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 |
|---|---|---|---|---|---|---|---|
t basis $N_R$, keeping for simplicity the $N$ dependence implicit, and $q(N_R) = 2^{-N}\left( \begin{array}{c} N \\ N_R \end{array} \right)$ is the probability to have exactly $N_R$ states from the Reject basis. Note that $P_R(m;\alpha, N_R)$ is calculated under the assumption that the Accept observable is measured dur... | 3,401 | 4,349 | 3,422 | 3,058 | 3,348 | 0.772981 | github_plus_top10pct_by_avg |
the inelastic tunnel current are classified by the power of the electron-phonon coupling $ \lambda^{\rm tip}_{\mu\nu}$ in the tunneling Hamiltonian. We note again that the additional inelastic contributions arise from phonon absorption and emission *during* the tunneling process, while all electron scattering processes... | 3,402 | 1,685 | 1,633 | 3,247 | null | null | github_plus_top10pct_by_avg |
-2+\widetilde{\alpha}_{i,i',\ell,\theta}$. We have, $$\begin{aligned}
\label{eq:posl_3}
&& \P_{\theta}\Big[\sigma^{-1}(i) = \ell, \sigma^{-1}(\i) > \ell \Big] \nonumber\\
&=& \sum_{\substack{j_1 \in S \\ j_1 \neq i,\i}} \Bigg(\frac{\exp(\theta_{j_1})}{W} \sum_{\substack{j_2 \in S \\ j_2 \neq i,\i,j_1}} \Bigg(\frac{\ex... | 3,403 | 2,505 | 2,352 | 2,955 | null | null | github_plus_top10pct_by_avg |
parentheses with some choice of operations. By induction we can define the *central letter* $c(w)$ of a dimonomial: if $w\in D$, then $c(w)=w$, otherwise $c(w_1{\mathbin\vdash}w_2)=c(w_2)$ and $c(w_1{\mathbin\dashv}w_2)=c(w_1)$. Let $c(w)=a_k$. If $D$ is 0-dialgebra, then $w=(a_1{\mathbin\vdash}\ldots{\mathbin\vdash}a... | 3,404 | 1,168 | 3,055 | 3,220 | 1,230 | 0.792364 | github_plus_top10pct_by_avg |
ceptible again. Therefore, individuals might change their state from susceptible to infected, and vice versa, repeatedly ($S\leftrightarrows I$).
- The *Susceptible-Infected-Removed* (SIR), which extends the SI model to take into account a removed state. Here, an individual can be infected just once because when the... | 3,405 | 3,646 | 4,009 | 3,295 | null | null | github_plus_top10pct_by_avg |
olic polynomial and let ${\mathbf{v}}\in \Lambda_+$ be such that $D_{\mathbf{v}}h \not \equiv 0$. Then
1. $D_{\mathbf{v}}h$ is hyperbolic with hyperbolicity cone containing $\Lambda_{++}$.
2. The polynomial $h({\mathbf{x}})-yD_{\mathbf{v}}h({\mathbf{x}}) \in {\mathbb{R}}[x_1,\ldots, x_n,y]$ is hyperbolic with hyper... | 3,406 | 2,268 | 2,382 | 3,052 | null | null | github_plus_top10pct_by_avg |
nvariant under translations in the independent variables $\MM{q}$. For each of these symmetries, Noether’s theorem yields a conservation law $$(L_j^\alpha z^j_{,\beta}-L\delta^\alpha_\beta)_{,\alpha}=0.$$ Such conservation laws can equally well be obtained by pulling back the quasi-conservation law (\[ofcl\]) to the ba... | 3,407 | 1,791 | 3,068 | 3,258 | 3,679 | 0.770758 | github_plus_top10pct_by_avg |
he estimation of the weight matrix in the RBFN is derived from the Lyapunov theory, which guarantees stability of the closed-loop system as presenting in the following theorem.
**Theorem 2.** Given the adaptation mechanism (\[eq34\]), the proposed control scheme (\[eq35\]) can guarantee the closed-loop DAR system (\[e... | 3,408 | 1,875 | 3,267 | 3,305 | null | null | github_plus_top10pct_by_avg |
communicates with the three active neutrinos.
One of the authors (H.M.) thanks Enrique Fernandez-Martinez for interesting discussions about the relationship between high-scale and low-scale unitarity violation. He expresses a deep gratitude to Instituto Física Teórica, UAM/CSIC in Madrid, for its support via “Theoret... | 3,409 | 434 | 3,730 | 3,378 | 1,183 | 0.793031 | github_plus_top10pct_by_avg |
}}{\partial D^{(r)}}\frac{\partial D^{(r)}}{\partial v}\, ,$$ from which follows that, in the vicinity of the transition fixed point $(A^*, B^*, C^*, D^*)$ of the two-polymer system, the mean number of contacts $\langle M^{(r)}\rangle$, for large $r$, behaves as $\langle M^{(r)}\rangle\sim \lambda_{D}^r
\label{eq:lambd... | 3,410 | 1,126 | 3,126 | 3,259 | 3,543 | 0.771641 | github_plus_top10pct_by_avg |
oposition 2. The strategy however is not doing this with one particular null geodesic, but with all the geodesics $\gamma_\Lambda(\lambda)$ generated by the points $\Lambda$ in $O'$. The resulting minimum for a given geodesic, denoted by $I_{\Lambda}$, is not necessarily a continuous function in $O'$ but, by Property 2... | 3,411 | 4,028 | 3,407 | 3,009 | null | null | github_plus_top10pct_by_avg |
tures, the AOG makes it easier to transfer CNN patterns to other part-based tasks.
**Unsupervised/active learning:**[` `]{} Many methods have been developed to learn object models in an unsupervised or weakly supervised manner. Methods of [@Gpt_WeaklyCNN; @WeaklyMIL; @OurICCV15AoG; @ObjectDiscoveryCNN_2] learned with ... | 3,412 | 652 | 3,322 | 2,892 | 1,646 | 0.787262 | github_plus_top10pct_by_avg |
we obtain (see Figure \[fig:1stpiv\])
$$\raisebox{0.2pc}{\includegraphics[scale=0.17]{1stpiv1}}~~~=~~~
\raisebox{-0.5pc}{\includegraphics[scale=0.17]{1stpiv2}}~~~+~~
\sum_b~\raisebox{-1.7pc}{\includegraphics[scale=0.17]{1stpiv3}}$$
$$\begin{aligned}
{\label{eq:pre-1st-exp}}
{{\langle \varphi_o\varphi_x \rangle}}_\... | 3,413 | 1,552 | 2,408 | 3,355 | null | null | github_plus_top10pct_by_avg |
punctatum* (CPC 18974). a, b. Sporulating colonies on potato-dextrose agar; c--h. macroconidiophores showing rachis; i, j. rachis showing pimple-like denticles; k. conidia. --- Scale bars = 10 μm.](per-28-113-g009){#F9}
![*Zasmidium angulare* (CPC 18942). a--d. Macroconidiophores showing apical conidiogenous loci; e.... | 3,414 | 4,049 | 3,139 | 3,424 | null | null | github_plus_top10pct_by_avg |
tion with the mapping $J\to J'$ gives the required homomorphism ${\mathrm{Di}}{\mathrm{SJ}}\langle X\rangle\to J'$.
A *bar-unit* of a 0-dialgebra $D$ is an element $e\in D$ such that $x{\mathbin\dashv}e=e{\mathbin\vdash}x=x$ for every $x\in D$ and $e$ belongs to the associative center of $D$ that is $$(x,e,y)_\times=(... | 3,415 | 1,973 | 2,188 | 3,143 | 2,895 | 0.776253 | github_plus_top10pct_by_avg |
loma of Gratitude from the Red Cross of Spain on p. 592. It is
left blank here as well.
In the Index and the text, mention of the "Duke of Parmella should have
been "Duke of Palmella", which appears correctly elsewhere. Both have been
corrected.
No systematic attempt was made to verify the accuracy of page references... | 3,416 | 5,722 | 1,082 | 2,713 | null | null | github_plus_top10pct_by_avg |
assuming success of all arithmetic calls. In a second phase, we characterize successful arithmetic calls as a constraint problem, the solution of which determines the non-terminating queries.
Keywords: non-termination analysis, numerical computation, constraint-based approach
author:
- |
Dean Voets[^1] $~~~~~$... | 3,417 | 2,733 | 1,157 | 2,533 | null | null | github_plus_top10pct_by_avg |
_{e} \rho E \lsim 50 \, \text{ (g/cm}^3) \text{GeV}$. See e.g., figure 3 of ref. [@Minakata:2015gra]. Clearly, it excludes the interesting region of “IceCube resonance” due to sterile neutrino mass of eV scales [@Nunokawa:2003ep], for which an entirely different theoretical framework would be necessary.
Then, we notic... | 3,418 | 2,321 | 3,609 | 3,425 | 3,817 | 0.769921 | github_plus_top10pct_by_avg |
ace the shift of the second peak. Curves are shifted upwards by 40 units for clarity.[]{data-label="fig:fkt2"}](fig5a "fig:"){width="4.25cm"}  it follows that $\mu^{(n)}(f)$ is ${\left\vert G^{(n)} \right\vert}^{-1/2}$-Lipschitz as a function of $Y^{(n)}$, and so $${\mathbb{P}}\left[{\left\vert \mu^{(n)}(f) - {\mathbb{E}}\mu^{(n)}(f)\bigr) \right\vert}
\ge t \right] \le 2 e^{-c t \sqrt{{\left\vert G^{(... | 3,423 | 1,748 | 2,544 | 3,115 | null | null | github_plus_top10pct_by_avg |
re general form of the restriction on the inclusion that is needed for image continuity to behave well for subspaces of $Y$.
**Theorem A2.3.** *Let* $q\!:(X,\mathcal{U})\rightarrow(Y,\textrm{FT}\{\mathcal{U};q\})$ *be an image continuous* *function. For a subspace* $B$ of $(Y,\textrm{FT}\{\mathcal{U};q\})$,$$\textrm{F... | 3,424 | 2,741 | 3,706 | 3,028 | 3,146 | 0.774523 | github_plus_top10pct_by_avg |
_{{\mathbb{R}}^{d}}\left\vert s_{t}(x,y)\right\vert
_{q_{1}+q_{2}}\psi _{\kappa }(y)\times \left\vert f(y)\right\vert dy \\
&\leq \frac{C}{(\lambda t)^{\theta_0(q_1+q_2+\theta_1)}} \left\Vert
f\right\Vert _{\infty }\int_{{\mathbb{R}}^{d}}\frac{\psi _{\pi
(q_{1}+q_{2},\kappa +d+1)}(x)}{\psi _{\kappa +d+1}(x-y)}\times \p... | 3,425 | 1,406 | 1,083 | 3,490 | null | null | github_plus_top10pct_by_avg |
_system}\\
\frac{d\E({\mathbf{u}})}{dt} & = \R({\mathbf{u}}). \label{eq:dEdt_system}\end{aligned}$$
A standard approach at this point is to try to upper-bound $d\E / dt$ and using standard techniques of functional analysis it is possible to obtain the following well-known estimate in terms of $\K$ and $\E$ [@d09] $$\... | 3,426 | 4,154 | 3,274 | 3,111 | null | null | github_plus_top10pct_by_avg |
so $\b^2(x,y)=-k$, whereas the link $\{c(y,x),L_y\}$ is a Whitehead link so $\b^2(y,x)= -1$. We claim further that, as long as $k\neq 0$, for $\textbf{any}$ basis $\{X,Y\}$ of $H^1(M)$, $\b^2(X,Y)\neq 0$. It will then follow from Theorem \[linear\] that the first Betti number of $M$ will grow sub-linearly in **any** f... | 3,427 | 3,892 | 2,976 | 3,122 | null | null | github_plus_top10pct_by_avg |
replacing ${\mathfrak{h}}\oplus{\mathfrak{h}}^*/ {{W}}$, $\operatorname{Hilb(n)}$ and ${\mathcal{P}}$ by $H_c{\text{-}{\textsf}{mod}}$, $B{\text{-}{\textsf}{qgr}}$ and $eH_c$, respectively. Then Corollary \[morrat-cor\] shows that $eH_c$ still induces a derived equivalence between the two categories. Indeed, it is even... | 3,428 | 2,701 | 1,361 | 3,161 | 1,749 | 0.786063 | github_plus_top10pct_by_avg |
a more fair comparison, we conducted the second baseline based on two-stage fine-tuning, namely *Fast-RCNN (2 fts)*. This baseline first fine-tuned the VGG-16 using numerous object-box annotations in the target category, and then fine-tuned the VGG-16 using a few part annotations.
The third baseline was proposed in [@... | 3,429 | 409 | 3,861 | 3,379 | 1,980 | 0.783918 | github_plus_top10pct_by_avg |
v}$ is the monomial $\prod_{i\in I}X_i^{v_i}$ for some independent commuting variables $\{X_i\}_{i\in I}$. \[hua\].
Since $A_{\Gamma,\v}(q)\in\Z[q]$, we see by Theorem \[hua\] and Lemma \[Exp\], that $M_{\Gamma,\v}(q)$ also has integer coefficients.
Comet-shaped quivers {#comet}
--------------------
Fix strictly pos... | 3,430 | 2,043 | 3,498 | 3,209 | 1,022 | 0.795521 | github_plus_top10pct_by_avg |
[1](#gcbb12419-tbl-0001){ref-type="table-wrap"}). The genotypes used were *M. sinensis*,*M. sacchariflorus*,*M. sinensis* × *M. sacchariflorus* hybrids and an *M. sacchariflorus var robustus* which were representative of those in the mixed population and mapping family. At the end of each growing season (January--Marc... | 3,431 | 344 | 2,858 | 3,474 | 2,093 | 0.78283 | github_plus_top10pct_by_avg |
@derrida1986random; @keeling2005networks]. Therefore, $\psi$ is estimated as the rate of $N i (k-2)$ to the number of all edges $N k$ in the thermodynamic limit. That is, $\psi=i (k-2)/k$. Below, we focus on the case $k=3$.
Let $P(s,i,t)$ be the probability density of $s(t)=s$ and $i(t)=i$. Then, $P(s,i,t)$ obeys the ... | 3,432 | 5,022 | 1,163 | 2,894 | null | null | github_plus_top10pct_by_avg |
ne is denoted by ${\cal L}_i$ where we have separated a constant vacuum energy contribution, $V_{i}$. The following equations result from varying the action in Eqn.(2) with respect to the metric, \[1,2,3\]: $$\begin{aligned}
\frac{1}{f^2}\left[ (\frac{\dot{v}}{v})^2 \right] - \frac{1}{f^2}
\left[\frac{f''}{f} + (\frac{... | 3,433 | 4,740 | 2,612 | 2,809 | null | null | github_plus_top10pct_by_avg |
$ the random variable parameterized by $\alpha$. The expected value $$E(Y)=\int p(\alpha) P_{bind}^{\cal{B}}(m,\alpha)[1-P_{bind}^{\cal{A}}(m,\alpha)]{\mathbf d\alpha} %\equiv \bar{P}_{ch}(m)$$ is nothing but the [*expected probability to cheat*]{} $\bar{P}_{ch}(m)$ (note that due to $P^{\cal{B}}_{bind}(m, \alpha) \app... | 3,434 | 1,403 | 3,520 | 3,278 | 3,760 | 0.770271 | github_plus_top10pct_by_avg |
e outcome of the sample splitting. The claimed results follows almost directly from , with few additional technicalities. The first difficulty is that the least squares estimator is not always well-defined under the bootstrap measure, which is the probability distribution of $n$ uniform draws with replacement from $\ma... | 3,435 | 3,106 | 3,431 | 3,095 | null | null | github_plus_top10pct_by_avg |
ameters increases exponentially with $k$ which may result in overfitting [@murphy] since we can always produce better fits to the data with more model parameters.]{}]{} To demonstrate this behavior, we produced a random navigational dataset by randomly (uniformly) picking a next click state out of a list of arbitrary s... | 3,436 | 5,557 | 3,108 | 2,793 | null | null | github_plus_top10pct_by_avg |
barrier are characterized by the formation of quasiregular mound structures differently from those obtained using the original model that exhibits irregular structures within the intervals of size and time we investigated. These plots also show a coarsening of the mounds represented by the first minimum displacement a... | 3,437 | 401 | 2,446 | 3,266 | null | null | github_plus_top10pct_by_avg |
Assume moreover that there exist a constant $c>0$ and $s\in[0,1]$ such that for $u\in C_c^\infty({\mathbb{R}}^d)$ $$\label{additional AS Svhrödinger example}\int_{{\mathbb{R}}^d}m_1(\xi)|u(\xi)|^2 {\mathrm{d}}\xi\leq c\|u\|_{H^s({\mathbb{R}}^d)}.$$Consider the non-autonomous Cauchy problem $$\label{Schroedinger operato... | 3,438 | 2,350 | 1,918 | 3,207 | null | null | github_plus_top10pct_by_avg |
**vol. 11 (1), (2009), 17-33. preprint: arXiv:0711.0540**
K. Gruher and P. Salvatore, *Generalized string topology operations* Proc. Lond. Math. Soc. (3) **96 (2008), 78Ð106.**
J.A. Lind, *Bundles of spectra and Algebraic $K$-theory*, preprint arXiv:1304567
J. P. May and J. Sigurdsson, [Parametrized homotopy theory... | 3,439 | 1,938 | 1,289 | 2,340 | null | null | github_plus_top10pct_by_avg |
unctions of $x$, be the maximum integer no greater than $x$ and the minimum integer no less than $x$, respectively. Let $\floor{\w}_\ell$ and $\ceil{\w}_\ell$ be the vectors generated from $\w$ by applying the corresponding operation on the $\ell$-th element only. $\0$ denotes an all-zero vector, and $\I$ denotes an id... | 3,440 | 1,155 | 2,057 | 3,340 | 1,390 | 0.79019 | github_plus_top10pct_by_avg |
t: $$\begin{aligned}
m & \leq & \frac {tr A} {\sum_{i \neq j} |A_{ij}|} =
\frac {n(1+\alpha)}
{\delta n^2 (\beta - \alpha) + ((1-\delta) n^2 - n) \alpha} \\
& = &
\frac {n+ \frac {\delta n} {\lambda_2} - 1}
{\delta n (\frac {n+\delta n} {\lambda_2} - 1) + ((1-\delta) n - 1)
(\frac {\delta n} {\lambda_2} - 1)}
<
4 \fra... | 3,441 | 2,971 | 3,113 | 3,012 | 3,820 | 0.769896 | github_plus_top10pct_by_avg |
= \!{(i\eta)}^{\!\!^m}\!\! \sqrt{\!\!\tfrac{ n!}{(m+n)!} } \,
\text{e}^{-\frac{\eta}{2}^{\!2}} L_{n}^{m}\!\left(\eta^{2}\right), \end{aligned}$$ where we used Eq. (\[Omegme\]). With the above two partition functions, we can calculate $\mathcal L$ in Eq. (\[nlfinal\]). Before the presentat... | 3,442 | 1,486 | 2,851 | 3,327 | null | null | github_plus_top10pct_by_avg |
{\partial\ln \rho_{e}^{(0)\alpha\alpha'} }{\partial P}
&=&-\beta P\delta_{\alpha\alpha'}\;.\end{aligned}$$ Equations (\[eq:c\]) and (\[eq:cstar\]) become $$\begin{aligned}
\frac{d}{dt}{\psi}_{\alpha}(X,t)
&=&
-iE_{\alpha}\psi_{\alpha}(X,t)\nonumber\\
&-&\sum_{\beta}P\cdot d_{\alpha\beta}
\left(1-\frac{\beta}{2}E_{\alph... | 3,443 | 1,017 | 958 | 3,718 | null | null | github_plus_top10pct_by_avg |
rder and a right I-order in $Q$, we say that $S$ is an *I-order* in $Q$ and $Q$ is a semigroup of *I-quotients* of $S$. It is clear that, if $S$ a left order in an inverse semigroup $Q$, then it is certainly a left I-order in $Q$; however, the converse is not true (see for example [@GG] Example 2.2).
A left I-order in... | 3,444 | 881 | 2,743 | 3,073 | 3,339 | 0.773007 | github_plus_top10pct_by_avg |
hat acts nontrivially on the base, acts nontrivially on a rank 8 bundle, that subgroup of the gauge group is locally duplicating the effect of one of the ten-dimensional left-moving GSO projections. If one starts with a Spin$(32)/{\mathbb Z}_2$ string, then the dual looks locally like an $E_8 \times E_8$ string.
In th... | 3,445 | 2,002 | 2,975 | 3,229 | null | null | github_plus_top10pct_by_avg |
]; we leave it to the reader to write down these conditions precisely. Thus $T$ has a trace-like property with respect to the product in ${{\mathcal C}}$, and this motivates our terminology.
Recall now that ${{\mathcal C}}$ is a $k$-linear abelian category. To define Hochschild homology, we have to assume that it is e... | 3,446 | 2,747 | 2,092 | 3,239 | 1,707 | 0.786589 | github_plus_top10pct_by_avg |
6 24.66 40 penicillin-binding protein 3
\* 2648343 A:5 C:192 C:37 ... | 3,447 | 6,129 | 1,183 | 2,222 | null | null | github_plus_top10pct_by_avg |
k=0}^{\infty} \frac {(-y)^k D_{\mathbf{v}}^k}{k!} \right) h({\mathbf{x}})= (1-yD_{{\mathbf{v}}})h({\mathbf{x}}),$$ from which the lemma follows.
Note that $({\mathbf{v}}_1,\ldots,{\mathbf{v}}_m) \mapsto h[{\mathbf{v}}_1,\ldots,{\mathbf{v}}_m]$ is affine linear in each coordinate, i.e., for all $p \in {\mathbb{R}}$ and... | 3,448 | 2,435 | 2,488 | 3,094 | null | null | github_plus_top10pct_by_avg |
tioned on the rank breaking due to previous separators $\{G_{j,a'}\}_{a'<a}$ that are ranked higher (i.e. $a'<a$), which follows from the next lemma.
\[lem:consistency\] For a position-$p$ rank breaking graph $G_p$, defined over a set of items $S$, where $p \in [|S|-1]$, $$\begin{aligned}
\label{eq:grad_eq6}
\P\B... | 3,449 | 2,747 | 2,652 | 2,983 | null | null | github_plus_top10pct_by_avg |
m by defining a new unknowns $v_j$, for $j=2,3$, by setting v\_j(x,,):=S\_j(R\_j\^[-1]{}())u\_j(x,,R\_j\^[-1]{}()), i.e. v\_j(x,,R\_j(E))=S\_j(E)u\_j(x,,E). Then we find that =R\_j’(E)=[1]{} =[1]{}, and so, after writing $$\begin{aligned}
{2}
\tilde{f}_j(x,\omega,\eta):=S_j(R_j^{-1}(\eta))f_j(x,\omega,R_j^{-1}(\eta)),
... | 3,450 | 1,482 | 893 | 3,591 | null | null | github_plus_top10pct_by_avg |
2}\nu\nu_{0}}{4}X(-\nu)\nonumber \\
\int_{0}^{1}W(\mu)\phi(\mu,\nu^{\prime})\phi(\mu,-\nu)d\mu & = & \frac{c\nu^{\prime}}{2}(\nu_{0}+\nu)\phi(\nu^{\prime},-\nu)X(-\nu)\nonumber \end{aligned}$$
where the half-range weight function $W(\mu)$ is defined as
$$W(\mu)=\frac{c\mu}{2(1-c)(\nu_{0}+\mu)X(-\mu)}\label{Eqn: W(mu)... | 3,451 | 3,190 | 3,144 | 3,155 | null | null | github_plus_top10pct_by_avg |
y regular function. The fractional Dirichlet problem and variants thereof appear in many applications, in particular in physical settings where anomalous dynamics occur and where the spread of mass grows faster than linearly in time. Examples include turbulent fluids, contaminant transport in fractured rocks, chaotic d... | 3,452 | 2,109 | 1,862 | 3,273 | null | null | github_plus_top10pct_by_avg |
ce given by the postulated gravitational dual background constructed in [@Frolov:2005dj]. Upon setting all three deformation parameters equal this reduces to the $\beta$-deformation with enhanced ${\cal N}=1$ supersymmetry and hence we will proceed with the general case.
Rather remarkably the string $\sigma$-model in ... | 3,453 | 2,251 | 1,540 | 3,296 | 2,193 | 0.781894 | github_plus_top10pct_by_avg |
effective mass plots of the two-point correlators and the extracted mass $E_1^-$ of the negative-parity state cannot be reliable. Leaving aside these failures, we try to extract $g_A^{0-}$. The result is added in the lower panel in Fig. \[AxialVectorC\] as a faint-colored symbol, which is consistent with those obtaine... | 3,454 | 1,502 | 3,620 | 3,342 | null | null | github_plus_top10pct_by_avg |
l heterotic string spectra. It is possible to apply the same methods to the A/2 model to formulate a mathematical theory of sheaf cohomology of orbifolds, and this has been done in [@manion-toappear].
Briefly, the A/2 model is a heterotic analogue of the A model topological field theory. If $X$ is a smooth space and $... | 3,455 | 2,602 | 2,858 | 3,156 | 1,190 | 0.792924 | github_plus_top10pct_by_avg |
esearch interests include statistics, machine learning, and computer vision.
[Song-Chun Zhu]{} Song-Chun Zhu received a Ph.D. degree from Harvard University, and is a professor with the Department of Statistics and the Department of Computer Science at UCLA. His research interests include computer vision, statistical ... | 3,456 | 940 | 3,187 | 3,187 | 1,202 | 0.79281 | github_plus_top10pct_by_avg |
the difference in the method of bounding diagrams for the expansion coefficients. Take the $0^\text{th}$-expansion coefficient for example. For percolation, the BK inequality simply tells us that $$\begin{aligned}
{\label{eq:pi0perc-comp}}
\pi_p^{{\scriptscriptstyle}(0)}(x)\leq{{\mathbb P}}_p(o{\underset{\raisebox{5pt... | 3,457 | 1,474 | 1,997 | 3,281 | 2,220 | 0.781754 | github_plus_top10pct_by_avg |
ere $\rm{diam}_D(H_n):=\sup_{g,h\in H_n} D(g,h)=\sup_{g\in H_n} D(g,1)$.
Suppose on the contrary that there exist $\varepsilon>0$ and a sequence $(h_n)_n\subseteq G$ such that $h_n\in H_n$ and $D(h_n,1)\geq \varepsilon$. Since $G$ is compact, the sequence without loss of generality converges to some $h\in G$. By the c... | 3,458 | 2,413 | 2,322 | 3,108 | null | null | github_plus_top10pct_by_avg |
ere the orbital occupancy can be 0, 1 or 2, a core set where the orbitals are doubly occupied and a virtual set of empty orbitals then the total Hamilton, $\hat{H}$ and Fink’s Hamiltonian, $\hat{H}_{0}$ can be expressed in second quantization as,
$$\hat{H}=\sum_{ij}t_{ij}a_{i}^{\dagger}a_{j}+\sum_{ijkl}\Braket{ij|kl}a... | 3,459 | 2,797 | 2,973 | 3,200 | null | null | github_plus_top10pct_by_avg |
$HH_0(A,M)$); therefore the map $\rho_0$ extends to a map $\rho_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}:H_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}(\Delta^{opp},M^\Delta_\#) \to HH_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}(A,M)$. To prove that $\rho_{{\:\raisebox{3pt}{\text{\circle*{1.5}}}}}$ is an isomorphism for... | 3,460 | 2,744 | 2,491 | 2,926 | 2,715 | 0.777624 | github_plus_top10pct_by_avg |
rgin}{-69pt}
\begin{document}$$\begin{aligned} \varepsilon _{\pm }({\vec {k}}) =-2t_2\alpha _1({\vec {k}})\cos \phi \pm \sqrt{m({\vec {k}})^{2} + t_1^{2}|\Omega ({\vec {k}})|^{2}}\;. \end{aligned}$$\end{document}$$The size of the bands can be bounded by $\documentclass[12pt]{minimal}
\us... | 3,461 | 3,318 | 258 | 3,550 | 1,568 | 0.788181 | github_plus_top10pct_by_avg |
} x } } \\
\end{array}
\right].
\label{exp-H0}\end{aligned}$$ Then, the perturbed Hamiltonian is given by $$\begin{aligned}
\hat{H}_{1} &=& {\bf X}^{\dagger} \tilde{H}_{1} {\bf X}
=
\left[
\begin{array}{cc}
0 & (UX)^{\dagger} A W \\
W^{\dagger} A (UX) & W^{\dagger} A W \\
\end{array}
\right].
\label{hat-H1}\end{al... | 3,462 | 2,307 | 3,188 | 3,268 | 3,678 | 0.770761 | github_plus_top10pct_by_avg |
11–143.
A. Sakai. Asymptotic behavior of the critical two-point function for spread-out Ising ferromagnets above four dimensions. *Unpublished manuscript* (2005).
A. Sakai. Diagrammatic estimates of the lace-expansion coefficients for finite-range Ising ferromagnets. *Unpublished notes* (2006).
B. Simon. Correlation... | 3,463 | 1,700 | 2,197 | 2,794 | 2,885 | 0.776318 | github_plus_top10pct_by_avg |
NONSYN T:6 G:140 G:37 `aaacctaacacg`
`attattgaacat` sulfatase f... | 3,464 | 637 | 3,484 | 3,369 | null | null | github_plus_top10pct_by_avg |
1}=\textrm{IT}\{ g;\mathcal{V}\}$.$\qquad\square$
As we need the second part of these theorems in our applications, their proofs are indicated below. The special significance of the first parts is that they ensure the converse of the usual result that the composition of two continuous functions is continuous, namely t... | 3,465 | 3,491 | 3,320 | 3,204 | null | null | github_plus_top10pct_by_avg |
nchrotron radiation. The anti-DID impacts also the hit rate on the VXD due to beamstrahlung electrons, by reducing the number of backscattered electrons travelling backwards from further along the beam line.
[r]{}[0.5]{}
{width="0.5\columnwidth"}
The anti-DID reduces by roughly 30% the number of ... | 3,466 | 1,181 | 2,960 | 3,748 | 2,080 | 0.782957 | github_plus_top10pct_by_avg |
an inverted parabolic barrier with the cross-section given by: $$\sigma = \frac{R_C^2}{2E}\hbar\omega \cdot ln \left \{ 1+exp\left [\frac{2\pi}{\hbar\omega}(E-V_C)\right] \right \}$$ where E is the incident energy, V$_C$ is the barrier height, R$_C$ is the radius of interaction and $\hbar$$\omega$ is the barrier curva... | 3,467 | 3,676 | 4,075 | 3,372 | null | null | github_plus_top10pct_by_avg |
parental genotypes [@pone.0025810-Aleza1]. As triploid hybrids are sterile [@pone.0025810-Cameron1], only some of the diploid genotypes that are known to be cross-fertile with clementine mandarin were considered PPDs. Plot B was composed of a population of 477 hybrids belonging to a rootstock breeding program. These hy... | 3,468 | 6,141 | 2,418 | 2,474 | null | null | github_plus_top10pct_by_avg |
hadowing effect.
For the inner anisotropy factor $f_{\mathrm{disc}}$, we simply assume $$\begin{aligned}
f_{\mathrm{disc}}(\theta)\propto\sin\theta\,,
\label{eq:11} \end{aligned}$$ which corresponds to radiation from an infinitely thin disc (recall that we define $\theta$ as the angle from the equatorial plane). Altho... | 3,469 | 3,444 | 3,598 | 3,362 | null | null | github_plus_top10pct_by_avg |
ult}_{E_{P,i}} \sigma^*\omega_P$.
An $n$-th cyclic covering ramified along $\cC$ induces an $n$-th cyclic cover ramified along the divisor $\sigma^*\cC$ in $Y$ . One can define the line bundles $\mathcal{L}^{(k)}=\cO_Y(L^{(k)})$ as in , where $H$ is the pull-back in $Y$ of a projective line. The announced description ... | 3,470 | 3,242 | 1,034 | 3,391 | null | null | github_plus_top10pct_by_avg |
}\hbar\nabla_{\mathbf{r}}+\frac{e}{c}\vec{A}_{\mathbf{R}}(t)\right)\psi_{i,\mathbf{R}}(\vec{r},t) \nonumber \\
&& -\psi_{i,\mathbf{R}}(\vec{r},t)\left(-\mathrm{i}\hbar\nabla_{\mathbf{r}}-\frac{e}{c}\vec{A}_{\mathbf{R}}(t)\right)\psi_{i,\mathbf{R}}^{\ast}(\vec{r},t)\biggr\}.\end{aligned}$$ This microscopic current is av... | 3,471 | 2,216 | 3,036 | 3,439 | null | null | github_plus_top10pct_by_avg |
ective sample size is approximately $n_1\ell_1$, i.e. pairwise comparisons coming from small set size do not contribute without proper normalization. This gap in MSE corroborates bounds of Theorem \[thm:main\]. Normalization constant $C$ is $10^{3}/d^2$.
The Role of the Topology of the Data {#sec:role}
===============... | 3,472 | 1,703 | 1,187 | 3,461 | null | null | github_plus_top10pct_by_avg |
a group and $\sigma \in {{\rm Aut}\,}(H)$ an automorphism of $H$. We define the category $\mathcal{C}(H, \sigma)$ as follows: an object of $\mathcal{C}(H, \sigma)$ is a triple $(G, \alpha,
\beta)$ such that $(H, G, \alpha, \beta)$ is a matched pair of groups. A morphism $\psi : (G', \alpha', \beta') \rightarrow (G,
\al... | 3,473 | 2,169 | 2,558 | 3,107 | null | null | github_plus_top10pct_by_avg |
imates are more relaxed but sufficient for giving another robust argument in proving the instability, in particular not by contradiction. In another related paper, we are able to prove instability theorems of the spherical symmetric naked singularities under certain isotropic gravitational perturbations without symmetr... | 3,474 | 1,633 | 1,275 | 3,509 | null | null | github_plus_top10pct_by_avg |
or $$\begin{aligned}
D_0(k,\omega)=\bigg[\omega-\frac{k^2}{4m}+2\mu-\nu+i0^+\bigg]^{-1}
\label{D0}\end{aligned}$$ and the “polarization”, i.e., self-energy of the closed channel propagator, $\Pi(k,\omega)$ is given by: $$\begin{aligned}
\Pi(k,\omega)=g^2 \int \frac{dk'}{2\pi}
\Big[\omega-k'^2/m-k^2/4m+2\mu+i0^+\Big]^{-... | 3,475 | 1,001 | 2,042 | 3,470 | null | null | github_plus_top10pct_by_avg |
SC Customer Care 713-345-4727
The Portland Web Server will be going down for 20 min at 1:45 instead of
12:00 noon.
Regards,
Paul
Great - no changes
-----Original Message-----
From: Shah, Kal
Sent: Wednesday, February 06, 2002 4:14 PM
To: Kitchen, Louise
Subject: RE: Direct Mail Pack Letter
I've redrafted it.... | 3,476 | 773 | 3,421 | 3,055 | null | null | github_plus_top10pct_by_avg |
\sigma = 1$) and Tikhonov (using $\sigma = 0.2$) covariance functions, respectively. (d) & (e) reconstructions using CV with Laplacian and Tikhonov covariance functions, respectively []{data-label="fig:Parameter Choice Methods"}](LcurveChestLaplacian_sigman1 "fig:"){width="6.3cm"}]{} (306,138)[![(a) A ground truth of 2... | 3,477 | 894 | 2,795 | 2,930 | 425 | 0.810128 | github_plus_top10pct_by_avg |
---------------------------------
RR flux & IIB & IIA\
------------------------------------------------------------------------
$-m$ & $F_{x^1 x^2 x^3}$ & ${F}$\
------------------------------------------------------------------------
$-q_i$ & $F_{y^i x^j x^k}$ & $F_{x^i y^i}$\
-----------------------------------... | 3,478 | 2,174 | 2,215 | 3,231 | null | null | github_plus_top10pct_by_avg |
ta_{24} = 0.01$, and $\sin^2\theta_{34} = 0.1$ for $\Delta m^2_{41} = 0.1$ eV$^2$, and set all the CP phases to zero. Then, we cut out the $3\times3$ active neutrino mixing matrix, which is non-unitary.[^18] For the Standard Model mixing parameters in $U_{\text{\tiny PDG}}$, we take $\sin^2\theta_{12} = 0.3$, $\sin^2\t... | 3,479 | 1,370 | 3,393 | 3,688 | 785 | 0.800043 | github_plus_top10pct_by_avg |
rating $d\tau_{xz}/dz$ across the interface gives $$S = -\lim\limits_{\epsilon \to 0} \int \limits_{1-\epsilon}^{1+\epsilon}dz\langle v_{1x}v_{1z} \rangle = -\lim\limits_{\epsilon \to 0} \int \limits_{1-\epsilon}^{1+\epsilon}dz\frac{d}{dz}\langle \frac{d\Phi}{dz}\frac{\partial \Phi}{\partial x}\rangle$$ where $\langle ... | 3,480 | 2,430 | 3,605 | 3,181 | null | null | github_plus_top10pct_by_avg |
uad 1\leq j\leq n.$$
We claim that $c_{ji}=0$ for $i<j$ and that $|c_{ji}|>0$ whenever $i>j$ (and $c_{ji}\not=0$). Since $|u_i|\leq |u_{i+1}|$, we have $|a_i|\geq |a_{i+1}|$ for each $i$. Also $|c_{ji}|=|u_i|-|u_j|$ for all $i,j$ and so $c_{ji}=0$ if $|u_i|<|u_j|$. Thus both parts of the claim are clear when $|u_i|\no... | 3,481 | 2,789 | 2,857 | 3,085 | 2,986 | 0.775607 | github_plus_top10pct_by_avg |
3.2.1.8}$$ One can see, that two components $\chi_{l=0}^{(\pm)}(k,r)$ in (\[eq.3.2.1.2\]) represent convergent and divergent waves, that can be useful for analysis of propagation of the particle in the field $V_{2}(r)$. Thus, we have found an *exact analytical division of the total radial wave function into its converg... | 3,482 | 4,052 | 3,616 | 3,221 | null | null | github_plus_top10pct_by_avg |
psi}\gamma^\mu\partial^\nu\psi\,-\,
\partial^\nu\overline{\psi}\gamma^\mu\psi\right]\ ,$$ while fermion normal ordering is implicit of course. It then follows that the 1-particle states obtained by acting with the creation operators $b^\dagger(\vec{k},s)$ and $d^\dagger(\vec{k},s)$ on the Fock vacuum $|0\rangle$ are en... | 3,483 | 2,436 | 3,026 | 3,218 | null | null | github_plus_top10pct_by_avg |
o [(\[eq:IR-xbdNN\])]{} and the diagrammatic bound [(\[eq:piNbd\])]{}. It thus remains to show [(\[eq:pi-kbd\])]{} for $\pi_\Lambda^{{\scriptscriptstyle}(j)}(x)$ with $x\ne o$ and $j\ge1$.
The idea of the proof is somewhat similar to that of Proposition \[prp:exp-bootstrap\](iii) explained above. First, we take $|a_m|... | 3,484 | 1,930 | 3,357 | 3,263 | 1,015 | 0.795624 | github_plus_top10pct_by_avg |
{P}_2]= - \mathfrak{P}_3$, but since $[\mathfrak{M}_{23}, \mathfrak{P}_1]= [\mathfrak{P}_{2}, \mathfrak{P}_3]=0$ it is unimodular. In [@Borsato:2016ose] it was shown that the corresponding deformation is nevertheless equivalent to two non-commuting TsT transformations, with a non-linear coordinate redefinition in betwe... | 3,485 | 2,232 | 2,628 | 3,065 | null | null | github_plus_top10pct_by_avg |
imal stimulus and the average MUTF provides a count estimate. However, there is no guarantee that a particular single-stepped increase in response corresponds to a new, previously latent, MU, since it may instead be due to a phenomenon called alternation [@Bro76]. This occurs when two or more MUs have similar activatio... | 3,486 | 3,808 | 3,949 | 3,294 | null | null | github_plus_top10pct_by_avg |
|x\|$. For notational convenience, we drop the dependence on $\psi$, since all our bounds hold uniformly over all $\psi \in \mathcal{S}_n$. The first bound in on the norm of the gradient of $g_j$ is straightforward: $$\begin{aligned}
\nonumber
||G_j|| & \leq ||e_j|| \times \sigma_1\left( \left[ - \left( \alpha^\top \... | 3,487 | 2,372 | 2,673 | 3,115 | null | null | github_plus_top10pct_by_avg |
*4 - 7*b**2 + 3 wrt b?
-17928*b
Find the first derivative of -26*l*x**4 - 5072*l - 4*x**2 - x wrt x.
-104*l*x**3 - 8*x - 1
What is the third derivative of l*n**2*x**3 + 3*l*n**2 + l*n - 34*l*x**3 + 4*l*x**2 + 2 wrt x?
6*l*n**2 - 204*l
Find the third derivative of a**2*q**3*s**2 + 160*a**2*q**2*s**2 + 3*a**2*s - 540*a*q... | 3,488 | 1,644 | 1,583 | 3,071 | null | null | github_plus_top10pct_by_avg |
n for dotted spinors, the convention is that the contraction is taken from bottom-left to top-right, namely $$\begin{array}{r c l}
\overline{\psi}\,\overline{\chi}&=&
\overline{\psi}_{\dot{\alpha}}\,\overline{\chi}^{\dot{\alpha}}=
\epsilon_{\dot{\alpha}\dot{\beta}}\,\overline{\psi}^{\dot{\beta}}\,
\overline{\chi}^{\dot... | 3,489 | 1,746 | 1,645 | 3,297 | null | null | github_plus_top10pct_by_avg |
e denote $\theta_0(\eta) := \theta(\eta,0) = u(x,0)$.
\[lem:finite\_p\_bounded\] For all $\overline{q} \leq p < \infty$, there exists $C_{\overline{q}} = C_{\overline{q}}(p,M)$ and $C_M = C_M(p,{\|\theta_0\|}_{\overline{q}})$ such that if ${\|\theta_0\|}_{\overline{q}} < C_{\overline{q}}$ and $M < C_M$, then ${\|\thet... | 3,490 | 2,442 | 1,061 | 3,336 | null | null | github_plus_top10pct_by_avg |
20.7 51.7 Hysterectomy at 14 months Multiple myomas ranging from 0.6 to 3.4 cm; focal adenomyosis
1 Intramural 1.8 ... | 3,491 | 3,889 | 2,925 | 3,267 | null | null | github_plus_top10pct_by_avg |
ing that such an $M$ is ‘close’ to a $\GF(q)$-representable matroid.'
address: 'Department of Combinatorics and Optimization, University of Waterloo, Canada'
author:
- Jim Geelen
- Peter Nelson
title: The Structure of Matroids with a Spanning Clique or Projective Geometry
---
[^1]
Introduction
============
In \[\[hi... | 3,492 | 2,088 | 1,524 | 3,145 | null | null | github_plus_top10pct_by_avg |
}{ ( \Delta_{J} - \Delta_{I} ) } -
\frac{e^{- i h_{k} x} - e^{- i \Delta_{I} x} }{ ( h_{k} - \Delta_{I} ) }
\right]
\left\{ W^{\dagger} A (UX) \right\}_{I k}
\frac{ 1 }{ \Delta_{J} - h_{k} }
\left\{ (UX)^{\dagger} A W \right\}_{k J}
\nonumber \\
&+&
\left[ (ix) e^{- i \Delta_{I} x} +
\frac{e^{- i \Delta_{J} x} ... | 3,493 | 1,533 | 2,951 | 3,135 | null | null | github_plus_top10pct_by_avg |
s and complexity in all likely and unlikely places, and possibly because of it, it is necessary that we have a clear mathematically-physical understanding of these notions that are supposedly reshaping our view of nature. This paper is an attempt to contribute to this goal. To make this account essentially self-contain... | 3,494 | 4,719 | 3,956 | 3,242 | 3,934 | 0.769188 | github_plus_top10pct_by_avg |
otential overfitting), they are always a better fit for the data [@murphy].]{}]{} Thus, higher order models are naturally favored by their improvements in likelihoods. A more comprehensive view on this issue shows that there exists a broad range of established model comparison techniques that also take into the account... | 3,495 | 4,982 | 2,275 | 3,066 | 923 | 0.797575 | github_plus_top10pct_by_avg |
f the whole unseen testing set during the competition, while the accuracy score of predictions over the private subset was kept inaccessible for even testing until the end of the competition. Upon the end of the competition, the default ML frameworks proposed by the teams were tested over the entire testing set. Adopti... | 3,496 | 1,836 | 2,226 | 2,882 | null | null | github_plus_top10pct_by_avg |
on of the operators $b_\nu$. We therefore need to analyze our theory in this respect. Specifically, we show in this section that the total current STS spectra calculated in our theory do not depend on the choice of the basis for the operators $b_\nu$. Interestingly, however, this choice of basis does determine the part... | 3,497 | 4,180 | 2,850 | 3,181 | null | null | github_plus_top10pct_by_avg |
equency range, see Fig. \[fig:02\]. The solid lines show the experimental results, derived from the Fourier transform of the measured $S_{aa}(\nu)$ and $S^{\prime}_{aa}(\nu)$ via relation (\[eq:f\_ab\]) for the situations (a) 50$\Omega$ load (black), (b) open-end reflection (green, dark gray) and (c) hard-wall reflecti... | 3,498 | 480 | 2,303 | 3,392 | 805 | 0.799679 | github_plus_top10pct_by_avg |
ubsequence $(x_{i_{k}})_{k\in\mathbb{N}}$ converging to $x$, then a more direct line of reasoning proceeds as follows. Since the subsequence converges to $x$, its tail $(x_{i_{k}})_{k\geq j}$ must be in every neighbourhood $N$ of $x$. But as the number of such terms is infinite whereas $\{ i_{k}\!:k<j\}$ is only finite... | 3,499 | 1,004 | 2,392 | 3,264 | 2,399 | 0.780174 | github_plus_top10pct_by_avg |
n - 9. Let k(v) = -2*v + 2. Let b be k(7). Let p(m) = 4*m - 11. Let w be p(4). Let d(r) = 10*r**3 + 12*r - 22. Calculate b*j(x) + w*d(x).
2*x**3 - 2
Let d(m) = 21*m. Let i(u) = -2*u**3 + 3*u**2 - 5*u + 6. Let r be i(2). Let j(q) = 7*q. Calculate r*j(v) + 3*d(v).
7*v
Let o be 32/(-40) + 68/10. Let n(b) = -6*b - 1 + 0*b*... | 3,500 | 2,624 | 1,850 | 2,914 | null | null | github_plus_top10pct_by_avg |
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