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 |
|---|---|---|---|---|---|---|---|
mbda_z \\ \delta\end{smallmatrix}\right)} \}.
\end{aligned}$$ After choosing a basis of the lattice $\Lambda^*_{G_{\operatorname{ss}}}$ we arrive at the asserted formula (with $s' = \dim T_{G_{\operatorname{ss}}}$ and $u = t + r_H$).
We stress that the proof of is constructive: The maps $\mathcal A$ and $\mathcal B$... | 701 | 402 | 965 | 714 | 2,869 | 0.77643 | github_plus_top10pct_by_avg |
4.90 1118.00 37.21 80.63 50.92 283.50
**MGoF** 13.97 17.50 15.54 294.08 14.66 8.13 10.45 **8.01** **12.50** 3.13 5.00 250.10 18.42 8.75 11.86 **7.55**
-------------------- --... | 702 | 2,380 | 2,043 | 832 | null | null | github_plus_top10pct_by_avg |
y $\mathcal{U}$ imposed on it, then Eq. **(\[Eqn: TB\]) must also be satisfied in order that the topology generated by $_{\textrm{T}}\mathcal{B}$ is indeed $\mathcal{U}$. The next theorem connects the two types of bases of Defs. A1.1 and A1.2 by asserting that although a local base of a space need not consist of open s... | 703 | 1,842 | 1,042 | 712 | 2,143 | 0.782327 | github_plus_top10pct_by_avg |
east one propagating part which contains $1$ and $1'$ simultaneously. In the diagram of the standard expression of a seat-plan of $\Sigma^1_{n-\frac{1}{2}}$, the vertices $1$ and $1'$ are joined by a vertical line. Shrinking this vertical line to one vertex, we have one to one correspondences between $\Sigma^1_{n-\frac... | 704 | 1,016 | 660 | 661 | null | null | github_plus_top10pct_by_avg |
also targets the virus through increasing the endosomal pH and hinders the glycosylation process of the cellular receptors of SARS-CoV-2, which eventually blocks the viral attachment to the ACE2 receptors and inhibits the viral infection. (4) Moreover, the hydroxychloroquine obstructs the MAP-kinase pathway which resul... | 705 | 3,821 | 1,111 | 503 | null | null | github_plus_top10pct_by_avg |
ght)}+\\
& \quad +P{\left(a_2=1,b_4=1\right)}+P{\left(a_2=2,b_8=0\right)}+P{\left(a_3=0,b_8=2\right)}+P{\left(a_3=1,b_7=1\right)}+\\
& \quad +P{\left(a_3=2,b_4=2\right)}+P{\left(a_4=0,b_1=1\right)}+P{\left(a_4=1,b_2=1\right)}+P{\left(a_4=2,b_3=2\right)}+\\
& \quad +P{\left(a_5=0,b_6=2\right)}+P{\left(a_5=1,b_2=0\right)... | 706 | 1,246 | 1,393 | 866 | null | null | github_plus_top10pct_by_avg |
for all $\beta \in R^\chi _{+\infty }$. The set $$V'=\{\chi '\in V^\chi _{\underline{n}}\,|\,d(\chi ')\not=0 \}$$ is open in $V^\chi _{\underline{n}}$ and contains $\chi $. Thus by Prop. \[pr:X5dense\] the set $$V''=\{\chi '\in {\overline{{\mathcal{X}}}}_5\cap V^\chi _{\underline{n}}\,|
\,d(\chi ')\not=0\}$$ is Zari... | 707 | 752 | 805 | 698 | null | null | github_plus_top10pct_by_avg |
j_{\bar{z}}^g (z)
\nonumber \\
& &
+ \frac{g}{4} \log |z-w|^2 (\partial_z j_{\bar{z}}^g(z) - \partial_{\bar z} j^g_z(z)))
\nonumber \\
& &
+ (-1)^{ac} : j_z^c j_{\bar z}^a :(z)
\nonumber \\
& &
+ ( {(A)^{ac}}_{gh} \frac{\bar z - \bar w}{z-w} :j^{g}_{\bar z}
j^{h}_{\bar z}: (z) - ( {(B)^{ac}}_{gh} \log |z-w|^2 :j^{... | 708 | 981 | 1,037 | 799 | null | null | github_plus_top10pct_by_avg |
the pragmatics of $\mathcal{L}_{Q}^{P}$. We introduce the following assumption on $\mathcal{L}_{Q}^{P}$.
A$_{5}$. *Let a mapping* $\xi $* be given which interpretes the variable* $x$* in the rfs of* $\mathcal{L}_{Q}^{P}$* on a physical object in the state* $S$*. A proof that the rf* $E(x)$* is true (false) consists i... | 709 | 3,128 | 1,320 | 676 | 2,735 | 0.777407 | github_plus_top10pct_by_avg |
\mathbf{y}_*}$ is strictly diagonal.
Reference methods
-----------------
The GPR point estimates are compared with a state-of-the-art kNN algorithm. We select ten predictors from the (transformed) data using a simulated annealing -based optimization approach of [@Packalen2012] and use the most similar neighbor (MSN) ... | 710 | 198 | 305 | 776 | 1,332 | 0.790854 | github_plus_top10pct_by_avg |
^+(x,y),L_x\}$ is very similar to that of Figure \[satolevine\]). This means that $\pi_1(M)$ does **not** admit an epimorphism to $\mathbb{Z}\ast \mathbb{Z}$ since that would imply that $\{ L_x,L_y\}$ were a homology boundary link. But $\b^2(x,y)=-1$ precludes this by [@C2]. Nonetheless, further $c(yy...y,x)$ may be ta... | 711 | 190 | 807 | 742 | 3,163 | 0.774389 | github_plus_top10pct_by_avg |
by Fourier-transform of the slow-time phase fluctuations of individual comb lines $\tilde{A}_\mu(t)$, as $\delta\!f_\mu(t) = \frac{d}{dt} \arg(\tilde{A}_\mu(t))$.
As according to [@hendry_spontaneous_2018], the critical amplitude $F_C$ to which a soliton locks for this detuning ($\delta\omega>3\kappa$), based on pure... | 712 | 1,391 | 2,631 | 943 | null | null | github_plus_top10pct_by_avg |
In this section we will prove the following theorem.
### Main Theorem {#main-theorem .unnumbered}
There exists an integer $l_0$ such that for an arbitrary integer $l \ge l_0$, $n=2^l-2$ the Kervaire invariant given by the formula (1) is trivial. $$$$
### Proof of Main Theorem {#proof-of-main-theorem .unnumbered}
T... | 713 | 229 | 970 | 747 | null | null | github_plus_top10pct_by_avg |
\end{aligned}$$
Where we use properties of $h$ from Lemma \[l:hproperties\].
The last claim follows immediately from Lemma \[l:hproperties\].4.
[Defining q]{} \[ss:defining-q\]
In this section, we define the function $q$ that is used in Lemma \[l:fproperties\]. Our construction is a slight modification to the ... | 714 | 2,023 | 636 | 764 | null | null | github_plus_top10pct_by_avg |
\prod_{k=1}^{i-1}
\frac{(1-zT^k)}{(1-T^k)}.
\label{F}$$
By the Cauchy $q$-binomial theorem the sum equals $$\frac{1}{(1-w)}\prod_{n\geq
1}\frac{(1-wzT^n)}{(1-wT^n)}.$$Also$$\sum_\lambda
T^{|\lambda|}=\prod_{n\geq 1}(1-T^n)^{-1}.$$If we divide Formula (\[F\]) by this we finally get
$$1-(1-z)(1-w)\prod_{n\geq
1}... | 715 | 2,594 | 929 | 730 | null | null | github_plus_top10pct_by_avg |
`gi 87162179 ref` `415` `AKSEVWRQMMSD`
... | 716 | 5,343 | 311 | 224 | null | null | github_plus_top10pct_by_avg |
and $\Phi$. Together, cases A and B show that $\prod\Theta \not= \prod\Phi$ implies $\Theta \not= \Phi$. Applying the contrapositive principle[^12] gives $\prod\Theta = \prod\Phi$ if $\Theta = \Phi$.
\[T:SPACE\_UNIQ\_ENSEMBLE\] Any choice space has one unique generating ensemble: let $\Theta$ and $\Phi$ be two ensemb... | 717 | 767 | 1,994 | 831 | null | null | github_plus_top10pct_by_avg |
\pm)}(k,r) =
\bar{N}_{2}
\biggl( 1 \mp \displaystyle\frac{iW(r)}{k\alpha} \biggr)
e^{\pm ikr}
\label{eq.3.2.1.3}$$ and $$\bar{N}_{2} = i\displaystyle\frac{\bar{N}_{1}}{k\alpha N_{2}}
\label{eq.3.2.1.4}$$
In accordance with main statements of quantum mechanics, for applying such form of the radia... | 718 | 3,814 | 423 | 704 | null | null | github_plus_top10pct_by_avg |
${abs}(|\mathcal{C}_{i1}| - |\mathcal{C}_{i2}|) \leq 1$ [@dong2005ensembles]. This has been shown empirically to have little effect on the accuracy in most cases, while reducing the time taken to train nested dichotomies. Balanced selection has greater benefits for problems with many classes.
It is clear that the sam... | 719 | 4,255 | 1,394 | 460 | 422 | 0.810185 | github_plus_top10pct_by_avg |
s a unique strong solution $\Phi$ satisfying the initial and boundary values. Then $\phi(x,\omega,E):=\Phi(x,\omega,E_{\rm m}-E)$ is the solution of $(I+P_0)\phi=f$. This completes the proof of (\[inf4\]). The inequality (\[inf5\]) can be shown similarly as above and so the conclusion follows.
\[md-gene\] The previous... | 720 | 463 | 784 | 824 | null | null | github_plus_top10pct_by_avg |
pha)=\alpha l$ induces a bijection between the set $$\{ \alpha \in [K^{x}\backslash L /Q]\ ; x\alpha y \in H\},$$ and the set $$\{w\in [K^{x}\backslash L\cap H^{x}/ Q^{l}]\}.$$
- Let $\alpha\in L$ such that $x\alpha y \in H$. Since $y=lx^{-1}h$ we have: $$\begin{aligned}
x\alpha y \in H &\Leftrightarrow x\alpha ... | 721 | 910 | 717 | 766 | null | null | github_plus_top10pct_by_avg |
orse function is a Morse function such that the following hold ([@kitazawa]).
1. At distinct singular points the values are distinct.
2. Inverse images of regular values are disjoint unions of standard spheres.
3. A vertex of the Reeb graph such that the inverse image includes a singular point not giving a local ... | 722 | 1,519 | 2,293 | 820 | null | null | github_plus_top10pct_by_avg |
{} (232,30)[(b)]{} (395,30)[(c)]{}
Target FBP Matérn
--------------- ----- -------- -- -- --
Carved cheese 0.1 12604
: Computation times of the carved cheese (in seconds)[]{data-label="Computation time cheese"}
Discussion
----------
We have presented x-ray tomography recons... | 723 | 167 | 1,782 | 851 | null | null | github_plus_top10pct_by_avg |
-\lambda(t-s)}\lrp{\frac{L_N^2}{\epsilon}\lrn{y_s - y_0}_2^2 + L \lrn{y_s - y_0}_2} ds - \int_0^t e^{-\lambda(t-s)} G_s dA_s.
\end{aligned}$$ By taking derivatives, we see that $$\begin{aligned}
d\mathcal{L}_t
\leq& -\lambda f(z_t) dt + \lrp{\frac{L_N^2}{\epsilon}\lrn{y_t - y_0}_2^2 + L... | 724 | 2,098 | 838 | 734 | null | null | github_plus_top10pct_by_avg |
TNM (stage) Duration of follow-up after diagnosis (months) Site of metastasis Site of tomotherapy
--------- ----- ----- -------------------- -------------------- ----------------------------------------- ------------- ------------------------------------------------ -------------------- --------------------... | 725 | 5,141 | 355 | 337 | null | null | github_plus_top10pct_by_avg |
es labeled by $A,B$ where $A,B\in\{T,\Phi,R\}$. They are defined by $$\begin{aligned}
\mathbf{W}_{TT}^{(m\,h\,k)}&=\mathbf{W}^{(m\,h\,k)}\big|_{c_{\beta\neq 1}=0}\,, \\ {\nonumber}\mathbf{W}_{\Phi\Phi}^{(m\,h\,k)}&=\mathbf{W}^{(m\,h\,k)}\big|_{c_{\beta\neq 2}=0}\,, \\ {\nonumber}\mathbf{W}_{RR}^{(m\,h\,k)}&=\mathbf{W}... | 726 | 2,811 | 937 | 785 | null | null | github_plus_top10pct_by_avg |
loss of generality, we assume that $I_{n-k+1}$ corresponds to the first index (up to a permutation). We can rewrite ($\mathcal{P}_1$) (Proposition \[prop4\]) as:
$\underset{(1,v) \in \mathcal{V}_{1,k}}{\underset{v \in \mathbb{R}^{n-1}}{\arg\min}} {\|v\|}_1 $
Constraints in ($\mathcal{P}_1$) can be moved to the follo... | 727 | 2,955 | 1,002 | 709 | 3,464 | 0.772173 | github_plus_top10pct_by_avg |
1$ and $$\label{eq:s13}
H^a_{\rm eff}=H-i\lambda_W VV^\dag\,.$$ In this case the coupling is purely imaginary. For the two cases, where the antenna is terminated by a hard wall or an open reflecting end, we may assume $\alpha=0$, resulting in $\lambda_T=\tanh(i\varphi/2)=i\tan\varphi/2$, and $$\label{eq:s14}
H^... | 728 | 4,776 | 1,998 | 597 | 2,377 | 0.780411 | github_plus_top10pct_by_avg |
-------------
All 58 animals were continuously monitored over 6 months to exclude postoperative patellar luxations, deep wound infection, or empyema.
### Patellar luxation
The animals were examined daily over the first 5 weeks and weekly for the remaining observation period by adspection for clinical signs of patell... | 729 | 4,774 | 738 | 427 | null | null | github_plus_top10pct_by_avg |
hedged and leveraged, and nearly free of systematic market fluctuations. Equations (\[439\])-(\[442\]) provide approximate expressions valid to first order in $1/N$ for the properties of these portfolios.*]{}
3. Single-Index Model with Constant Residual Variance {#single-index-model-with-constant-residual-variance .u... | 730 | 1,125 | 1,459 | 803 | 3,063 | 0.775093 | github_plus_top10pct_by_avg |
---C50 1.389 (7)
P2---C63 1.835 (4) C49---H49 0.9500
P3---C57 1.820 (5) C50---H50 0.9500
P3---C51 1.831 (5) C51---C56 1.380 (7)
P3---C63 1.836 (4) C51---C52 1.387 (7)
P4---C39 1.823 (5) ... | 731 | 5,388 | 650 | 230 | null | null | github_plus_top10pct_by_avg |
(h, 1_G) j(1_H, g) =
\theta \bigl( \psi(h, 1_G)\bigl) \theta \bigl(\varphi(1_H, g)
\bigl) = \theta \bigl(\psi(h, 1_G) \varphi(1_H, g) \bigl)$$ that is $\theta$ is surjective. Thus $H\, {}_{\alpha}\!\!
\bowtie_{\beta} \, G$ is a quotient group of $X$.
We end the section with a problem that can be of interest for a furt... | 732 | 3,690 | 1,018 | 617 | null | null | github_plus_top10pct_by_avg |
lta R},\label{eq:radial_operator_uniform} \\
\Delta_\phi^2\Phi_{i,j,k} =& \frac{\Phi_{i,j-1,k}-2\Phi_{i,j,k}+\Phi_{i,j+1,k}}{R_i^2(\delta\phi)^2},\end{aligned}$$ while $\Delta_z^2$ is defined through Equation .
Logarithmic Cylindrical Grid
----------------------------
In logarithmic cylindrical coordinates, we disc... | 733 | 2,986 | 1,432 | 825 | 2,383 | 0.78034 | github_plus_top10pct_by_avg |
\pmod{3k}$, $Y \cap (S \times \{n\}) = \{x_2, x_3\} \times \{n\}$.\
We will now prove Theorem \[kodd\]. We know that if $X \subset \mathbb{Z}_{k+1}^2$ has one point in each row or column then $X$ is a hole of size $k+1$. Since $k+1$ is even, we can try to choose $X_n$ in each slice $\mathbb{Z}_{k+1}^2 \times \{n\}$ s... | 734 | 499 | 571 | 746 | 2,182 | 0.781955 | github_plus_top10pct_by_avg |
2 0.8665 0.3064 0.031\*
C12 0.6221 (2) 0.7741 (3) 0.35032 (18) 0.0191 (10)
H12 0.6426 0.7594 0.3262 0.023\*
C13 0.6964 (2) 0.5780 (3) 0.35824 (16) 0.0130 (9)
H13A 0.7378 ... | 735 | 4,329 | 438 | 438 | null | null | github_plus_top10pct_by_avg |
,J,P).
eq(A,A). plus(0,B,B). plus(s(A),B,s(C)):- plus(A,B,C).
![Moded SLD-tree $eq\_plus$[]{data-label="fig:eq_plus_symbolic"}](figs/eq_plus_symbolic.pdf){width="70ex"}
Substitutions on input variables express conditions for the clause to be applicable. The edge from node $N_2$ to $N_3$ shows that clause ... | 736 | 2,221 | 982 | 538 | 198 | 0.818866 | github_plus_top10pct_by_avg |
ho_{n-1}|< r_n\}$ and $\sigma_{B_n} = \inf\{t>0: X_t\not\in B_n\}$. The algorithm comes to an end at the random index $N = \min\{n\geq 0\colon \rho_n\not\in D\}$, again using the standard understanding that $\min\emptyset \coloneqq \infty$. See for example the depiction in Figure \[4stepsonly\].
![Steps of the walks-o... | 737 | 2,287 | 906 | 783 | null | null | github_plus_top10pct_by_avg |
0.000 0.000
BLB($n^{0.8}$) 0.002 0.000 0.000 0.004 0.002 0.000 0.000
SDB($n^{0.6}$) 0.000 0.000 0.000 0.000 0.000 0.000 0.000
SDB($n^{0.8}$) 0.000 0.000 ... | 738 | 5,097 | 192 | 426 | null | null | github_plus_top10pct_by_avg |
0.40177 (12) 0.49661 (5) 0.0332 (3)
P1 0.70165 (5) 0.64377 (8) 0.41615 (4) 0.0122 (2)
P2 0.90214 (5) 0.37198 (8) 0.63471 (4) 0.0119 (2)
P3 0.86722 (5) 0.16721 (8) 0.60311 (4) 0.0123 (2)
P4 0.68282 (5) ... | 739 | 4,559 | 232 | 407 | null | null | github_plus_top10pct_by_avg |
covariant derivative can be expressed in terms of the spin connection $\omega_{an m}$ as $\nabla_a=\partial_a+{1\over 2} \omega_{anm} \Sigma^{nm}$, where $\Sigma^{nm}={1\over 4}[\gamma^n,\gamma^m]$ are the generators of the Lorentz transformations in spin $1/2$ representation.
[^3]: One can see that for the conformall... | 740 | 276 | 383 | 647 | null | null | github_plus_top10pct_by_avg |
0.994 0.996 0.994
K=100 0.994 0.998 0.998 0.990 0.988 0.994 0.996
K=150 0.994 1.000 0.998 0.986 0.992 0.998 0.990
mVC 0.918 0.... | 741 | 4,952 | 260 | 434 | null | null | github_plus_top10pct_by_avg |
pi(C^\lambda,k)$ does not depend on the given $\Q$-resolution. Also, the following upper semi-continuity property will be useful.
\[lemma:propsM\] Under the above conditions:
1. \[lemma:propsM:epsilon\] $\cM_\pi(C^\lambda,k)=\cM_\pi(C^{\lambda+\varepsilon},k)$ for a sufficiently small $\varepsilon>0$.
2. \[lemma:p... | 742 | 423 | 740 | 802 | null | null | github_plus_top10pct_by_avg |
above, the original idea is to change only the complex coupling strength $\lambda_c$ to one channel $c$, while the measuring is done on one or two different channels $a,b\neq c$. We denote the resulting scattering fidelity by *coupling fidelity*. We present below an exact RMT prediction for this quantity.
The starting... | 743 | 2,608 | 1,235 | 768 | 2,693 | 0.777818 | github_plus_top10pct_by_avg |
and the Rubin et. al. data set [@Rubin1980]. Except the last set, the observed velocity curves is fitted to either $v^{\hbox{\scriptsize{p-iso}}}(r)$, or to a functionally similar velocity curve [@Cour]. The last set gives only the galactic rotation curves, and they have been fitted to $v^{\hbox{\scriptsize{p-iso}}}(r... | 744 | 4,808 | 494 | 524 | null | null | github_plus_top10pct_by_avg |
oplus H(1)$.
For this choice of a basis, the block associated to $\tilde{M}_0\oplus M_2$ of the image of a fixed element of $F_j$ in the special fiber of the smooth integral model associated to $L^j$ is $$\begin{pmatrix} id&0 &0\\ 0 &\begin{pmatrix} 1&\frac{1}{1+4b''}(-2z_j^{\ast})\\
0 & 1+\frac{1}{1+4... | 745 | 421 | 741 | 762 | 2,668 | 0.777997 | github_plus_top10pct_by_avg |
serve that for the convex set $G$ actually $\tau_{e,-}(y,\omega)=\infty$ for all $(y,\omega,E)\in \Gamma_{e,-}$.
\[tthcon\] The trace mappings $$\gamma_{e,\pm}:W^2(G_e\times S\times I)\to T^2(\Gamma_{e,\pm})$$ are (well-defined) bounded surjective operators with bounded right inverses (lifts) $L_{e,\pm}:
T^2(\Gamma_... | 746 | 357 | 749 | 876 | null | null | github_plus_top10pct_by_avg |
shida]{}, T. 2016, , 68, 16
, M., [Ohsuga]{}, K., [Wada]{}, K., [Susa]{}, H., & [Misawa]{}, T. 2013, , 65, arXiv:1212.3075
, G. S., [Ostriker]{}, J. P., & [Ciotti]{}, L. 2011, , 737, 26
, S. P., & [Haiman]{}, Z. 2002, , 569, 558
, K., [Mori]{}, M., [Nakamoto]{}, T., & [Mineshige]{}, S. 2005, , 628, 368
, K., [Schn... | 747 | 1,023 | 2,985 | 973 | null | null | github_plus_top10pct_by_avg |
\
\mathcal{Z}_i&1 \end{pmatrix} & \quad \textit{if $L_i$ is \textit{bound of type II}};\\
(m_{i,i})_1 & \quad \textit{if $L_i$ is \textit{free of type II}}.
\end{array} \right.$$
Here, $$\left\{
\begin{array}{l}
\mathcal{X}_i=(v_i)_1+(\delta_{i-2}e_{i-2}\cdot (m_{i-2, i})_1+\delta_{i+2}e_{i+2}\cdot (m_{i+2, i... | 748 | 3,556 | 674 | 509 | 2,616 | 0.778415 | github_plus_top10pct_by_avg |
ults efficiently from practical sample sizes.
Keywords: software, safety, hazard, demonstration, operational profile, automata, confidence, statistics
author:
- '\'
title: Software Safety Demonstration and Indemnification
---
\[section\] \[theorem\][Lemma]{} \[theorem\][Corollary]{} \[theorem\][Conjecture]{} \[th... | 749 | 160 | 1,405 | 539 | null | null | github_plus_top10pct_by_avg |
ng are equivalent statements.*
\(1) *$D$ is dense in $X$*.
\(2) *If $F$ is any closed set of $X$ with $D\subseteq F$, then $F=X$*; *thus the only closed superset of $D$ is $X$.*
\(3) *Every nonempty (basic) open set of $X$ cuts $D;$ thus the only open set disjoint from $D$ is the empty set $\emptyset$.*
\(4) *The e... | 750 | 1,630 | 1,778 | 770 | 1,231 | 0.792355 | github_plus_top10pct_by_avg |
1
Note that only 48 children could be included in the analyses, due to the age restrictions of some of the questionnaires (FES and PSS).
2
Obtained by fitting a second model, including the subscales of the FES, inst... | 751 | 53 | 1,295 | 944 | null | null | github_plus_top10pct_by_avg |
e can prove Lemma $\ref{lem:4-1-3}$.
We use the following formula [@andrews_askey_roy_1999 p.22, Theorem 6.5.1]: $$\begin{aligned}
\G(2a) = \frac{2^{2a - 1}}{\sqrt{\pi}} \G(a) \G\left(a + \frac{1}{2} \right). \end{aligned}$$ From this and Lemma $\ref{lem:4-1-1}$, we have $$\begin{aligned}
2 \G(2a) - a \G(a)^{2}
&= \f... | 752 | 2,601 | 909 | 811 | 3,284 | 0.77348 | github_plus_top10pct_by_avg |
!= j, i != "y" && j != "y", and both i and j are adjacent to each other.
I'm having difficulty concocting an algorithm to create an adjacency matrix provided a char[][] array. I've defined the rules, but finding constraints for iteration is problematic.
A:
Try this:
static void set(boolean[][] aM, int cols, int row0,... | 753 | 997 | 15 | 708 | 50 | 0.831505 | github_plus_top10pct_by_avg |
=1$.
(The order of the rules in $m_r$ is arbitrary). Additionally, $M$ contains the starting and the terminating matrices $$(S'\to [S] S \overline{A_1} \cdots \overline{A_m}) \mbox{ and } (\overline{S} \to {\lambda},\overline{A_1} \to {\lambda}, \ldots,\overline{A_m} \to {\lambda}),$$ where $V=\{S,A_1,\ldots,A_m\}$. I... | 754 | 1,862 | 1,735 | 774 | 1,300 | 0.791397 | github_plus_top10pct_by_avg |
nt of $F_j$ in the even orthogonal group associated to $M_0''$, where $M_0''$ is a Jordan component of $Y(C(L^j))=\bigoplus_{i \geq 0} M_i''$. As in the above case (1), there are 3 cases depending on whether $(a+a')/2$ is a unit or not, and whether $M_1=\oplus H(1)$ (possibly empty) or $M_1=A(4b'', 2\delta, \pi) \oplus... | 755 | 804 | 945 | 792 | 3,162 | 0.77442 | github_plus_top10pct_by_avg |
i*. Note that a small value is added to *Y~i~* for the logarithm.
Adding epigenetic effects
-------------------------
Discrete values representing epigenetic states of a gene *i* are added to the regression model
where *H* is the type of histone mark (neither mark=1.0, H3K27me3=2.0, bivalent mark=3.0, H3K4me3=4.0), ... | 756 | 112 | 2,109 | 874 | 1,458 | 0.789311 | github_plus_top10pct_by_avg |
19 (17.6) 38 (24.2) 0.75 (0.12, 4.88) C/T 27 (17.1) 5 (13.5) 2.70 (0.20, 35.75)
T/T 2 (1.9) 3 (1.9) 0.4332 1 T/T 2 (1.3) 1 (2.7) 0.7216 1
C/C + C/T 106 (98... | 757 | 4,328 | 784 | 352 | null | null | github_plus_top10pct_by_avg |
that the $S2R_p$ policy is defined to reference the $P2P$ values regardless of whether the $P2P_p$ policy itself is active.
The separation kernels of VxWorks MILS, LynxSecure, INTEGRITY-178B and PikeOS meet the security functionalities and security assurance requirements in SKPP.
### Data Separation Properties
Data... | 758 | 1,983 | 2,093 | 777 | 505 | 0.807656 | github_plus_top10pct_by_avg |
scending aorta (50 mm) and diffuse atherosclerotic disease, without any obstructive lesions. Elective transfemoral TAVI was scheduled.
{#ytz069-F1}
######
Blood tests results
Parameters (... | 759 | 5,001 | 358 | 294 | null | null | github_plus_top10pct_by_avg |
nd{aligned}$$ where $g$ takes values in the supergroup $G$ and $Tr'$ indicates the non-degenerate bi-invariant metric. We will use the normalization and results of [@Ashok:2009xx]. The Wess-Zumino-Witten points are given by the equation $1/f^2 = |k|$. Note that the action is invariant under group inversion $g \leftrigh... | 760 | 430 | 1,356 | 848 | null | null | github_plus_top10pct_by_avg |
{-\beta }}\Big).
\end{aligned}$$ Recall that $\beta '_\nu \not={\alpha }_{i_1}$, since $\nu >1$. Moreover, $$\begin{aligned}
&e^{(1-{b^{\chi}} ({\alpha }_{i_1})){\alpha }_{i_1}}{\sigma }_{i_1}^{\chi _2}\Big(
\frac {1-e^{-\bfun{\chi _2}({\alpha }_{i_1}){\alpha }_{i_1}}}
{1-e^{-{\alpha }_{i_1}}}\Big)\\
... | 761 | 1,007 | 665 | 795 | null | null | github_plus_top10pct_by_avg |
the ket, which will terminate upon raising the highest-weight state. Therefore the vector bases with different weights $k, k^\prime$ are orthogonal.
Since we have also proved that vector bases with different $m$ and $h-k$ are orthogonal, the proof of orthogonality for vector bases is done. It may not be obvious that ... | 762 | 2,108 | 940 | 776 | null | null | github_plus_top10pct_by_avg |
-t0A2_Table A2
######
LCMS analysis of FIX-PCC pre-filtrate following filtration with 6 μm filter.
Accession Description Score Coverage MW \[kDa\] calc. pI
----------- ----------------------------------------------- --------- ---------- ------------ ----------
P00... | 763 | 5,107 | 270 | 270 | null | null | github_plus_top10pct_by_avg |
again by abuse of language) the partial order induced on $\phi _{AD}^{Q}/\approx $ by the preorder defined on $\phi _{AD}^{Q}$. Then, let us show that $(\phi
_{AD}^{Q}/\approx ,\prec )$ is order isomorphic to $(\mathcal{L(S)},\subset
) $.
Let us consider the mapping
$f_{\approx }:[\delta ]_{\approx }\in \psi _{AD}^{Q... | 764 | 1,483 | 692 | 815 | null | null | github_plus_top10pct_by_avg |
n as Eq. . We substitute the highest-weight metric perturbation into the left hand side of the linearized Einstein equation and the result is given by Eq. .
$$\begin{aligned}
{}
h^{(m\,h\,0)}_{ab} &=
R^h e^{im\Phi}
\left[
\begin{array}{cccc}
R^{+2}C_{TT}(u)
& R^{+1} C_{T\Phi}(u)
& R^{+0}C _{TR}(... | 765 | 2,009 | 997 | 760 | null | null | github_plus_top10pct_by_avg |
{T}}$ involves a semistandard homomorphism which does not occur in any other ${\psi_{2,2}}\circ{\hat\Theta_{T'}}$ (except possibly for a tableau $T'$ already ruled out in the paragraph above). So we may restrict attention to those $T$ having at most one $2$ and one $3$ in the first row.
Now return to ${\psi_{2,1}}\cir... | 766 | 291 | 537 | 809 | 165 | 0.821369 | github_plus_top10pct_by_avg |
redict future video frames in a self-supervised manner. Remarkably, the model is able to capture a wide variety of seemingly disparate phenomena observed in visual cortex, ranging from single unit response dynamics to complex perceptual motion illusions. These results suggest potentially deep connections between recurr... | 767 | 119 | 1,346 | 603 | null | null | github_plus_top10pct_by_avg |
\pi t_i\\ \pi y_i&1+\pi x_i&\pi z_i\\ v_i&u_i&1+\pi w_i \end{pmatrix}=
\begin{pmatrix} \mathrm{id}+\pi s_i^{\prime}&\pi r_i^{\prime}&\pi^2t_i^{\prime}\\ \pi^2y_i^{\prime}&1+\pi^2x_i^{\prime}&\pi^2z_i^{\prime}\\ \pi v_i^{\prime}&\pi u_i^{\prime}&1+\pi^2w_i^{\prime} \end{pmatrix}.$$
4. If $i$ is even and $L_i$ is ... | 768 | 4,164 | 343 | 552 | null | null | github_plus_top10pct_by_avg |
computed, the app sets the system in UM and manages the model transfer to the MCU. This operation allows to correctly store the personalized model in the Flash memory of the MCU and use it for real-time classification. The communication protocol sends 3 types of packets containing the following: the general configurat... | 769 | 56 | 874 | 755 | 2,351 | 0.780647 | github_plus_top10pct_by_avg |
dth"}
### Topics navigation {#subsubsec:topicalnavi .unnumbered}
#### Wikigame topic dataset
Performing our analyses by representing Wikipedia pages by their topical categories shows a much clearer and more interesting picture as one can see in Figure \[fig:paths\_cat\]. Similar to above we can see (A) that the log ... | 770 | 3,253 | 1,835 | 822 | null | null | github_plus_top10pct_by_avg |
ions can then be solved automatically in the constraint-based approach, based on Proposition 3 of [@DBLP:journals/corr/abs-0912-4360].
\[prop:rem\_imp\] Let $prem$ be a polynomial over $n$ variables and $conc$ a polynomial over 1 variable, both with natural coefficients, where $conc$ is not a constant. Moreover, let $... | 771 | 297 | 1,503 | 907 | 285 | 0.814737 | github_plus_top10pct_by_avg |
# General characteristics of the study population (N = 277).
{#pone.0231480.t001g}
Characteristics Genotypes
---------------------------------- ---------------- ------------- ------------- ------------
Gender N (%) ... | 772 | 630 | 935 | 996 | null | null | github_plus_top10pct_by_avg |
s^{-q}(\alpha'_{n,j}) (-q,q) - \alpha'_{n,j} \s^{q}(\beta_{m,s}) (q,-q).$$
Using the equalities $(-p,p)=\s^{-p}((p,-p))$ and $(-q,q)=\s^{-q}((q,-q))$, the last equality above can be rewritten as follows $$\label{1=ab}
1 = (1-\s^{-p})(a) + (1-\s^{-q})(b)$$ where $a = \alpha_{n,i} \s^{p}(\beta'_{m,t}) (p,-p) \in K[H]$ a... | 773 | 486 | 862 | 782 | null | null | github_plus_top10pct_by_avg |
)\
&+&4 d\_F \_f $\frac{\Lambda}{4\pi T}$\^[2]{}+O\[\^6\]. The renormalized quark free-energy is given as F\_q\^r &=&- d\_F \_f(1+12\^2 ) +4 d\_F \_f where $\hat \Lambda=\Lambda/2\pi T$ and $\hat \mu=\mu/2\pi T$.
Gauge boson free-energy in a strongly magnetized medium {#gauge_boson}
----------------------------------... | 774 | 215 | 1,679 | 997 | null | null | github_plus_top10pct_by_avg |
_j)$. But then, $\psi_i$ and $\psi'_j$ are necessarily of degree $-s$. The exactness of $\textbf{D} (\mathcal O^!)$ at the degree $-s$ implies that $\psi$s of the degree $-s$ are exact, i.e. there are elements $\Psi_i, \Psi'_j\in \textbf{D}(\mathcal O^!)$ such that $\psi_i={\partial}(\Psi_i)$, $\psi'_j ={\partial}(\Psi... | 775 | 505 | 703 | 850 | 3,596 | 0.771314 | github_plus_top10pct_by_avg |
model or in an ensemble setting.'
author:
- |
Tim Leathart, Eibe Frank, Bernhard Pfahringer and Geoffrey Holmes\
Department of Computer Science, University of Waikato, New Zealand
bibliography:
- 'multi\_subset\_nd.bib'
title: Ensembles of Nested Dichotomies with Multiple Subset Evaluation
---
Introduction
==... | 776 | 580 | 1,133 | 457 | 2,466 | 0.779528 | github_plus_top10pct_by_avg |
among the AMI inpatients and there was no significant difference in mortality rates among males and females (28% *vs* 19.4%; *P*=0.10).
In our study, binary logistic regression analysis identified only three predictor variables for the prognosis of AMI inpatients \[[Table 1](#T0001){ref-type="table"}\]. Patients repor... | 777 | 3,252 | 726 | 329 | null | null | github_plus_top10pct_by_avg |
Load()
A:
generic_visit is called when a custom visitor (ie visit_Name) can't be found. Here's a piece of code I wrote recently with ast.NodeVisitor: https://foss.heptapod.net/pypy/pypy/-/blob/80ead76ab428100ffeb01109c7fc0d94f1048af2/py/_code/_assertionnew.py It interprets the AST nodes to gain debugging inform... | 778 | 4,630 | 282 | 563 | null | null | github_plus_top10pct_by_avg |
^{x}L}}$ up to $(H\cap {\ ^{x}L})$-conjugacy, is an $R$-basis of $\mu_{R}(G)$.
Section $3$ of [@tw].
\[prop\_b\] The Mackey algebra $\mu_{R}(G)$ is isomorphic to $RB(\Omega_{G}^{2})$, where $\Omega_{G}$ is the $G$-set: $\sqcup_{L\leqslant G} G/L$.
The proof can be found in Proposition $4.5.1$ of [@bouc_green]. Let u... | 779 | 753 | 955 | 725 | null | null | github_plus_top10pct_by_avg |
om a node $N_b$ to a node $N_e$, is identified based on three properties. The path should be applicable, independent from the concrete terms represented by the input variables. Therefore, the first property states that no substitutions on input variables may occur between $N_b$ and $N_e$. The second property states tha... | 780 | 3,384 | 1,814 | 753 | 1,409 | 0.789951 | github_plus_top10pct_by_avg |
(a_5=0,b_2=0\right)}+P{\left(a_5=1,b_1=2\right)}+P{\left(a_5=2,b_6=2\right)}+P{\left(a_6=0,b_8=1\right)}+\\
& \quad +P{\left(a_6=1,b_5=0\right)}+P{\left(a_6=2,b_7=2\right)}+P{\left(a_7=0,b_3=1\right)}+P{\left(a_7=1,b_6=0\right)}+\\
& \quad +P{\left(a_7=2,b_1=0\right)}+P{\left(a_8=0,b_6=1\right)}+P{\left(a_8=1,b_3=0\rig... | 781 | 1,841 | 1,364 | 931 | null | null | github_plus_top10pct_by_avg |
h{b_{2}-p_{1,2}} & \ensuremath{1-a_{1}-b_{2}+p_{1,2}} & \multicolumn{1}{c|}{\ensuremath{1-a_{1}}}\tabularnewline\cline{1-4} \cline{6-9} & \ensuremath{b_{1}} & \ensuremath{1-b_{1}} & & & & \ensuremath{b_{2}} & \ensuremath{1-b_{2}} & \tabularnewline\cline{2-3} \cline{7-8} \multicolumn{1}{c}{} & & \multi... | 782 | 2,400 | 1,226 | 797 | null | null | github_plus_top10pct_by_avg |
er branes in the construction. This calculation was made in detail in [@Dfoam], where we refer the interested reader for further details. Here we mention only the results relevant for the present discussion.
![*Schematic representation of a D-particle space-time foam model with bulk density $n^\star (r) $ of D-particl... | 783 | 2,245 | 2,849 | 910 | 3,429 | 0.772444 | github_plus_top10pct_by_avg |
finish we give the details for $k=10$. In order to study the cokernel of $\pi^{(10)}$, let us fix a basis $\mathcal{B}_1 := \{ x^5, x^4y, x^3y^2, x^2y^3, xy^4, y^5, x^2 z, xyz, y^2z \}$ of $H^0(\PP^2_w,\mathcal{O}_{\PP^2_w}(k-5))$ and a basis $\mathcal{B}_2 = \langle 1,y_1,y_1^2,y_1^3,y_1^4,z_1 \rangle_\CC \oplus \lang... | 784 | 1,630 | 757 | 830 | null | null | github_plus_top10pct_by_avg |
ribution. We then have $$\begin{aligned}
\label{eq:Epsilarge}
E_\Psi &\approx \sqrt{2}\left(\left(1-\beta\right){\mathrm{erf}}^{-1}\left(1-\frac{2}{\Psi}\right)+\beta\mathrm{erf}^{-1}\left(1-\frac{2}{e\Psi}\right)\right),\end{aligned}$$ where $\beta$ denotes the Euler’s constant. Substituting into completes the proof.
... | 785 | 835 | 1,136 | 847 | null | null | github_plus_top10pct_by_avg |
\circ{\hat\Theta_{T}}$ over all $T\in{\calu}$, we get zero. A similar argument applies in the case $d=v$.
If $1\ls d<v$ and $t=2$, then we have ${\psi_{d,t}}\circ{\hat\Theta_{T}}=0$ for each $T\in{\calu}$ just using Lemma \[lemma5\]. Now take $2\ls d<v$ and $t=1$, and consider a tableau $T\in{\calu}$. There are a sing... | 786 | 558 | 885 | 794 | 320 | 0.813436 | github_plus_top10pct_by_avg |
lpha^2 F^2 \over 4}
\bigg ({\rm sin^2}\phi + {\alpha^2 \ {\rm sin^2}\theta \over
F^2}\bigg) +{\tau_0 \tau_1 \alpha^3 F \over 2}\rm sin\theta
cos\phi
\bigg] \Psi = \varepsilon\Psi\end{aligned}$$ $$\Rightarrow H_\tau\ \Psi = \varepsilon \Psi.$$
Calculational scheme
====================
To proceed with a basis set exp... | 787 | 3,858 | 1,080 | 705 | null | null | github_plus_top10pct_by_avg |
a.eps){width="\colwidth"} {width="\colwidth"}\
{width="\colwidth"} {width="\colwidth"}
Results {#sec:results}
=======
Detected host galaxies {#sec:resolved}
----------------------
Using the above criteria for detecting a residual host galaxy, we find nine of the 23 ... | 788 | 32 | 1,298 | 966 | null | null | github_plus_top10pct_by_avg |
me from single or double powers in $W$ in $\hat{H}_{1}$ are always accompanied by the matter potential in the form of $WA$ or $W^{\dagger} A$, as in eq. (\[H1-matrix\]). That is, perturbative effect of $W$ is always accompanied by matter potential, and hence can always be dealt with matter perturbation theory. It is th... | 789 | 787 | 1,174 | 916 | null | null | github_plus_top10pct_by_avg |
ight\Vert}_{L^\infty(G\times S)}^{1/2}
{\left\Vert \int_S \tilde{\sigma}(\cdot,\cdot,\omega',E) d\omega'\right\Vert}_{L^\infty(G\times S)}^{1/2},\end{aligned}$$ where ${\left\Vert K(E)\right\Vert}$ is the norm of $K(E)$ as an operator in $L^2(G\times S)$. Hence under the assumption (\[ass2a\]) the operator $K(E):L^2(G\... | 790 | 206 | 462 | 906 | null | null | github_plus_top10pct_by_avg |
\otimes_{[B]}X.$$ This defines a natural isomorphism $u^\ast\cong \big((u\times\id)^\ast\lI_B\big)\otimes_{[B]}-\colon{\sD}^B\to{\sD}^A$, thereby exhibiting $u^\ast$ as a weighted colimit.
Similarly, if we fix $X\in{\sD}(A)$, then by the partial morphism $$\label{eq:par-mor-wcolim}
(-\otimes_{[A]}X)\colon{\sV}^{A\op}\... | 791 | 496 | 1,342 | 823 | null | null | github_plus_top10pct_by_avg |
Delta\equiv -w_2^{-1} \mod (w_0w_1)$ and define $$\label{eq:Mj}
M_j:=(\Delta w_2+1)\deg_w \cC_j,\quad \text{ for all } j=1,..,r,$$ then $M_j$ satisfies \[prop:5\]. By construction $M=(\Delta w_2+1)\deg_w \cC $ which proves \[prop:4\] and $\frac{M}{\deg_w \cC}=\Delta w_2+1$ satisfies \[prop:6\]. Since $\Delta$ can be ch... | 792 | 459 | 219 | 970 | 2,028 | 0.783333 | github_plus_top10pct_by_avg |
ated as ${\mathsf{Stab}_L}(\Phi)$ for very small classes $\Phi$ of functors such as $\{\emptyset\}$ and $\{\emptyset,\ulcorner\}$. Can they also be generated as ${\mathsf{Stab}_L}({\mathsf{Abs}_L}(\Upsilon))$ for “manageable” collections $\Upsilon$ of derivators? For instance, are there “universal” pointed or stable de... | 793 | 758 | 2,130 | 967 | null | null | github_plus_top10pct_by_avg |
-1/2$. There is a multiplicity of left vacua, arising from $\lambda^{7-14}$. Let $|m\rangle$ denote a vacuum with $m$ +’s and $8-m$ -’s, [*i.e.*]{} annihilated by $m$ $\lambda$’s and $8-m$ $\overline{\lambda}$’s, then under the action of the generator of ${\mathbb Z}_4$, it is straightforward to check that $|m=0,4,8\r... | 794 | 2,064 | 1,841 | 893 | null | null | github_plus_top10pct_by_avg |
\pi^{*}H = c E$. Note that $\pi^{*} D_1 = \hat D_1 + \frac{1}{d} E$ and $\pi^{*} D_2 = \hat D_2 + \frac{p}{d} E$. Then, $$\begin{aligned}
\pi^{*} L^{(k)} &= -k \pi^{*} H + \sum_{i=1}^r {\left \lfloor \frac{kn_i}{n} \right \rfloor} \hat D_i
+ \left( \frac{1}{d} {\left \lfloor \frac{kn_1}{n} \right \rfloor} + \frac{p}{d... | 795 | 335 | 514 | 856 | null | null | github_plus_top10pct_by_avg |
gle=2n(\lambda)+|\lambda|=\sum_i(\lambda'_i)^2$, where $\lambda'=(\lambda'_1,\lambda'_2,\dots)$ is the dual partition. Note also that $(\lambda\cup\mu)'=\lambda'+\mu'$. Define $$\|\lambda\|:=\sqrt{\langle\lambda',\lambda'\rangle}=\sqrt{\sum_i\lambda_i^2}.$$ The following inequality is a particular case of the theorem o... | 796 | 1,118 | 1,090 | 864 | null | null | github_plus_top10pct_by_avg |
in previous steps. This question is the motivation for reverse inference, which considers automata operating backwards.
### Iterative converse {#S:ITERATIVE_CONVERSE}
Let $\langle \Psi, \Phi \rangle$ be a basis with persistent-volatile partition $\Psi = \Phi\Xi$ and step space ${\mathbb{S}} = \Lambda \times {\mathsc... | 797 | 1,878 | 897 | 850 | null | null | github_plus_top10pct_by_avg |
the model is shown in Fig. \[fig:skt\].
![Sketch of the model of colloidal dumbbells (bright yellow and dark red spheres) and droplets (white spheres). Shown are the diameters of colloidal species 1, $\sigma_{1}$, colloidal species 2, $\sigma_{2}$, and droplet $\sigma_{d}$. (a) In the initial stages the droplet captu... | 798 | 2,292 | 2,047 | 890 | null | null | github_plus_top10pct_by_avg |
l response value and its displacement *w.r.t.* its parent latent pattern. Please see the appendix for details.
Based on the above node definitions, we can use the AOG to parse each given image $I$ by dynamic programming in a bottom-up manner.
### Learning And-Or graphs {#sec:learnAOG}
The core of learning AOGs is to... | 799 | 155 | 840 | 839 | 538 | 0.806357 | github_plus_top10pct_by_avg |
e-dependent measurements or measurements of correlated $D^0\overline{D}^0$ pairs.
In principle, using the above observables the system Eqs. (\[eq:decomp-1\])–(\[eq:decomp-4\]) is exactly solvable as long as the data is very precise. In the CP limit the branching ratio measurements $(i)$ and the strong phase $(ii)$ are... | 800 | 1,733 | 1,623 | 909 | 1,882 | 0.784718 | github_plus_top10pct_by_avg |
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