is also unavoidable and due to the fact that we require high probability bounds, where we want the tail probability to decrease at least polynomially in $d$. We discuss the role of the topology of the data in Section \[sec:ro... | 1,485 | 425 | 307 | 1,587 | 235 | 0.816951 | github_plus_top10pct_by_avg |
us $\operatorname{{\mathbf{E}}\text{-deg}}{\mathfrak{h}}^*=1$ and $\operatorname{{\mathbf{E}}\text{-deg}}{\mathfrak{h}}= -1$. For an ${\mathbf{E}}$-graded module (or, indeed, any ${\mathbb{Z}}$-graded module) $M=\bigoplus_{i\in{\mathbb{Z}}}M_i$, we write the corresponding Poincaré series as $p(M,v)=\sum v^i\dim_{\mathb... | 1,486 | 3,085 | 1,536 | 1,345 | 3,710 | 0.77055 | github_plus_top10pct_by_avg |
\mathrm{Ker~}\tilde{\varphi}(R)$ be a lift of $m$. By using an argument similar to the paragraph just before Equation (\[ea20\]) of Step (1), if we write the $(1, 2), (1,3), (2,3), (2,2)$-blocks of the $(i, i)$-block of the formal matrix product $\sigma({}^t\tilde{m})\cdot h\cdot \tilde{m}$ as $\pi\cdot\xi^{(i-1)/2}\cd... | 1,487 | 1,027 | 1,861 | 1,397 | 3,824 | 0.769859 | github_plus_top10pct_by_avg |
to compute high-probability bounds for $(\hat G - G) V G^\top$ and $G (\hat
V - V)G^\top$.
We first bound $(\hat G - G) V G^\top$. For any $j$ and $l$ in $\{1,\ldots,s\}$ and using the Cauchy-Schwartz inequality, we have that $$\label{eq::aaa}
\left| \left( \hat{G}_j - G_j \right) V G_l^\top \right| \leq \lambda_... | 1,488 | 3,557 | 1,874 | 1,237 | null | null | github_plus_top10pct_by_avg |
in LVAD patients, as shown in [Table 2](#t0002){ref-type="table"}. The pooled odds ratio (OR) of 30-day mortality was 3.66 (95% CI, 2.00--6.70, *I*^2^ = 71%, [Supplementary Figure S3](https://doi.org/10.1080/0886022X.2020.1768116)) and the pooled OR of 1 year mortality was 2.22 (95% CI, 1.62--3.04, *I*^2^ = 0%, [Suppl... | 1,489 | 478 | 935 | 1,618 | null | null | github_plus_top10pct_by_avg |
x_{(k+1)\delta} - \by_{(k+1)\delta})}\\
=& \E{f(x_{\delta} - y_{\delta})}\\
\leq& e^{-\lambda \delta} \E{f(x_0 - y_0)} + 6\delta (L+\LN^2) \epsilon\\
=& e^{-\lambda \delta} \E{f(\bx_{k\delta} - \by_{k\delta})} + 6\delta (L+\LN^2) \epsilon
\end{aligned}$$ Applying the above recursively gi... | 1,490 | 3,796 | 1,101 | 1,320 | null | null | github_plus_top10pct_by_avg |
ring of a particle in the spherically symmetric field with a barrier and with orbital quantum number $l=0$. In such case, we have: $$\begin{array}{ll}
W(r) =
\displaystyle\frac{2\beta - \alpha}{f(\bar{r})} -
\displaystyle\frac{\beta}{\bar{r}}, &
\mbox{при } 2\beta \ne \alpha,
\end{array}
\label{... | 1,491 | 2,856 | 2,026 | 1,546 | null | null | github_plus_top10pct_by_avg |
p
\sqrt{\frac{ \log p + \log n}{n} } \right) \geq 1 - \frac{1}{n},$$ for some universal constant $C>0$. Clearly, the scaling in $p$ is worse.
[**Proof of Lemma \[lemma::horrible\].**]{} Throughout, we drop the dependence on ${\widehat{S}}$ in our notation and assume without loss of generality that ${\widehat{S}}= \{1... | 1,492 | 3,595 | 1,533 | 1,241 | null | null | github_plus_top10pct_by_avg |
Vascular invasion 0.472 0.492
Absent 72 33 39
Present 32 17 15
Cirrhosis ... | 1,493 | 478 | 1,408 | 1,604 | null | null | github_plus_top10pct_by_avg |
e desired net in $A$ by $${\textstyle \chi(N_{\beta},\beta)=x_{\beta}\in N_{\beta}\bigcap A}$$ where the family of nonempty decreasing subsets $N_{\beta}\bigcap A$ of $X$ constitute the filter-base in $A$ as required by the directed set $_{\mathbb{D}}N_{\beta}$. It now follows from Eq. (\[Eqn: DirectionIndexed\]) and t... | 1,494 | 1,710 | 2,554 | 1,614 | 1,702 | 0.786649 | github_plus_top10pct_by_avg |
_R\^x (\_R\^x )\^ .
Using the standard definition of the Passarino-Veltman functions, B\_0(p, m\_1, m\_2) &=& 16 \^2\
p\_B\_1(p, m\_1, m\_2) &=& 16 \^2 \[passvelt\] ,we get B\_[LR]{}\^x &=& \_R\^x (\_L\^x )\^ B\_0 (p, , m\_[\_x]{})\
A\_[L]{}\^x &=& - \_L\^x (\_L\^x )\^ B\_1 (p, , m\_[\_x]{})\
A\_[R]{}\^x &=& - \_R\^x ... | 1,495 | 241 | 1,836 | 1,597 | null | null | github_plus_top10pct_by_avg |
ight|
\approx \left|{\mathbf{I}}_{N_r}+\frac{\rho}{L_t} {\mathbf{H}_{\psi,V}}{\mathbf{H}_{\psi,V}}^H\right|\notag\\
&= \left|{\mathbf{I}}_{N_r}+\frac{\rho}{L_t} {\mathbf{H}}_{\psi}{\mathbf{H}}_{\psi}^H\right|.\end{aligned}$$ Based on , we find that a fast selection of reconfiguration state can be achieved by direc... | 1,496 | 1,652 | 1,709 | 1,466 | 4,062 | 0.768381 | github_plus_top10pct_by_avg |
intermittent compound Poisson process.
#### Ordinary Poisson process {#S:INTERMITTENT_POISSON}
(Ordinary) Poisson processes are characterized simply by their rate or intensity:
- its fundamental rate $\lambda$, which is the expected number of arrivals per unit time.
Let $\lambda$ be the rate of a Poisson process.... | 1,497 | 6,211 | 1,607 | 628 | 1,006 | 0.795872 | github_plus_top10pct_by_avg |
senting a *chaotic substate of* the system represented by the solution of the neutron transport equation — combine with the functional components $\phi(\pm\nu_{0},\mu)$ to produce the well-defined, non-chaotic, experimental end result of the neutron flux $\Phi(x,\mu)$.
The solution (\[Eqn: CaseSolution\_FR\]) is obtai... | 1,498 | 2,450 | 1,498 | 1,444 | 3,705 | 0.770578 | github_plus_top10pct_by_avg |
and only if $D_u\cap D_t\neq \emptyset$ (that is, the $d$-choices of the $t$-th ball and the $u$-th ball contain a common bin).
We say a subgraph of ${\mathcal{C}}_m$ with vertex set $\{D_{t_1},\ldots, D_{t_k}\}$ is $c$-*loaded* if every bin in $D_{t_1}\cup D_{t_2}\cup \cdots \cup D_{t_k}$ has at least $c$ balls.
Ou... | 1,499 | 3,861 | 2,800 | 1,455 | 1,672 | 0.786935 | github_plus_top10pct_by_avg |
w)^2} :j^c_{L,z} \phi:(w) \cr
& \quad + \frac{\Delta_{\phi}:j^a_{L,z} \phi:(w)}{(z-w)^2} + \frac{:j^a_{L,z}\p \phi:(w)}{z-w} + \mathcal{O}(z-w)^0\end{aligned}$$ Using equation we obtain : $$\begin{aligned}
\label{TjphiStep1}
T(z) :j^a_{L,z}\phi:(w) &= -\frac{c_+}{c_++c_-}\frac{t^a \phi(w)}{(z-w)^3}
+\frac{(\Delta_\phi... | 1,500 | 591 | 797 | 1,625 | null | null | github_plus_top10pct_by_avg |
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