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 |
|---|---|---|---|---|---|---|---|
k} \to K(\Z/4,1)$ such that the characteristic mapping $\zeta: L^{n-4k} \to K(\Z/2 \int \D/4,1)$ of the $\Z/2
\int \D_4$-framing of the normal bundle over $L^{n-4k}$ is reduced to a mapping with the target $K(\I_b,1)$ such that the following equation holds: $$\zeta = i(\kappa_a \oplus \mu_a),$$ where $i: \Z/2
\oplus \Z... | 501 | 589 | 742 | 547 | null | null | github_plus_top10pct_by_avg |
\lVert x-y\rVert_2.
$
2. $U$ has a stationary point at zero: $\nabla U(0) = 0.$
3. There exists a constant $m>0, \LR, R$ such that for all $\lrn{x-y}_2 \geq R$, $$\label{e:convexity_outside_ball}
\lin{ \nabla U(x) - \nabla U(y),x-y} \geq m \lrn{x-y}_2^2.$$ and for all $\lrn{... | 502 | 496 | 555 | 569 | 1,982 | 0.783896 | github_plus_top10pct_by_avg |
her process such as mantle cooling may be necessary for Earth-like plate tectonics. Understanding the type of tectonics that might take place on a planet before plate tectonics, how much land and weatherable rock can be created through non-plate-tectonic volcanism, and the factors that then allow for Earth-like plate t... | 503 | 1,251 | 2,003 | 638 | null | null | github_plus_top10pct_by_avg |
letting $d_i'=d_i=0$, we have $$\label{ea16}
d_i'=\pi(x_i'+ z_i'+w_i')=0.$$ This is an equation in $B\otimes_AR$. Thus there is exactly one independent linear equation among $x_i', z_i', w_i'$.
5. The $(2\times 2)$-block is $$1+2 f_i'=1+2 f_i+2\pi(u_i'+\pi x_i').$$ By letting $f_i'=f_i=0$, we have $$\lab... | 504 | 771 | 558 | 531 | 2,272 | 0.78125 | github_plus_top10pct_by_avg |
H38B 0.6446 0.0288 0.4212 0.016\*
C39 0.6064 (2) 0.1611 (3) 0.49084 (16) 0.0119 (8)
C40 0.5981 (2) 0.2566 (3) 0.50130 (18) 0.0187 (10)
H40 0.6324 0.2970 0.5143 0.022\*
... | 505 | 3,608 | 304 | 359 | null | null | github_plus_top10pct_by_avg |
cup H_x\subset H$. From the classification of Lie subgroups of $\PSL(2,\Bbb{C})$, we deduce that $H$ is conjugate to a subgroup of $Rot_\infty$. Hence $H_y=H_x$ and so $x=y$.
\[t:rf\] Let $\Gamma\subset \PSL(2,\Bbb{C})$ be a discrete group. Then $\Gamma$ is conjugate to a subgroup $\Sigma$ of $\PSL(2,\Bbb{R})$ such t... | 506 | 178 | 639 | 499 | null | null | github_plus_top10pct_by_avg |
ddots}\pushoutcorner&0\ar@{}[dr]|{\ddots}\pushoutcorner&\\
&&&&&&&&
}
}$$
While $\pi^\ast$ points at the constant morphism in the middle of , for every $n$ the remaining $2n$-th adjoints to $\pi^\ast$ classify suitable iterated rotations of this morphism.
[^1]: In a weak sense; see below.
---
abstract: 'It is shown... | 507 | 121 | 624 | 587 | null | null | github_plus_top10pct_by_avg |
)}{q(x)}dx$$
Jensen-Shannon Divergence
-------------------------
Let $P,Q$ be discrete probability distributions, *Jensen-Shannon Divergence* between $P$ and $Q$ is defined to be:
$$JSD(P||Q) = \frac{1}{2}KLD(P||M) + \frac{1}{2}KLD(Q||M)$$
where $\displaystyle M = \frac{1}{2}(P+Q)$.
A more generalized form is defi... | 508 | 903 | 804 | 610 | 1,759 | 0.785908 | github_plus_top10pct_by_avg |
uirement.
onTouch gives you Motion Event. Thus, you can do a lot of fancy things as it help you separate state of movement. Just to name a few:
ACTION_UP
ACTION_DOWN
ACTION_MOVE
Those are common actions we usually implement to get desire result such as dragging view on screen.
On the other hand, onClick doesn't giv... | 509 | 933 | 640 | 440 | null | null | github_plus_top10pct_by_avg |
$\frac{d}{dx} y_{3}(a, x)$ $+\infty$ $+$ $+$ $+$ $+$ $+$ $0$ $-$ $0$
$y_{3}(a, x)$ $-$ $-$ $-$ $-$ $0$ $+$ $+$ $+$ $0$
$\frac{d}{dx} y_{2}(... | 510 | 4,116 | 360 | 325 | null | null | github_plus_top10pct_by_avg |
atinkumarg.github.io/personal-portfolio, run:
npm run deploy
> personal-portfolio@0.1.0 deploy C:\react-projects\personal-portfolio
> gh-pages -d build
Cloning into 'node_modules\gh-pages\.cache\git@github.com!jatinkumarg!personal-portfolio.git'...
git@github.com: Permission denied (publickey).
fatal: Could not re... | 511 | 388 | 157 | 885 | 92 | 0.826824 | github_plus_top10pct_by_avg |
--------------------------------------------------------------------------------------------------------------------------
State Count
-------------------------------------------------------------------- ----------------... | 512 | 2,470 | 987 | 576 | null | null | github_plus_top10pct_by_avg |
N OPTIONS {#sim7930-sec-0002}
===================================================================
Consider that IPD have been obtained from *i* = 1 to *K* related randomized trials, each investigating a treatment effect based on a continuous outcome *Y* (say, blood pressure); that is, the mean difference in outcome va... | 513 | 454 | 2,442 | 662 | 850 | 0.798941 | github_plus_top10pct_by_avg |
) that $g(t_{\leftarrow})$ be an element of $_{\rightarrow}T$, unless of course
$$g(t_{\leftarrow})=t_{\leftarrow},\label{Eqn: fixed point}$$
which because of (\[Eqn: ChainedTower\]) may also be expressed equivalently as $g(c_{\leftarrow})=c_{\leftarrow}\in C_{\textrm{T}}$. As the sequential totally ordered set $_{\r... | 514 | 2,013 | 1,418 | 565 | 999 | 0.796002 | github_plus_top10pct_by_avg |
$\psi_j$ is similar to and simpler than that of the above cases when $N_0$ is *of type $I^e$* and so we skip it.\
2. Assume that $M_0$ is *of type $I^e$* and $L_j$ is *of type $I^o$*. We write $M_0=N_0\oplus L_j$, where $N_0$ is unimodular with odd rank so that it is *of type $I^o$*. Then we can write $N_0=(\oplus_{\... | 515 | 917 | 429 | 559 | 2,038 | 0.783273 | github_plus_top10pct_by_avg |
s monotonically with frequency. Thus $\lambda_{\rm oe}$ and $\lambda_{\rm hw}$ are oscillating in counter phase, see Eq. (\[eq:s14\]). This induces a corresponding oscillation in the strength of the fidelity decay as seen in Fig. \[fig:03\]. For a more quantitative discussion we compare the experimentally determined fi... | 516 | 2,166 | 1,782 | 550 | null | null | github_plus_top10pct_by_avg |
(r)[2-8]{} Base Arrangement \[0, 0, 1\] \[0, 1, 0\] \[0, 1, 1\] \[1, 0, 0\] \[1, 0, 1\] \[1, 1, 0\] \[1, 1, 1\]
[\[1, 1, 1\]]{} 0.219 **0.190** 0.249 0.648 0.773 ... | 517 | 2,224 | 1,407 | 602 | null | null | github_plus_top10pct_by_avg |
general structure known as a *family*. We employ nomenclature abridged from Halmos [@pH74 p. 34] as follows:
Let $I$ and $X$ be non-empty sets, and $\varphi \colon I \to X$ be a mapping. Each element $i \in I$ is an *index*, while $I$ itself is an *index set*. The mapping $\varphi$ is a *family*; its co-domain $X$ is ... | 518 | 2,549 | 1,421 | 608 | 865 | 0.798615 | github_plus_top10pct_by_avg |
this section, we present experimental results that validate the importance of noise covariance in predicting the test error of Langevin MCMC-like algorithms. In all experiments, we use two different neural network architectures on the CIFAR-10 dataset [@krizhevsky2009learning] with the standard test-train split. The f... | 519 | 264 | 1,219 | 621 | 2,430 | 0.779819 | github_plus_top10pct_by_avg |
relate the entropy $H(x)$ to the compression rate $R(x)$, we obtain the following inequalities: $$H(x)\leq{R(x)}\leq{H(x)+1}.$$ Let $\Sigma=\{\sigma_{1},\sigma_{2},\ldots,\sigma_{t}\}$ be an alphabet and $c:\Sigma\times\Sigma^{\leq{1}}\rightarrow\{0,1\}^{+}$ an adaptive code of order one constructed as shown in section... | 520 | 456 | 811 | 535 | 2,782 | 0.777013 | github_plus_top10pct_by_avg |
e breakdown of the assumption in the analysis.
Discussion
==========
Our model showed a power law $v\sim\mu^{-1/2}$ under the assumptions that $r\ll1/\lambda_+$ and $\ell\gg1/\left|\lambda_-\right|$. In this section, we compare experimental results with the numerical results in Eq. (\[eq:v\]) in order to check whethe... | 521 | 390 | 1,423 | 689 | 3,014 | 0.775442 | github_plus_top10pct_by_avg |
:=f^{-}f(U)\subseteq X$ be the saturation of an open set $U$ of $X$ and $\textrm{comp}(V):=ff^{-}(V)=V\bigcap f(X)\in Y$ be the component of an open set $V$ of $Y$ on the range $f(X)$ of $f$. Let $\mathcal{U}_{\textrm{sat}}$, $\mathcal{V}_{\textrm{comp}}$ denote respectively the saturations $U_{\textrm{sat}}=\{\textrm{... | 522 | 364 | 939 | 553 | 2,444 | 0.779688 | github_plus_top10pct_by_avg |
t $\phi = \gamma \mid {{\operatorname{dom}{\Phi}}}$. For each $i \in {{\operatorname{dom}{\Phi}}}$, the non-empty sets $\Phi(i) = \Theta\Phi(i)$ by definition \[D:DYADIC\_ENSEMBLE\_PRODUCT\]. Since by construction $\phi(i) \in \Theta\Phi(i)$, and $\Phi(i) = \Theta\Phi(i)$, then $\phi(i) \in \Phi(i)$ for $i \in {{\opera... | 523 | 1,350 | 729 | 556 | null | null | github_plus_top10pct_by_avg |
case of multiple options, one is chosen at random. Otherwise, the particle tries to diffuse to the neighbor $i'$ with a probability given by [@Leal_JPCM] $$\label{prob}
P_{\delta h}(i,i')=
\left\{
\begin{array}{cl}
1, & \textrm{if } ~ |\delta h|<2\\
\frac {1}{|\delta h|}, & \textrm{if } ~ |\delta h|\geq 2
\end{array... | 524 | 372 | 1,671 | 737 | 333 | 0.812977 | github_plus_top10pct_by_avg |
lert("saveDrivers FAILED!");
}
},
error: function() { alert("saveDrivers FAILED!"); }
};
$.ajax(mySettings);
}
The error I receive says Unrecognized field "userID" not marked as ignorable.
Please help I am at my wits end.
A:
Can you try map... | 525 | 73 | 194 | 558 | 767 | 0.800419 | github_plus_top10pct_by_avg |
WMTF response level rather than describing a distinct MU.
In light of these concerns, the marginal likelihood estimates are adjusted according to Section \[sec:ML\] with a conservative lower bound of ${\mu_{\min}}=15$mN to guard against small MUs that, when firing, are indistinguishable from other combinations. The c... | 526 | 1,728 | 1,388 | 607 | null | null | github_plus_top10pct_by_avg |
uality follows from the assumption that $n\ell \geq 2^{12}d\log d$.
### Proof of Lemma \[lem:prob\_bottomlbound\]
Without loss of generality, assume that $\i < i$, i.e., $\ltheta^*_{\i} \leq \ltheta^*_i$. Define $\Omega$ such that $\Omega = \{j: j\in S, j \neq i,\i\}$. For any $\beta_1 \in [0,(\ell-2)/\ell]$, define ... | 527 | 1,351 | 1,072 | 555 | null | null | github_plus_top10pct_by_avg |
, in this limit, the dynamics becomes reversible regardless of $m$. For low temperatures, one can write $\cosh \beta x \approx \tfrac{1}{2}{\rm e}^{\beta |x|}$ to find $$\label{limZ-T3}
\!\!\!\frac{\mathcal Z_{\pm}(\lambda_f)}{\mathcal Z(\lambda_i)} \!\to \!
\lim_{\beta\to\infty} \!\!
\left[\!(1\!-\!\delta_{m0}) {... | 528 | 1,043 | 612 | 609 | null | null | github_plus_top10pct_by_avg |
athclap{\alpha \in R_{G,+}}} \left( 1 + e^{-\alpha} + e^{-2\alpha} + \ldots \right) \\
&= \sum_{\mathclap{\beta \in \Lambda^*_G}} \phi_{R_{G,+}}(\beta) e^{-\beta},
\end{aligned}$$ where $\phi_{R_{G,+}}$ is the *Kostant partition function* given by the formula $$\label{kostant partition function}
\phi_{R_{G,+}}(\b... | 529 | 2,853 | 1,073 | 476 | 3,918 | 0.769294 | github_plus_top10pct_by_avg |
or all $i$ and $Z_i\otimes_A R$ for all even integer $i$.
- $m $ maps $A_i\otimes_A R$ into $B_i\otimes_A R$ for all $i$.
- $m $ maps $W_i\otimes_A R$ into $(X_i\cap Z_i)\otimes_A R$ for all even integer $i$.
- $m $ maps $B_i^{\perp}\otimes_A R$ into $A_i^{\perp}\otimes_A R$ for all odd integer $i$.
Then, by ... | 530 | 1,525 | 721 | 604 | null | null | github_plus_top10pct_by_avg |
bda\}-5.$$
(-1,.5) node\[above left\] [$\mathcal{C}_1$]{} to\[out=-60,in=180\] (0,0) to\[out=180,in=60\] (-1,-.5); (-1,0)–(.5,0) node\[right\] [$\mathcal{C}_2$]{};
(2.5,0)–(5.5,0) node\[right\] [$E_\nu$]{}; (3,0) circle \[radius=.1\] node\[below left\] [$\frac{1}{2}(1,1)$]{}; (5,0) circle \[radius=.1\] node\[below\] ... | 531 | 309 | 373 | 577 | null | null | github_plus_top10pct_by_avg |
] T\_[C,0]{}u=,u\_[\_-]{}=0,u(,,E\_[m]{})=0. where $$\tilde{\bf f} := {\bf f}-T_C(L({\bf g})).$$
By the Trotter’s formula, the semigroup $G(t)$ generated by $T_{C,0}$ is given by \[calceq2\] G(t) = \_[n]{}(T\_[B\_0]{}(t/n)T\_[A\_0]{}(t/n)T\_[-(+C I)]{}(t/n)T\_[K\_C]{}(t/n))\^n, where the convergence is uniform on comp... | 532 | 460 | 1,022 | 594 | null | null | github_plus_top10pct_by_avg |
), -(2b-1)(2b'-1))$ is *unimodular of type II*. Thus we can write $$M_0=(\oplus_{\lambda}H_{\lambda})\oplus \left( Be_1'\oplus Be_2' \right)
\oplus \left(Be_3'\oplus Be_4'\right).$$ For this basis, the image of a fixed element of $F_j$ in the special fiber of the smooth integral model associated to $L^j$ is $$\begi... | 533 | 1,502 | 791 | 600 | 2,807 | 0.776821 | github_plus_top10pct_by_avg |
$k=0.5$); (c) the real part of the wave function is shown (at $k = 0.3, 0.5, 0.7$, $C=1$) \[fig.3\]](f04.eps "fig:"){width="50mm"}
In Fig. \[fig.4\] an evident picture of behavior of the imaginary part of the wave function close to point $r=0$ with continuous change of the wave vector $k$ and the parameter $C$ is sho... | 534 | 93 | 1,028 | 740 | 885 | 0.798321 | github_plus_top10pct_by_avg |
node comprised of 40 $2.4\,{\rm GHz}$ intel Skylake processors. We measure the wall clock time using the [MPI\_Wtime]{} function, after a call to [MPI\_Barrier]{} to synchronize all processors. We run the job with [SLURM –exclusive]{} option to make sure that other jobs do not interfere with ours.
For the weak scalin... | 535 | 397 | 1,570 | 656 | null | null | github_plus_top10pct_by_avg |
c{\ell^2}{\kappa^2}.\end{aligned}$$ Since, the above inequality is true for any fixed $i,\i$ and $j \in \Omega$ such that event $E$ holds, it is true for random indices $i,\i$ and $j \in \Omega$ such that event $E$ holds, hence the claim is proved.
### Proof of Lemma \[lem:bl\_prob2\]
Let $\widehat{\sigma}$ denote a ... | 536 | 379 | 693 | 644 | 1,228 | 0.792382 | github_plus_top10pct_by_avg |
percolation. , 29:577–623, 2001.
J. Jacod and A.N. Shiryaev. . Springer-Verlag, Berlin, 1987.
J. Norris and A.G. Turner. Hastings-levitov aggregation in the small-particle limit. 2011. submitted.
L.P.R. Pimentel. Multitype shape theorems for first passage percolation models. , 39(1):53–76, 2007. submitted.
M. Tala... | 537 | 165 | 873 | 526 | null | null | github_plus_top10pct_by_avg |
lic codes in Theorem 2.1.
[**Theorem 2.1** ]{}[@Boucher1; @Boucher2] *Let $C$ be a skew cyclic code ($\sigma$-cyclic code) of length $n$ over $\mathbb{F}_q$ generated by a right divisor $g(x)=\sum_{i=0}^{n-k-1}g_ix^i+x^{n-k}$ of $x^n-1$. Then\
* *(i) The generator matrix of $C$ is given by*
$$\left(
\begin{array}{... | 538 | 701 | 539 | 582 | 3,152 | 0.774452 | github_plus_top10pct_by_avg |
iterated adjoints {#sec:fun}
===============================
In particular, \[thm:stab-op\] implies that we can characterize $\Phi$-stability in terms of iterated adjoints to constant morphism morphisms. In this section we describe what this looks like more concretely in the pointed and stable cases.
\[prop:char-ptd... | 539 | 270 | 707 | 581 | 700 | 0.802144 | github_plus_top10pct_by_avg |
dels?
P.S. I use laravel 5.4
Brands Table:
id | name
-----------
1 | Adidas
2 | Nike
3 | Puma
Categories Table:
id | name
-----------
1 | Clothes
2 | Luxury
3 | Sport Wear
User_Interests Table:
id | user_id | type | reference_id
-----------------------------------------
1 | 113 | 'brand' |... | 540 | 1,563 | 600 | 605 | null | null | github_plus_top10pct_by_avg |
ed asymptotic solutions using a global numerical solution. The solution for the evolution of the scale factor in the quantum limit has the form $$a=\xi(-\tau+\beta)^p
\label{solution1}$$ where $p=2/(4-n)$. The solution in the classical limit we obtain putting simply $l=2$ what gives $D=1$ and $p=1/2$. The constants of ... | 541 | 943 | 969 | 671 | 2,536 | 0.779082 | github_plus_top10pct_by_avg |
$+$ $OS$
int4 $+$ $+$ $+$ $OS$
int5 $+$ $+$ $+$ $OS$
int6 $+$ $+$ $+$ $OS$
in... | 542 | 4,991 | 209 | 296 | 3,393 | 0.772707 | github_plus_top10pct_by_avg |
l} \; \mbox{if and only if}\; i = k\; \mbox{and}\; j=l.$$
In the array, the rows are the $\mathcal{R}$-classes of $\mathcal{B}$, the columns are the $\mathcal{L}$-classes and the $\mathcal{H}$-classes are points. There is only one $\mathcal{D}$-class; that is, $\mathcal{B}$ is a bisimple monoid (hence simple).
Follow... | 543 | 1,151 | 800 | 589 | 2,655 | 0.778102 | github_plus_top10pct_by_avg |
72---C71 120.2 (4)
C10---C9---H9 120.3 C73---C72---H72 119.9
C9---C10---C11 120.8 (5) C71---C72---H72 119.9
C9---C10---H10 119.6 C72---C73---C74 120.2 (4)
C11---C10---H10 119.6 C72---C73---H73 119.9
C12---C11---C10 120.2 (5) C74---C73... | 544 | 4,363 | 1,344 | 469 | null | null | github_plus_top10pct_by_avg |
$\underline{G}'$ and $G^{\circ}$ is the identity component of $G$. In our case, $G$ is the unitary group $\mathrm{U}(V, h)$, where $V=L\otimes_AF$. Since $\mathrm{U}(V, h)$ is connected, $G^{\circ}$ is the same as $G$ so that $[G:G^{\circ}]=1$.
Then based on Lemma 3.4 and Section 3.9 of [@GY], we finally have the fol... | 545 | 339 | 630 | 620 | 2,550 | 0.778964 | github_plus_top10pct_by_avg |
1--3 times/week 846 0.85 0.48 −0.09, 1.78 843 0.003 0.003 −0.003, 0.009 845 0.60 0.34 −0.06, 1.26
4--6 times/week 157 −0.47 0.79 −2.01, 1.07 157 −0.003 0.005 −0.012, 0.007 158 −0.47 0.56 −1.56, 0.62
Daily 90 0.44 ... | 546 | 3,681 | 159 | 399 | null | null | github_plus_top10pct_by_avg |
leotide polymorphisms stratified by gender in HCV-1 and HCV-2 infected patients receiving PEG-IFNα-RBV therapy with and without a RVR in a Chinese population in Taiwan**
**HCV-1** **HCV-2**
------------... | 547 | 3,589 | 328 | 382 | null | null | github_plus_top10pct_by_avg |
ne\phi^{*3,4}\}|R\rangle_{pqrs}^{(4,5,6)}$. These states transform as a vector–like representations of $SU(2)_B \times U(1)_B$.
- $\{\overline\phi^{5,6}\}|R\rangle_{pqrs}^{(4,5,6)}$ or $\{\overline\phi^{*5,6}\}|R\rangle_{pqrs}^{(4,5,6)}$. These states transform as a vector–like representations of $SU(2)_C \times U(1... | 548 | 309 | 1,226 | 738 | null | null | github_plus_top10pct_by_avg |
function $\overline{c_{F}}$ is given by:
- $\overline{c_{F}}(\lambda)=\lambda$,
- $\overline{c_{F}}({\sigma_{1}\sigma_{2}\ldots\sigma_{m}})=$ $c_{F}(\sigma_{1},\lambda)$ $c_{F}(\sigma_{2},\sigma_{1})$ $\ldots$ $c_{F}(\sigma_{n-1},{\sigma_{1}\sigma_{2}\ldots\sigma_{n-2}})$ $c_{F}(\sigma_{n},{\sigma_{1}\sigma_{2}\... | 549 | 94 | 838 | 561 | null | null | github_plus_top10pct_by_avg |
nsely dotted](0,.13-1*.125)--++(0,1*.25);\end{tikzpicture}}},;{\hat\imath},;{{\begin{tikzpicture}[baseline=0cm]\draw[thick,densely dotted](0,.13-1*.125)--++(0,1*.25);\end{tikzpicture}}},;{b\!\!+\!\!2})$}},\end{aligned}$$]{} and $i-3$ more applications of Lemma \[lemma7\] show that ${\hat\Theta_{T''[i]}}={\hat\Theta_{S}... | 550 | 854 | 696 | 646 | 444 | 0.809581 | github_plus_top10pct_by_avg |
e rest of the data $\mathbf{y}_{-j}$. These likelihoods are used to monitor the predictive performance of the model. This performance is used to estimate the generalization error, and it can be used to carry out model selection [@kohavi1995study; @Rasmussen2006; @vehtari2017practical].
The Bayesian CV estimate of the ... | 551 | 81 | 2,097 | 670 | 1,610 | 0.787646 | github_plus_top10pct_by_avg |
, we should emphasize that the flow changes considerably when the parameters are varied and we have the freedom to choose the walls of the tool among the flow lines for certain fixed parameters $c_i(t)$. Moreover, the velocity and the orientation of the feeding (extraction) can vary somewhat for a given shape of the to... | 552 | 2,095 | 943 | 710 | 3,691 | 0.770663 | github_plus_top10pct_by_avg |
)(60,40)
\qbezier[20](120,60)(100,60)(100,40)
\qbezier[20](120,20)(100,20)(100,40)
\qbezier[20](120,60)(140,60)(140,40)
\qbezier[20](120,20)(140,20)(140,40) \put(40,20){\circle*{3}}
\put(40,60){\circle*{3}} \put(120,20){\circle*{3}}
\put(120,60){\circle*{3}}
\put(170,37){\small 2)} \qbezier[20](210,60)(230,60)(230,40)... | 553 | 63 | 1,137 | 673 | null | null | github_plus_top10pct_by_avg |
rangle-\0{1}{\sqrt{1- \langle L\rangle ^2} }
\langle \delta L\rangle +
O\left(\langle \delta L^2\rangle\right)\,.$$ In the center-symmetric phase $\langle L\rangle =0$, c.f. . Under center transformations $L$ transforms according to (\[eq:centertrafo\]) $L\to Z\, L$ with $Z=\pm 1$ and hence $ \delta L\to Z\, \delta ... | 554 | 3,038 | 1,070 | 554 | null | null | github_plus_top10pct_by_avg |
along with the increasing of difficulty level), besides, the blocks that participants should complete would also increase along with the increasing of difficulty level, and the error times allowed in one level would also be changed based on difficulty level. This kind of design could ensure that the treatment of WM tra... | 555 | 5,671 | 622 | 168 | null | null | github_plus_top10pct_by_avg |
kly increasing along the first row and down the first column. Let $\sigma=\sum_{T\in{\calu}}{\hat\Theta_{T}}$.
\[sigmahom2\] With the notation and assumptions above, we have ${\psi_{d,t}}\circ\sigma=0$ for all $d,t$.
For $d\gs v$ and $t=1$, we use the same argument as that used in several proofs above: for $T\in{\cal... | 556 | 286 | 825 | 645 | 606 | 0.804472 | github_plus_top10pct_by_avg |
\delta
_{1}}^{\bot }\Cup (\mathcal{S}_{\delta _{1}}\Cap \mathcal{S}_{\delta _{2}})$.
Let us observe now that $\mathcal{L}_{QD}^{P}$ obviously inherits the notions of p-validity and order defined in $\mathcal{L}_{Q}^{P}$ (Sec. 3.4). Hence, we can illustrate the role of the connective $I_{Q}$ within $\mathcal{L}_{QD}^{P... | 557 | 477 | 1,038 | 637 | null | null | github_plus_top10pct_by_avg |
commute in . Such a derivator is pointed and for every $X\in{\sD}^\square$ the canonical morphism $$\label{eq:stable-lim-II}
C(F_2X)\toiso F(C_1X)$$ is an isomorphism (). For every $x\in{\sD}$ we consider the square $$X=X(x)=(i_\lrcorner)_!\pi_\lrcorner^\ast x\in{\sD}^\square.$$ The morphism $\pi_\lrcorner^\ast\colon{\... | 558 | 530 | 908 | 586 | null | null | github_plus_top10pct_by_avg |
icular cases of GA codes.
Let $\Sigma$ and $\Delta$ be two alphabets and $F:N^{*}\times\Sigma^{+}\rightarrow\Sigma^{*}$ a function, where $N$ is the set of natural numbers, and $N^{*}=N-\{0\}$. A function $c_{F}:\Sigma\times\Sigma^{*}\rightarrow\Delta^{+}$ is called a if its unique homomorphic extension $\overline{c_{... | 559 | 1,302 | 760 | 634 | null | null | github_plus_top10pct_by_avg |
0.058 0.058 0.058 0.048 0.062 0.068 0.062
K=100 0.056 0.062 0.058 0.054 0.052 0.054 0.044
K=150 0.046 0.062 0.058 0.054 0.058 0.054 ... | 560 | 4,861 | 257 | 292 | null | null | github_plus_top10pct_by_avg |
he good elements at the beginning of the list.
Currently, my function to generate the random indices looks essentially as follows:
def pick():
p = 0.2
for i in itertools.count():
if random.random() < p:
break
return i
It does a good job, but I wonder:
What's the name of the generated ... | 561 | 3,903 | 215 | 511 | 510 | 0.807474 | github_plus_top10pct_by_avg |
that the right-hand side is nonzero only when $x$ and $y$ are connected by a chain of bonds with *odd* currents (see Figure \[fig:RCrepr\]).
![\[fig:RCrepr\]A current configuration with sources at $x$ and $y$. The thick-solid segments represent bonds with odd currents, while the thin-solid segments represent bonds wi... | 562 | 74 | 503 | 619 | 1,503 | 0.788798 | github_plus_top10pct_by_avg |
t(\frac{1 + P^{(0)}_{m+1,n}}{P^{(2)}_{m+1,n}} - \frac{1+P^{(0)}_{m-1,n}}{P^{(2)}_{m-1,n}} \right),\end{gathered}$$
where
\[eq:N5-P-G\] $$\begin{gathered}
P^{(0)}_{m,n} = \phi^{(0)}_{m-1,n} \phi^{(0)}_{m,n} \phi^{(0)}_{m+1,n} \phi^{(1)}_{m,n}, \\
P^{(1)}_{m,n} = \phi^{(0)}_{m-1,n} \big(\phi^{(0)}_{m,n}\big)^2 \phi^{(0... | 563 | 1,997 | 1,010 | 671 | null | null | github_plus_top10pct_by_avg |
\delta_{\tilde{p}(v)}\,\Psi\ =&\ p(v)\Psi - X\eta F\Xi D_{\tilde{p}(v)}F\Psi\,,
\label{p tilde Psi}\end{aligned}$$
where the former is determined so as to induce $$\begin{aligned}
\delta_{\tilde{p}(v)}A_\eta\ =&\
D_\eta\Big( A_{p(v)}- f\xi_0\big(QA_{\tilde{p}(v)} + [F\Psi,\,F\Xi D_{\tilde{p}(v)}F\Psi]\big)\Big)
\no... | 564 | 2,184 | 1,015 | 653 | null | null | github_plus_top10pct_by_avg |
plicity, we take $\epsilon$ and $\tau$ to be fixed but we will keep explicit track of these quantities in the constants.
Since each coordinate of $\hat{\gamma}_{{\widehat{S}}}$ is an average of random variables that are bounded in absolute value by $2(A+\tau) + \epsilon$, and $\mathbb{E}\left[
\hat{\gamma}_{{\widehat{... | 565 | 1,584 | 712 | 598 | null | null | github_plus_top10pct_by_avg |
$ for some formal expansion $\tilde{z}_i''^{\ddag}$. Here, if $m$ is a formal matrix of size $a\times b$, then $m^{\dag}$ is the $(a, b)^{th}$-entry of $m$ (resp. $(a-1, b)^{th}$-entry of $m$) if $L_i$ is *of type* $\textit{I}^o$ (resp. $\textit{I}^e$).
Note that $$\left \{ \begin{array}{l}
z_i+\delta_{i-2}... | 566 | 1,696 | 1,190 | 654 | 3,301 | 0.773352 | github_plus_top10pct_by_avg |
.00035
5000 .00014
10000 .00007
: Indifference proportion[]{data-label="Ta:INDIFFERENCE_PROPORTION"}
#### Indemnification formula {#S:UPPER_BOUND}
The indemnification formula provides a statistical upper bound on hazard intensity. Indemnification data may be expressed a... | 567 | 1,015 | 593 | 695 | 1,313 | 0.791208 | github_plus_top10pct_by_avg |
convention that $\H^{[0]}(z,w):=1$. It is known by work of Göttsche and Soergel [@Gottsche-Soergel] that the mixed Hodge polynomial $H_c\left(X^{[n]};q,t\right)$ is given by $$H_c\left(X^{[n]};q,t\right)
=(qt^2)^n\H^{[n]}\left(-t\sqrt{q}, \frac{1}{\sqrt{q}}\right).$$
We have $$\H^{[n]}(z,w)=\H_{(n-1,1)}(z,w).$$ \[conj... | 568 | 441 | 746 | 593 | 3,961 | 0.768941 | github_plus_top10pct_by_avg |
od as a marginalisation of ${\boldsymbol{\mu}}$ and substituting the definition produces the first equality by: $$\begin{aligned}
\tilde{f}(y_{1:T}|s_{1:T}) =\int \tilde{\pi}({\boldsymbol{\mu}}) f(y_{1:T}|{\boldsymbol{\mu}},s_{1:T}) d{\boldsymbol{\mu}}= \frac{\int_M \pi({\boldsymbol{\mu}})f(y_{1:T}|{\boldsymbol{\mu}}... | 569 | 711 | 1,189 | 683 | 1,998 | 0.783728 | github_plus_top10pct_by_avg |
ne-forms $\{\text{d}\tau,\text{d}\varphi,\text{d}\psi\}$ via $$\mathbf{V}^{(m\,h\,k)}= V_{i}^{(m\,h\,k)}\text{d}x^i,\quad x\in\{\tau,\varphi,\psi\}\,.$$ The covector components are given by $$\begin{aligned}
V_{j}^{(m\,h\,k)} \propto
\begin{bmatrix}
v^{(m\,h\,k)}_{\tau}(\sin \psi )^{-1} \\
v^{(m\,h\,k)}_{\v... | 570 | 3,514 | 474 | 391 | null | null | github_plus_top10pct_by_avg |
\,
\label{eq:sigma-full} \\
%
A_{l'l}=|A_{l'}| |A_{l}|\; , \;\;A_l= C_l
N_l(E)\,e^{i\delta_l(E)}\int_0^{r_0}dr j_l(q_lr)\; , \nonumber \\
%
q_l=\sqrt{2M(E-V_l)}\; , \;\;
\phi_{l'l}(E) = \phi^{(0)}_{l'l} + \delta_{l'}(E) - \delta_{l}(E)\, ,
\nonumber
%\end{aligned}$$ where $N_l$ is defined by matching condition on th... | 571 | 2,273 | 924 | 674 | null | null | github_plus_top10pct_by_avg |
\{j,k\}$ such that $i_\nu =j$ if $\nu $ is even and $i_\nu =k$ if $\nu $ is odd. Let $\chi '=r_{i_0}r_{i_1}\cdots r_{i_{m-1}}(\chi )=
r_{i_1}r_{i_2}\cdots r_{i_m}(\chi )$ (by (R4)), and $$\Lambda '={t}_{i_0}{t}_{i_1}\cdots {t}_{i_{m-1}}^\chi (\Lambda ),\quad
\Lambda ''={t}_{i_1}{t}_{i_2}\cdots {t}_{i_m}^\chi (\Lamb... | 572 | 1,180 | 527 | 627 | null | null | github_plus_top10pct_by_avg |
chosen top level category. Thus, in this new dataset we replaced each navigational step over a page with an appropriate Wikipedia category (topic) and the dataset contains paths of topics which users visited during navigation (see Figure \[fig:pathexample\]). Figure \[fig:histograms\] illustrates the distinct topics an... | 573 | 1,139 | 1,420 | 505 | null | null | github_plus_top10pct_by_avg |
{kl}=\Lambda_{kl}\Lambda_{ij}$ , (v) $\Lambda_{jk} z_k \partial_k = z_j \partial_j$ .
The sign reversing operator $\Lambda_j$ may be defined by its action on the coordinates of the $j$-th particle as $\Lambda_j f(z_1,..,z_j,.., z_N)=
f(z_1,..,-z_j,.., z_N)$. This operator is (i) self-inverse $\Lambda_{j}^{-1} = \Lambd... | 574 | 247 | 529 | 682 | null | null | github_plus_top10pct_by_avg |
ve viewpoint if we endow $\mathcal{L}_{QD}^{P}$ with some further derived pragmatic connectives which can be made to correspond with connectives of physical QL. To this end, we introduce the following definitions.
D$_{1}$. *We call* quantum pragmatic disjunction *the connective* $A_{Q}$* defined as follows.*
*For eve... | 575 | 2,528 | 883 | 679 | null | null | github_plus_top10pct_by_avg |
tition-function .unnumbered}
----------------------------------------------------
If $G$ is semisimple, we can find $s, t \in {\mathbb Z}_{\geq 0}$ and group homomorphisms $A \colon {\mathbb Z}^s \rightarrow {\mathbb Z}^t$ and $B \colon \Lambda^*_G \oplus \Lambda^*_G \rightarrow {\mathbb Z}^t$ such that $$\label{bliem... | 576 | 172 | 714 | 711 | 1,743 | 0.786186 | github_plus_top10pct_by_avg |
termined by the least significant two bits of $a$, $b$ and $m$.
The new algorithm
-----------------
The algorithm works with two non-negative integers $a$ and $b$, where multiples of the smaller one is subtracted from the larger. To compute the Jacobi symbol we maintain these additional state variables: $$\begin{alig... | 577 | 4,712 | 266 | 588 | 978 | 0.79649 | github_plus_top10pct_by_avg |
t\in \{1,2,\ldots, n\} \mid \{i,j\}\in E_t\}|{\leqslant}2n^{1-\varepsilon}$$ for some constant $\varepsilon\in(0, 1)$. This property is called $\varepsilon$-visibility.
\[thm:s2c\] Let $(G^{(1)},\ldots, G^{(n)})$ be a regular dynamic graph which satisfies the $\varepsilon$-visibility condition, for some $\varepsilon\... | 578 | 1,124 | 1,032 | 585 | 1,675 | 0.786892 | github_plus_top10pct_by_avg |
-------------------------------------------------------------------------- ------------- -------------------- ----------------------------------------------- ------------- ------------- ------------ ---------- ---------- ----------
Age, year ... | 579 | 472 | 920 | 801 | null | null | github_plus_top10pct_by_avg |
CA \- 107.5 35.0 109.8 95.4 2158 19 0.75 382 130 9
GP16 CA \- 108.6 36.0 115.3 95.4 2939 26 1.03 677 240 43
GP01 ... | 580 | 4,396 | 320 | 235 | null | null | github_plus_top10pct_by_avg |
algebra $K(H)[X, X^{-1}; \s] = K(H)[Y, Y^{-1}; \s^{-1}]$ where $K(H)$ is the field of rational functions in the variable $H$ and the automorphism $\s$ of $K(H)$ is given by the rule $\s(H) = H-1$. By [@Bav-DixPr5 Proposition 2.1(1)], the centralizer $C_B(P_p)$ of the element $P_p$ in $B$ is a Laurent polynomial algebr... | 581 | 2,552 | 700 | 625 | null | null | github_plus_top10pct_by_avg |
act-sde}$ and $\eqref{e:discrete-clt}$ over an epoch which consists of an interval $[k\delta , (k+n)\delta)$ for some $k$. The coupling in consists of four processes $(x_t,y_t,v_t,w_t)$, where $y_t$ and $v_t$ are auxiliary processes used in defining the coupling. Notably, the process $(x_t,y_t)$ has the same distributi... | 582 | 257 | 743 | 633 | 1,630 | 0.787396 | github_plus_top10pct_by_avg |
n{aligned}
X \otimes_{[B]} \big((\id\times u\op)^\ast\lI_B\big) &\cong (\id\times u\op)^\ast X\\
Y \otimes_{[A]} \big((\id\times u\op)_!\lI_A\big) &\cong (\id\times u\op)_! Y\end{aligned}$$ In fact, these dual base change objects are actually isomorphic to the first two swapped: $$\begin{aligned}
(\id\times u\op... | 583 | 269 | 985 | 663 | 3,403 | 0.772648 | github_plus_top10pct_by_avg |
on of the 1-form $\omega\in T_u^\ast U$ with the vector field $\gamma\in T_uU$ and similarly for the vector field $\bar{\gamma}\in T_uU$. Multiplying the equations (\[eq:2.8\]) by the 1-form $\omega\in\Phi$ we get
\[eq:2.9\] |<>|=0.
We look for the compatibility condition for which the system (\[eq:2.9\]) does ... | 584 | 2,740 | 1,292 | 652 | null | null | github_plus_top10pct_by_avg |
f [<span style="font-variant:small-caps;">Best-$1$-Arm</span>]{} from the perspective of instance-wise optimality.'
author:
- |
Lijie Chen Jian Li\
Institute for Interdisciplinary Information Sciences (IIIS), Tsinghua University
bibliography:
- 'team.bib'
title: On the Optimal Sample Complexity for Best Arm Id... | 585 | 70 | 653 | 541 | null | null | github_plus_top10pct_by_avg |
s, and 60°C for 60 s. A melt curve was performed in order to verify single PCR products. The comparative threshold cycle (*C~T~*) method was used to quantify transcripts, with the ribosomal *rrs* gene serving as the endogenous control. Δ*C~T~* values were calculated by subtracting the *C~T~* value of the control gene f... | 586 | 2,031 | 1,091 | 657 | null | null | github_plus_top10pct_by_avg |
y denominator, as shown in (\[Omega-1st-order\]). Then, higher order correction terms are always accompanied by the energy denominators which are composed of some of the first three in (\[expansion-parameters\]), and therefore they are suppressed. The unique exception for it is the terms generated only by $\Omega [1]_{... | 587 | 1,008 | 1,102 | 713 | null | null | github_plus_top10pct_by_avg |
labeled as input. $\hfill \square$
As stated, we want to prove that every query in the denotation of the considered moded query is either non-terminating or terminates due to the evaluation of an integer condition. To achieve this, we need to guarantee that integer constructors are repeatedly evaluated with a free var... | 588 | 3,872 | 1,652 | 623 | 1,028 | 0.795431 | github_plus_top10pct_by_avg |
left( \wedge^{m_n} {\cal E}_n^{\alpha^{-1} *}
\otimes \wedge^{p_n} {\cal E}_n^{\alpha^{-1} }
\otimes \wedge^{\ell_n} T_n^{\alpha^{-1} *}
\otimes \wedge^{k_n} T_n^{\alpha^{-1} } \right)
\\
& & \hspace*{3.5in} \left.
\otimes {\cal F}^{\alpha^{-1}}_+ \otimes
\sqrt{ K_{\alpha^{-1}} \otimes \det {\cal E}^{\alpha^{-1} }_0 ... | 589 | 221 | 565 | 697 | null | null | github_plus_top10pct_by_avg |
$v_{i+1}=(0,\cdots, 0, 1, 0)$) of size $1\times n_{i+1}$ if $L_{i+1}$ is *of type* $\textit{I}^o$ (resp. *of type* $\textit{I}^e$).
5. Assume that $i$ is odd and that $L_i$ is *bound of type I*. Then $$\delta_{i-1}v_{i-1}\cdot {}^tm_{i, i-1}+\delta_{i+1}v_{i+1}\cdot {}^tm_{i, i+1} = \pi m_{i,i}^{\ast\ast}$$ such that... | 590 | 3,009 | 605 | 542 | 2,407 | 0.780068 | github_plus_top10pct_by_avg |
ran}{\Phi}}}$.
\[D:DYADIC\_SPACE\_PRODUCT\] Let $\Theta$ and $\Phi$ be disjoint ensembles. The dyadic space product of $\prod\Theta$ and $\prod\Phi$ is $$\prod \Theta \prod \Phi = \prod \Theta\Phi$$ (that is, with $\Upsilon = \Theta\Phi$, the set of all $\Upsilon$-choices).
\[D:DYADIC\_CHOICE\_PROD\] Let $\Theta$ and... | 591 | 2,092 | 1,689 | 649 | null | null | github_plus_top10pct_by_avg |
ceptible state. At a given time $t$, the network management system updates a module of a controller with software that contains a bug, as shown in Fig. \[fig:prop2\]. As a result, this node becomes infected and propagates the failure (e.g., the bug) to his neighbors, as observed in Fig. \[fig:prop3\]. The epidemic cont... | 592 | 14 | 2,336 | 844 | null | null | github_plus_top10pct_by_avg |
solutions are $$t_{hit} = 2n \pi \left( \frac{2c + 1}{\beta} \right)$$ where $c$ ranges over the non-negative integers. At these points in time, the value of $P[1]$ is $$\frac{1}{2} + \frac{1}{2}e^{-(2c+1)\frac{p \pi}{\beta}}$$ which immediately yields Theorem 2.
The breakpoint case $p = 4k$
--------------------------... | 593 | 137 | 1,369 | 703 | null | null | github_plus_top10pct_by_avg |
dient Richardson number ($Ri_g = N^2/S^2$); where, $S$ is the magnitude of wind shear.
It is evident that the simulations with larger cooling rates result in smaller $\mathcal{L}$ as would be physically expected. In contrast, $\eta$ marginally increases with higher stability due to lower $\overline{\varepsilon}$. The ... | 594 | 1,173 | 2,745 | 754 | 120 | 0.824316 | github_plus_top10pct_by_avg |
-v^{i})^{-1}$. On the other hand, the coinvariant ring $ {\mathbb{C}}[{\mathfrak{h}}]^{\text{co}{{W}}}$ has graded Poincaré polynomial $\sum_{\lambda} \sum_i [{\mathbb{C}}[{\mathfrak{h}}]_i^{\text{co} {{W}}} : \lambda] [\lambda]v^i$. By definition, this is just $\sum_{\lambda} f_{\lambda}(v)[\lambda]$. Combining these ... | 595 | 294 | 583 | 650 | 4,039 | 0.7685 | github_plus_top10pct_by_avg |
od{\Phi}}$. This chain of implication concludes that $(\phi_i \in {\prod{\Phi}}) \Rightarrow (\phi_{i+1} \in {\prod{\Phi}})$.
Use $\lbrace \phi_n \rbrace$ and $\lbrace \xi_n \rbrace$ to define another sequence $\lbrace {\mathbf{f}}_n \rbrace$ by setting ${\mathbf{f}}_i = (\phi_i\xi_i, \phi_{i+1})$. Since $\phi_i\xi_i ... | 596 | 195 | 962 | 728 | 2,090 | 0.782836 | github_plus_top10pct_by_avg |
possibly zero, by our convention) if $j$ is even (resp. odd).
\[t411\] The morphism $$\psi=\prod_j \psi_j : \tilde{G} \longrightarrow (\mathbb{Z}/2\mathbb{Z})^{\beta}$$ is surjective.
Moreover, the morphism $$\varphi \times \psi : \tilde{G} \longrightarrow \prod_{i:even} \mathrm{O}(B_i/Z_i, \bar{q}_i)_{\mathrm{red}}... | 597 | 3,033 | 753 | 513 | null | null | github_plus_top10pct_by_avg |
a,3,1^b)}$ unless $(u,v)\dom(a,3,1^b){^{\operatorname{reg}}}$, which is the partition $(\max\{a,b+2\},\min\{a-1,b+1\},2)$. So we may assume that this is the case, which is the same as saying $v\ls\min\{a+1,b+3\}$. For easy reference, we set out notation and assumptions for this section.
**Assumptions and notation in f... | 598 | 635 | 716 | 595 | 1,145 | 0.79359 | github_plus_top10pct_by_avg |
. $Y \cap (S \times \{n\}) = \{x_1, x_2\} \times \{n\}$.
In Case 1, each $\mathbb{Z}_{k+1}^{2}$ layer contains exactly one point of $Y$. $T$ then tiles the rest of the layer by Proposition \[onepoint\].
In Case 2, some of the layers contain two points of $Y$, and some of the layers contain no points. Holes of size 0... | 599 | 2,166 | 871 | 678 | 3,529 | 0.77173 | github_plus_top10pct_by_avg |
ta_{C}}\neq0$.
Showing the first statement is very easy, using Lemma \[lemma5\]. The only homomorphisms that occur in that lemma with non-zero coefficient are labelled by tableaux with more than $v$ $1$s in rows $2$ and $3$, and therefore by Lemma \[lemma7\] are zero.
Showing that ${\hat\Theta_{C}}\neq0$ is also stra... | 600 | 576 | 719 | 639 | 451 | 0.809483 | github_plus_top10pct_by_avg |
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