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s between SSB frequencies were evaluated by using one-way ANOVA or chi-squared tests, respectively. nutrients-12-01015-t002_Table 2 ###### Associations of sugar-sweetened beverage (SSB) consumption at 11 years with body mass index (BMI) z-score and overweight from 12 to 18 years in Hong Kong's "Children of 1997" bi...
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We follow part of the proof of [@bg.sol Corollary 1.5]. It follows from [@bgt.lin Theorem 2.5] that $A$ is contained in a union of at most $K^{O_n(1)}$ left cosets of a nilpotent subgroup $N$ of $GL_n({\mathbb{C}})$ of step at most $n-1$. By \[thm:malcev\] we may assume that $N\subset{\text{\textup{Upp}}}_n({\mathbb{C}...
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directions, say respectively $-\alpha_{r}$ and $\beta_{r}$ (modulo $2\pi$) with $\alpha_{r}\geq 0$, $\beta_{r}\geq 0$. Hence, $(\alpha_{r})_{r>0}$ and $(\beta_{r})_{r>0}$ are by construction non-increasing sequences of positive real numbers (by Proposition \[prop:<2\]).\ Let us consider $D_r$ the set of directions ...
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3$ exists and, in fact, can be explicitly computed using formulas given in Example \[desolex1\] (choose $\tilde{g}=0$ in Eqs. , , ), and it is \[comp17\] & \_0\^[-1]{}h=((\_0\^[-1]{}h)\_1,(\_0\^[-1]{}h)\_2,(\_0\^[-1]{}h)\_3),\ & (\_0\^[-1]{}h)\_1(x,,E) = \_0\^[t(x,)]{}e\^[-\_0\^t\_1(x-s,,E) ds]{}h\_1(x-t,,E)dt,\ &(\_0\...
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ful shorthand term, accurate models of the ionizing continuum must consider the entire population of hot main sequence and Wolf–Rayet stars. Wolf–Rayet stars maintain high line ratio values after the O stars have left the main sequence. Our updated models may aid interpretation of IRS spectra from SIRTF. We then test ...
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leads to the following order-of-magnitude estimate for the time delay between absorption and re-emission of a photon of energy $E$: $$\delta t_{D0} \; = \; C \sqrt{\alpha'} E , \label{delayD0}$$ where $C$ is an unknown and model-dependent coefficient, and $\alpha'$ is the Regge slope of the string, which is related to...
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, the theory is expected to be a gravity theory including matter fields. After all, the gauge symmetry of general coordinate transformation is always present. In Einstein’s theory of gravity, for a fluctuation of the metric g\_ = \_ + h\_ + , one can choose the vielbein to be symmetric e\_[a]{} = \_[a]{} + h\_[a]{}/2 ...
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, \quad \alpha,\beta = 1,2 \ ,$$ where we integrate over $a_\pm$. Now taking $\lambda \to 0$ and then integrating out $a_\pm$ we find $\partial_\pm v_3 = 0$ and indeed $v_3$ is frozen to a constant value. This final step is analogous to the Buscher procedure considered in [@Hoare:2016wsk]. The true target space of the...
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[adpure\] By [@hausel-letellier-villegas Appendix B] it is enough to prove that there is a smooth morphism $f:\mathfrak{M}\rightarrow\C$ which satisfies the two following properties: \(1) There exists an action of $\C^\times$ on $\mathfrak{M}$ such that the fixed point set $\mathfrak{M}^{\C^\times}$ is complete and f...
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S}})$, $\alpha_{{\widehat{S}}}(j) = \mathbb{E}[Y X_{{\widehat{S}}}(j)]$ and $\Sigma_{{\widehat{S}}} = \mathbb{E}[X_{{\widehat{S}}} X_{{\widehat{S}}}^\top]$. We remark that the regression projection parameter depends only on the selected model ${\widehat{S}}$, and not any estimate $\hat{\mu}_{{\widehat{S}}}$ of the regr...
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mega$ and the only solution for this condition is that the three-point energy correlator is identically zero. Analogously, we can proceed to higher point functions and conclude that all of them are zero at non-coincident points This is exactly what we get in the theory of free boson. Thus, we conclude that all energy c...
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of view, based on estimates –, there is no clear indication that a very large initial enstrophy $\E_0$ (or, equivalently, a high Reynolds number) should be a necessary condition for singularity formation in finite time. In fact, blow-up cannot be a priori ruled out as soon as condition is violated, which happens for a...
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-2D system: $\Lambda \sim 1/W \gg k_F$. Likewise, in the limit $W\ll d$, we can write the interlayer interaction as [@Li_Hwang_DasSarma10]: $$v_{12}({{\mathbf q}}) =-2\pi D^2 q e^{-qd} \left[\xi(\theta,\phi) +i \sin2\theta \cos\phi \right]\; . \label{eq:inter}$$ Note that for $\theta \ne 0$, this interaction is co...
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scussions in Section 8. Enhanced Symmetries =================== In this section, we discuss the enhanced symmetries in two dimensional (2D) field theory with boost symmetry and anisotropic scalings, using the method developed in [@Polchinski:1987dy] and [@Hofman:2011zj]. Usually for a theory with global symmetries, w...
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615203 from the European Research Council under the FP7. The work of DT is supported in part by the Belgian Federal Science Policy Office through the Interuniversity Attraction Pole P7/37, and in part by the “FWO-Vlaanderen” through the project G020714N and a postdoctoral fellowship, and by the Vrije Universiteit Bruss...
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orname{gr}_\Lambda e\Delta_c(\mu)$ is independent of $\mu$. We prove one such correspondence in this paper. Let ${\mathcal{P}}$ denote the Procesi bundle on $\operatorname{Hilb(n)}$, the vector bundle of rank $n!$ coming from Haiman’s $n!$ theorem, see . Then Corollary \[cohh-subsect\] proves: Corollary {#cohh-intro}...
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$, since here the topology of $D$ needs to be specified in order to speak of continuity of maps into $D$. In fact, in [@tanabe Corollary to Theorem 4.4.2, pp. 102-103] one equips $D$ with the graph norm of $A(0)$. Recall that for $t\in [0,T]$, the graph norm of $A(t)$ on $D(A(t))$ ($=D$) is defined as ${\left\Vert v\ri...
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of the eigenvalue $0$ of $L_*$ and $L_{rw*}$ and the multiplicity of the generalized eigenvalue $0$ of $L_{sym*}$ are equal the number of connected components $C_1 , \dots, C_k $ in the graph. For $L_*$ and $L_{rw*}$, the eigenspace associated to $0$ is spanned by the indicators of connected components $\left\{ 1_{C_i...
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>k_0$, $k_0$ depending on $K$ only, and for this $\lambda$ inequality (\[tineq\]) becomes $$\sup_{f:\|f\|_\infty\le C} {\Pr}\left\{\max_{2^{k-1}<n\le 2^{k}}\sqrt{\frac{n h_{n}}{\log h_{n}^{-1}}} ||\bar{f}_n-E\bar{f}_n||_{\infty}>\lambda\right\}\le C_2\exp\left(-\frac{3C_3L^2 h_{2^k}\log h_{2^k}^{-1}}{2^5}\right),$$ whe...
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\langle \rho \rangle$ where the stochastic averaging has to be performed over two noise processes $\xi_{\rm neq}$ and $\xi_{\rm eq}$. To this end we note that $\nabla \cdot F$ can be partitioned into two parts ; a constant part $\nabla \cdot F_0$ and a fluctuating part $\nabla \cdot F_1 (t)$, containing these noises. T...
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notonically increasing for $x\in(0,4\Omega_n^2\delta_n]\subset(0,\frac{r_n}{\mathrm{e}}]$. Finally, $\frac{r-r_n}{r_n}\le c_0$ follows from $$\begin{aligned} \frac{r-r_n}{r_n}\le\frac{4\Omega_n^2\delta_n}{|u_n|}=\exp\left(-\frac{\varphi_n^2}{2^8c_1\Omega_n^4}\right)\end{aligned}$$ since the right hand side tends to zer...
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t{crux}}\rbrace}\Vert}.$$ ### Evidence {#S:EVIDENCE} We propose that the same data used earlier for indemnification testing be re-used in a slightly different statistical context. Recall that an indemnification test has $N$ items among which are zero failures, where each item is a localized predecessor walk, and a co...
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for all $n\in\mathbb{N} $. Thus, it follows by Lemma 2.1 that $\bar{A}_{n}\in \ell_{q}$ for all $n\in\mathbb{N} $ and the equality $Ax=\bar{A}y$ holds which yields that $\bar{A}y\in X$, where $y=\widehat{F}x.$ Since every $y\in \ell_{p}$ is the assocaited sequence of some $x\in \ell_{p}(\widehat{F})$, we obtain that $\...
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and there are three of them that remain after considering the previous algebraic relations : $$\begin{aligned} \int d^4x \sqrt{-g} \curv{L}_3 = -\frac{1}{12} \int d^4x \sqrt{-g} \; \curv{L}_8 \quad \quad \text{;} \quad \int d^4x \sqrt{-g} \curv{L}_1 = - \int d^4x \sqrt{-g} \; \curv{L}_8 \end{aligned}$$ $$\be...
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\left( (g A_0^3 (\vec x)) \prod_{n=1}^{n = \infty} \left((2 \pi T n)^2 - (g A_0^3 (\vec x))^2\right) \right)^2\,. \label{eq:FPdet1}$$ Multiplying the determinant with a further constant normalisation $$\begin{aligned} \mathcal{N} = \left( \prod_{n=1}^{n = \infty} (2 \pi T n)^2 \right)^{-2}\,,\end{...
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=================== The KK bubbles considered above sample an infinite distance in moduli space. We can also consider charged dilatonic black hole spacetimes in which the dilaton excursion is finite but can be made arbitrarily large [@Garfinkle:1990qj]. The electrically charged solutions of [@Garfinkle:1990qj] are gi...
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426/8362 (5.1%) Walther et al. \[[@CIT0068]\] 2019 USA Patient...
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{E\in \mathcal{E}\mid S\in \mathcal{S}_{E}\}$. $\mathcal{E}_{S}^{\bot }=\{E\in \mathcal{E}\mid \varphi (S)\subset \chi (E)^{\bot }\}=\{E\in \mathcal{E}\mid S\in \mathcal{S}_{E}^{\bot }\}$. It can also be proved that $\mathcal{E}_{S}$ ($\mathcal{E}_{S}^{\bot }$) coincides with the set of all properties that have prob...
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pha/\pi$ that lead to what is usually called the radiative correction to the nuclear weak charge. Account of this very important correction gives the nuclear weak charge $Q_{W}$ measured in on-mass-shell electron scattering at zero momentum transfer, where $p^2=m^2$ and $q=0$. However, atomic PNC corresponds to a diffe...
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nce $\dim H^0(Y,\mathcal{L}^{(k)})=0$. Using Serre duality Theorem, we obtain that $$\dim H^2(Y,\mathcal{L}^{(k)})= \dim H^0\left(Y,\omega_Y\otimes{\mathcal{L}^{(k)}}^{-1}\right).$$ The inclusion of $H^0\left(Y,\omega_Y\otimes{\mathcal{L}^{(k)}}^{-1}\right)$ in $H^0(\PP^2,\mathcal{O}_{\PP^2}(k-3))$ can be understood a...
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^R_M({\mathcal{E}})$: $$\Omega^\infty (End^R(\vee_n R)) \to \Omega^\infty_M End^R_M({\mathcal{E}}) \to M.$$ By restricting to path components of those $R$-module endomorphisms that consist of equivalences, we get a subbundle, which we will call $ {\mathcal{G}}L_n({\mathcal{E}})$: $$GL_n(R) \to {\mathcal{G}}L_n({\ma...
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dE’ which is the hyper-singular integral form of $K_{22}$. Applying Lemma \[hadale\] we see that \[k22-a\] & [H]{}\_2((\_[22,2]{})(x,,,E))(E)\ =& ( \_[E]{}\^[E\_m]{}[[(\_[22,2]{})(x,,E’,E)]{}]{}dE’) - \_[E]{}\^[E\_m]{}[1]{}[E]{}(x,,E’,E)dE’\ & +( (\_[22,2]{})(x,,E’,E))\_[|E’=E]{}\ =& ( [H]{}\_1((\_[22,2]{})(x,,,E))(E)...
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n the inverse map generates the fluid motion itself. Elimination theorem ------------------- Eliminating the canonically conjugate variables $(\MM{l}, \MM{\pi})$ produces an equation of motion for $\MM{m}=\delta{\ell}/\delta\MM{u}$, which is constructed in the proof of the following theorem: The labels $\MM{l}$ and ...
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on $\pi_t(K)$ as $d$ is increased, shown in Fig. \[fig2\]. The large-$s$ phase has $k_s=0$ where, for these inactive rare trajectories, the exciton does not jump between eigenstates. Therefore, the exciton must remain localised. This result we confirm in Fig. \[fig3\](d), where we see that the $s$-biased steady-state o...
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pi$. So two subgroups are conjugate in $G$ if and only if they have the same order. \[ordre\] Let $\mathcal{P}$ be the set of divisors of $|G|$. Let us consider the following order on this set: let $p_1,p_2,\cdots, p_n$ be the prime divisors of $|G|$ such that $p_1 < p_2<\cdots <p_n$. Then $p_1<p_2<\cdots< p_n<p_1p_2<...
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of parameters found in the literature. The result is shown in Fig. \[fig4L4\] where the parameters were deliberately chosen as to imply $\Phi_n^m < 0$ in some of the examples, making Eq. (\[limZ-T2\]) invalid and causing the NL to diverge as $\beta \to \infty$. Although the parameters used to produce Fig.\[fig4L4\] ar...
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nom{i-1}{i}.$ Given $d$ and $N$ the integers $s_i$ exist and are unique. The Macaulay representation is among other things used for the study of Hilbert functions of graded modules, see for example [@green]. It is well known (see for example [@green]) that if $N$ and $M$ are two nonnegative integers with Macaulay repre...
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ncreasingly super-Poissonian temporal distribution for the jumps between lattice sites as disorder is increased. Remarkably, this dynamical behaviour exists even at infinite temperature. ![(Colour online.) Excitonic occupation of regions of an $N = n\times n$ disordered lattice, with $N=10^4$ sites, coupled to an infi...
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re $\varphi\equiv\{\varphi_x\}_{x\in\Lambda}$ is a spin configuration, $\{J_{x,y}\}_{x,y\in{{\mathbb Z}^d}}$ is a collection of spin-spin couplings, and $h\in{{\mathbb R}}$ represents the strength of an external magnetic field uniformly imposed on $\Lambda$. We say that the model is ferromagnetic if $J_{x,y}\ge0$ for a...
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-3)**2 + ((sqrt(5) - (-1 + sqrt(5))*-2) + 0)**2)*-6. -48294 + 72*sqrt(5) Simplify -5*((sqrt(304) - (0 + sqrt(304) + 3 - sqrt(304)) - sqrt(304))**2 + -4 - ((sqrt(304) - (2*-1*sqrt(304) - sqrt(304))) + (sqrt(304) + 1)*-5)**2). 200*sqrt(19) + 1620 Simplify 3*(1*-3*sqrt(396) + (sqrt(396) + 0)*2). -18*sqrt(11) Simplify sqrt...
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20).](jof-03-00020-g002){#jof-03-00020-f002} jof-03-00020-t001_Table 1 ###### In vitro antifungal activities of efinaconazole and itraconazole against common non-dermatophyte fungal agents of onychomycosis. Organism (Number of Isolates) Drug MIC (µg/mL) -------------...
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1; @bruno2] in what follows we will assume that the vector meson is predominantly a quark-antiquark state and that the spin and polarization structure is the same as in the photon [@dgkp; @nnpz; @sandapen; @KT] (for other approaches see, for example, Ref. [@pacheco]). As a consequence, the overlap between the photon an...
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_i$, where $i\in I$, are relatively prime. Identify ${\mathbb{Z}}^I$ with the root lattice by considering $\{{\alpha }_i\,|\,i\in I\}$ as the set of simple roots. Let $(\cdot ,\cdot ):{\mathbb{Z}}^I\to {\mathbb{Z}}^I$ be the (positive definite) symmetric bilinear form defined by $({\alpha }_i,{\alpha }_j)=d_ic_{ij}$. L...
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mpting to provide a solution for my problem. Unfortunately, his answer did not work for me! I began to look at all of my previous projects and noticed that the one I was having trouble with was the odd one out (because it was the only one that didn't work) and the factor that made it the odd one out, I found to be the ...
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n by or modify the private data of other partitions. Mediation specifies that an executing partition cannot use private data of one partition to modify private data of other partitions. Infiltration specifies that an executing partition cannot read private data of other partitions. The GWV policy implies the basic sep...
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For that, in turn, it suffices to check that for every $gH\in G/H$ we have $f(gH)=\tilde f(T'(g))$. We have $$\tilde f(T'(g))=\langle \int_H \delta(g\cdot h)-\delta(h)d\mu(h),\tilde f\rangle=\int_H \tilde f(g\cdot h)-\tilde f(h)d\mu(h)=f(gH)-f(H)=f(gH),$$ which finishes the proof. \[thm:MAPcompactgrp\] Let $G$ be a co...
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In classical fluids the same ambiguity occurs and it has been established, on physical grounds and by going beyond linearization, that using the material derivative is more correct [@maxey1983equation]. After all, using this material derivative in the equation of motion simply means that, under the above approximation...
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) = 2*x**3 - 4*x**2 - 4*x + 12. Let t be s(2). Put 5, 3, t, 0 in decreasing order. 5, t, 3, 0 Let q = -18.035 + 0.035. Let a = -21 - q. Put -0.2, a, 0 in ascending order. a, -0.2, 0 Let i = -2032 + 2037. Sort i, 38, -12 in descending order. 38, i, -12 Let f(b) = b - 6. Let m be f(5). Let z = -8 - -56. Let r = z + -43. ...
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his section, we discuss some structural properties of $1$-generator skew GQC codes over $\mathbb{F}_q$. Let $R=\mathbb{F}_q[x, \sigma]$ and ${\mathcal R}=R/(x^{m_1}-1)\times R/(x^{m_2}-1)\times\cdots\times R/(x^{m_l}-1)$. [**Definition 4.1** ]{} *Let $C$ be a $1$-generator skew GQC code generated by $c(x)=(c_1(x),\\ c...
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$ without boundary does not affect to the conclusions; for the construction of the Friedrich’s mollifier on $S$ we refer to [@fukuoka]). The above references are, however, valid only for problems in which the dimension of the kernel ${\rm Ker}(A_\nu)$, given below, is constant on $\Gamma$ (i.e. $A_\nu$ has constant mul...
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ividual reliability diagrams seems to compensate in the general picture of the aggregated one. The following subfigures show how the different calibration methods try to reduce ECE, occasionally increasing the error. As can be seen in Table \[table:mlp:balance:ece\], Dirichlet L2 and One-vs.Rest isotonic regression ob...
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odule by Lemma \[hi-basic-lem\]. By induction on $m$, it follows that $\operatorname{{\textsf}{ord}}^mN(i)$ is also free. The analogous results for $B_{ij}$ follow by multiplying everything on the right by $e$. {#cohh-subsect} We end the section by noting that Proposition \[pre-cohh\] provides an interesting connect...
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Attention**: **$\Delta\hat{y}$**: *0.002* **Babi Task 1** **Question**: Where is Sandra ? **Original Attention**: **Adversarial Attention**: **$\Delta\hat{y}$**: *0.003* **CNN-QA** **Question**:federal education minister @placeholder visited a @entity15 store in @entity17 , saw cameras **Original**: **Adversari...
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$. It can be seen that method I gives an inverted mass power spectrum which, on large scales, is systematically less steep, or less steeply falling, than the input (i.e. the slope of the inverted power spectrum is less negative than the actual one; see Fig. \[pinvp\_ks\] for a log-log plot of the power spectra). To un...
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}).toList(), ); } }, ), ), ), In the beginning, I only had one project to connect to and the data was correct. But now I successfully connect to another project with the correct user-uid, but the data is always from the default project which ...
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^- &\rightarrow & W_L^+ W_L^- \,, Z_L Z_L \;, \\ W_L^\pm W_L^\pm & \rightarrow & W_L^\pm W_L^\pm \,.\end{aligned}$$ In analogy to the pion scattering in QCD, the scattering amplitudes of these processes can be expressed in terms of an amplitude function $A(s,t,u)$. Their scattering amplitudes are then expressed as $$...
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, 669, 525 Wood-Vasey, W. M., et al. 2004, , 616, 339 Xu, J., et al. 1994, , 435, 274 [lllccc]{} UT Date& JD$-$2,450,000 & Phase (d) &F435W & F555W & F775W\ 05/21/2006&3876.0 & +90.0 &18.71(04) &17.36(02) &16.46(02)\ 12/25/2006&4094.0 & +308.0&21.48(06) &20.56(09) &19.69(02)\ [lllllc]{} Object & $r$(pixel) & $j$(pixe...
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------------ ---------------------------------------- ---------- ------------- : Peccei-Quinn charges of the fermions and scalars Because of our chosen charge assignments, only the field $\sigma$ couples to the colored fermion $\psi$, i.e. $${\cal L}_Y = f \sigma \bar \psi_L \psi_R + h.c.$$ Hence it also couples to...
4,058
2,072
3,593
3,698
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github_plus_top10pct_by_avg
r the graded structure of ${\mathcal{J}}$ under the $\operatorname{{\textsf}{ord}}$ gradation and write the induced order filtration as ${\mathcal{J}}= \bigcup {\mathcal{J}}^m$, for ${\mathcal{J}}^m = \operatorname{{\textsf}{ord}}^m {\mathcal{J}}= \bigoplus_{0\leq i\leq m} \operatorname{{\textsf}{ogr}}^i{\mathcal{J}}$....
4,059
3,586
2,030
3,790
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github_plus_top10pct_by_avg
linear regime, the stable modes are nonlinearly driven by the unstable modes. In these previous calculations, the homogeneous nature of the system made the set of linear eigenmodes a complete basis: at every time $t$ and wavevector $\mathbf{k}$, the state vector $\mathbf{f}$ could be expanded in a basis of the eigenm...
4,060
4,259
4,300
3,901
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github_plus_top10pct_by_avg
o $F_{\nabla}\cap {{\operatorname}{O}_{p'}(A)}=1$. Analogously, $F_{\nabla}\cap B=1$. Now, we will use the above facts on the actions of $C$ (and so $B$) and $\langle y \rangle$ on the set $\Omega$ to see that the minimal normal subgroup $N$ in our minimal counterexample cannot be a $p'$-group. The proof of the next ...
4,061
2,911
2,025
3,841
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github_plus_top10pct_by_avg
o the commonly used method of filtered backprojection.' address: | $^1$Department of Electrical Engineering and Automation, Aalto University, Finland\ $^2$Department of Information Technology, Uppsala University, Sweden\ author: - 'Zenith Purisha$^1$, Carl Jidling$^2$, Niklas Wahlstr[ö]{}m$^2$, Thomas B. Sch[ö]...
4,062
2,463
1,725
3,478
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github_plus_top10pct_by_avg
$\delta_2$, the correction to the heavy Higgs-bottom coupling ignoring the $\Delta_1$ contribution, and $\delta_{12}$, the correction to this coupling including the $\Delta_1$ contribution. The parameter $\delta_\Phi$ is defined in the text. The region within the vertical dashed lines is where most of the points from ...
4,063
1,844
2,767
3,819
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github_plus_top10pct_by_avg
verned by the Schrödinger equation $$\begin{aligned} i \frac{d}{dx} \nu = H \nu. \label{evolution}\end{aligned}$$ Given the flavor basis Hamiltonian $H$, the $S$ matrix is given by $$\begin{aligned} S = T \text{exp} \left[ -i \int^{x}_{0} dx^{\prime} H(x^{\prime}) \right], \label{S-matrix-def}\end{aligned}$$ where $T...
4,064
1,635
2,749
3,876
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github_plus_top10pct_by_avg
production strengths are constant within a $m_X$ bin. The PWA model includes five [${\ensuremath{\pi^+}}{\ensuremath{\pi^-}}$]{}isobars[@compassExotic]: ${\ensuremath{\pi}}{\ensuremath{\pi}}$ $s$-wave, ${\ensuremath{\rho}}(770)$, ${\ensuremath{f_0}}(980)$, ${\ensuremath{f_2}}(1270)$, and ${\ensuremath{\rho_3}}(1690)$. ...
4,065
1,749
2,984
3,877
2,450
0.779618
github_plus_top10pct_by_avg
: $ \begin{smallmatrix} & | & \\ & \downarrow & \\ \rightarrow & & \rightarrow \\ & \downarrow \end{smallmatrix} . $ Vertical input channel is twice as long as horizontal input channel. Vertical input is constant [True]{}: Physarum is always inoculated their....
4,066
6,130
3,536
3,605
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github_plus_top10pct_by_avg
d and analyzed during the current study have been deposited in the GEO database under the accession code: [GSE145717](https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE145717), for microarray data and [GSE145680](https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE145680) for RNA sequencing. The authors declare ...
4,067
3,829
273
3,825
631
0.803601
github_plus_top10pct_by_avg
dyadic integers as follows, where, for ease of notation we set $\textbf{1}_{i,n}(t):=I(|t-X_i|<h_nB)$ and $\textbf{1}_{ih}(t)=I(|t-X_{i}|<hB)$: $$\begin{aligned} \label{eq1} &&\Pr\left\{\max_{2^{k-1}<n\le 2^{k}}\sqrt{\frac{n h_{n}}{\log h_{n}^{-1}}} ||\bar{f}_n-E\bar{f}_n||_{\infty}>\lambda\right\} \notag\\ &&~~~\le\Pr...
4,068
2,987
2,014
3,828
null
null
github_plus_top10pct_by_avg
erthwaite corrected CI is given by $$\hat{\theta} \pm t_{\upsilon;1 - \frac{\alpha}{2}}\sqrt{{Var}\left( \hat{\theta} \right)},$$ where $t_{\upsilon;1 - \frac{\alpha}{2}}$ is as in the KR correction, but the original (unadjusted) variance of $\hat{\theta}$ is used. Note that, while the denominator degrees of freedom ca...
4,069
2,330
2,577
3,150
323
0.813405
github_plus_top10pct_by_avg
n-v_{[i,1]}$ and $\mu_j^i=v_{[i,j-1]}-v_{[i,j]}$ for $j>1$). Hence $\Delta$ yields an integral-valued quadratic from on $\Z^I$. Let $(\cdot,\cdot)$ be the associated bilinear form on $\Z^I$ so that $$\label{pairing-defn} (\v,\v)=2\Delta(\muhat).$$ Let $\e_0$ and $\e_{[i,j]}$ be the fundamental roots of $\Gamma$ (vector...
4,070
3,010
3,292
3,712
2,722
0.777556
github_plus_top10pct_by_avg
rate an $s$-step nilpotent group then $P(x;L)$ is said to be a *nilprogression* of step $s$, and in this instance we write $P_{\text{\textup{nil}}}(x;L)$ instead of $P(x;L)$. A set $P$ is said to be a *coset nilprogression* of rank $r$ and step $s$ if there exists a finite subgroup $H\subset P$, normalised by $P$, such...
4,071
3,298
2,546
3,781
736
0.801135
github_plus_top10pct_by_avg
tistical; @anastasiou2019normal] which establish CLT results for SGD with very small step size (rescaled to have constant variance). These work generally focus on the setting of “OU process near a local minimum”, in which the diffusion matrix is constant. Finally, a number of authors have studied the setting of heavy-...
4,072
2,555
2,162
3,784
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github_plus_top10pct_by_avg
n}'\textrm{s Law})\\ & \neq & \emptyset,\end{array}$$ so that no finite subcollection of $\mathcal{G}$ can cover $X$. Compactness of $X$ now implies that $\mathcal{G}$ too cannot cover $X$ and therefore $$\bigcap_{\alpha}F_{\alpha}=\bigcap_{\alpha}(X-G_{\alpha})=X-\bigcup_{\alpha}G_{\alpha}\neq\emptyset.$$ The proof ...
4,073
3,194
3,872
3,753
2,864
0.776451
github_plus_top10pct_by_avg
rangle}}_\Lambda{{\langle \varphi_u\varphi_{v'_1} \rangle}}_\Lambda{{\langle \varphi_{v'_1} \varphi_{v'_2} \rangle}}_\Lambda&{\nonumber}\\[7pt] +{{\langle \varphi_{v_1}\varphi_{v_2} \rangle}}_\Lambda{{\langle \varphi_{v_2}\varphi_{ v'_1} \rangle}}_\Lambda{{\langle \varphi_{v'_1}\varphi_u \rangle}}_\Lambda{{\langle \v...
4,074
3,599
3,763
3,594
3,344
0.77299
github_plus_top10pct_by_avg
ol{r}},t)=(\hbar/m) \nabla \phi({\boldsymbol{r}},t)$. This velocity can also be obtained from the superfluid current ${\boldsymbol{J}}({\boldsymbol{r}},t)$ as $${\boldsymbol{J}} = \frac{\hbar}{2 m i} \left(\psi^*\nabla\psi - \psi\nabla\psi^* \right) =\rho {\boldsymbol{v}} \ . \label{eq:current}$$ $\psi^*$ denotes the ...
4,075
3,454
3,779
3,773
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github_plus_top10pct_by_avg
x \sqrt{-G}G^{tt}\phi^*\left(-2\omega^2-2qA_t\omega\right)\phi\nonumber\\ \calQ_\phi&=-q\int d^4 x \sqrt{-G}G^{tt}J_t=-\frac{q}{\omega} E_\phi\;. \label{eq:charge}\end{aligned}$$ Here we have used the equation of motion and assumed Dirichlet conditions at $\rho=\rho_0$, which is sufficient to prevent energy or charge f...
4,076
2,121
3,831
3,736
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github_plus_top10pct_by_avg
lowing. In Region III, $\rho\ll\Lambda_{DE}/2\pi$, and $\kappa^2(\rho)\approx (1+4^{1+\alpha_\lambda})/\chi\lambda_{DE}^2$; Eq. $(\ref{rhoGEOM})$ reduces to the undriven, modified Bessel equation. As such, the density vanishes exponentially fast in this region on the scale $1/\kappa(r)$. This sets $r_{II} = [\chi/(1+4...
4,077
3,949
3,270
3,699
3,221
0.77391
github_plus_top10pct_by_avg
} \,\left(n_\infty/10^5\,{\mathrm{cm^{-3}}}\right) \left(M_{\mathrm{BH}}/10^3\,M_\odot\right)$, because $\dot{M}_{\mathrm{B}}$ is proportional to $M_{\mathrm{BH}}^2\,n_\infty$ while $\dot{M}_{\mathrm{E}}$ to $M_{\mathrm{BH}}$. High energy photons emitted by the BH accretion disk create a surrounding [H[ii]{} ]{}bubble...
4,078
3,418
3,941
3,800
null
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github_plus_top10pct_by_avg
oint of the moduli space remains a current primary field after deformation of the kinetic term in the action. Thus one can consistently think of the current algebra primaries as the group element $g$ taken in the representation $\mathcal{R}$. It also implies that at the WZW points the current primaries are the affine p...
4,079
2,843
1,192
3,862
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github_plus_top10pct_by_avg
\mathbb S}}_0,{{\mathbb S}}_1,{{\mathbb S}}_2,{{\mathbb S}}_3):{{\mathbb G}}_{{\bf N}}={\mathop{\Dot{\bigcup}}}_{i=0}^{ \raisebox{-3pt}{$\scriptstyle3$}}{{\mathbb S}}_i,\;{\partial}{{\mathbb S}}_0={\partial}{{\mathbb S}}_3=\{o,x\},\;{\partial}{{\mathbb S}}_1=\{o,y\},\;{\partial}{{\mathbb S}}_2=\{y,x\}\Big\}.\end{align...
4,080
1,053
3,002
3,953
3,383
0.772746
github_plus_top10pct_by_avg
tor pion-nucleon coupling we have used the standard values: $$m_{\pi}=138.0~{\rm MeV}~~~~\;\;\;\;\frac{\;f_{\pi}^{2}}{4\pi}=0.08\;.$$ In addition, the zero-range Landau-Migdal term accounts for the contact part of the isovector channel of the nucleon-nucleon interaction $$V_{\delta \pi} = g' {\left}( \frac{f_{\pi}}{m_{...
4,081
3,262
3,833
3,710
2,976
0.775653
github_plus_top10pct_by_avg
estimate the parameters. One approach is to compute the maximum a posteriori (MAP) estimate of the parameters by using, for example, gradient-based optimization methods [@Rasmussen2006]. However, using this kind of point estimate loses the uncertainty information of the hyperparameters and therefore in this article we ...
4,082
2,261
1,890
3,938
1,997
0.783738
github_plus_top10pct_by_avg
he density of the gas. This equation of state makes the Jeans mass, as well as the ratio of the Jeans length and the SPH smoothing kernel, independent of the density. Gas particles whose proper density exceeds $n_\mathrm{H}\ge0.1$ cm$^{-3}$ while they have temperatures $T\le10^5$ K are moved on to this equation of stat...
4,083
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4,057
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github_plus_top10pct_by_avg
***Initial Topology.*** In Fig. \[Fig: Initial-Final\](b), consider $Y_{1}=h(X_{1})$, $e\rightarrow i$ and $f\rightarrow h_{<}\!:X_{1}\rightarrow(h(X_{1}),\textrm{IT}\{ i;\mathcal{V}\})$. From $h^{-}(B)=h^{-}(B\bigcap h(X_{1}))$ for any $B\subseteq Y$, it follows that for an open set $V$ of $Y$, $h^{-}(V_{\textrm{comp...
4,084
1,893
3,714
3,745
2,523
0.779192
github_plus_top10pct_by_avg
nsets: Correlation functions averaged over 1 and 10 samples for the original WV model at time $t=10^5$ showing that the oscillations observed in single samples are not due to regular structures.](gamma_wv1d.pdf "fig:"){width="0.8\linewidth"}\ ![\[hh\_corr\_time\]Main panels: Height-height correlation function for the W...
4,085
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1,166
3,916
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github_plus_top10pct_by_avg
with crosses and squares corresponding to the cases with Neumann and Dirichlet conditions, respectively. Figure \[fig:dgf\](b) zooms in the section with $|R_i-R_{-1}| \le 10^{-4}$ into linear scale, with the inset plotting the DGF from the Neumann condition for $-9.4\times 10^{-5} \le R_i - R_{-1} \le -9.0\times 10^{-...
4,086
1,909
3,867
3,989
2,774
0.777057
github_plus_top10pct_by_avg
rivative of -1/540*b**6 + 0*b + 0*b**2 + b**3 - 1/180*b**5 + 0*b**4 - 1. Let u(c) be the third derivative of h(c). Factor u(i). -2*i*(i + 1)/3 Factor 4*s + 12*s**3 + 4*s**4 + 1 + 4 - 5 + 12*s**2. 4*s*(s + 1)**3 Let i(y) be the second derivative of -2*y**7/63 - 14*y**6/45 - 6*y**5/5 - 22*y**4/9 - 26*y**3/9 - 2*y**2 + 12...
4,087
1,885
2,902
3,649
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github_plus_top10pct_by_avg
lood products. Proton-pump inhibitor (IBP) therapy, domperidone and sucralfat. ...
4,088
4,936
3,253
3,707
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github_plus_top10pct_by_avg
neutrino mass term $(m_\nu)_{\ell{{\ell^\prime}}}\,\overline{(\nu_{\ell L}^{})^c}\,\nu_{{{\ell^\prime}}L}^{}/2$ where $(m_\nu)_{\ell{{\ell^\prime}}} = \sqrt{2}\, v_\Delta\, h_{\ell{{\ell^\prime}}}$. The scalar potential in the HTM can be written as $$\begin{aligned} V_{{\text{HTM}}}&=& -m_\Phi^2\, \Phi^\dagger \Phi ...
4,089
2,239
3,491
3,752
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github_plus_top10pct_by_avg
icient for empirical adequacy, we assume that the set $\Omega$ of all possible configurations of distance relations between $N\in\mathbb{N}$ matter points can be represented as follows: \[def:dist\] Let $\mathcal M=\{1,2,\dots,N\}$ and $\mathcal E=\{(i,j)\,|\,i,j\in\mathcal M, i\neq j\}$. The set $\Omega$ comprise...
4,090
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github_plus_top10pct_by_avg
T}_{d}}$, the (\[eq14\]) can be simplified by $$\label{eq15} \begin{array}{r@{}l@{\qquad}l} & {{{{\dot{x}}}}_{1}}={{{{x}}}_{2}} \\ & {{{{\dot{x}}}}_{2}}={{M}^{-1}}(\theta ){u}+{{M}^{-1}}(\theta ).K(\theta ,\dot{\theta },\ddot{\theta }) \\ \end{array}.$$ It can be clearly seen that the system uncertainties are now inc...
4,091
1,288
1,533
4,184
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github_plus_top10pct_by_avg
uad . \label{allRRfields}\end{aligned}$$ A single T-duality along the $a$ direction acts on the RR fields in the obvious way: if an $n$-form potential $C_n$ of one theory has no index parallel to $a$, it is mapped to the $(n+1)$-form $C_{n+1}$ of the other theory where the extra index is $a$, and vice versa. It is clea...
4,092
2,209
3,459
3,792
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null
github_plus_top10pct_by_avg
.14_{stat}\pm0.07_{sys}$ events were expected. The Poisson probability to see two or more events in the SK-IV livetime given an expected rate of 0.23 events is 2.3%. One of the two candidates was previously found in Ref. [@2016miura]. The other candidate is more ambiguous since it lacks a Michel electron. This may be a...
4,093
3,731
3,966
3,762
3,740
0.77041
github_plus_top10pct_by_avg
oted by $L^{n-4k}_x$, $L^{n-4k}_y$. The immersed submanifold $g_2(N^{n-2k}) \cap U^{reg}_{\Delta}$ is divided into two components. The first component is formed by pairs of points $(\bar x, \bar x')$ with the $3\varepsilon_3$-close images $(\kappa(\bar x), \kappa(\bar x')$ on $\RP^s$. This component is denoted by $g_2...
4,094
2,804
3,259
3,689
2,893
0.776259
github_plus_top10pct_by_avg
time-homogeneous) SDEs. This refines a result given in [@DHP11], Proposition 49, which implies that the $G$-normal distribution can be represented by Itô integrals with respect to a Brownian motion. Approximation of $G$-normal distribution ---------------------------------------- Let $X_1, X_2, \cdots$ be a sequence ...
4,095
2,672
1,990
4,002
3,898
0.769427
github_plus_top10pct_by_avg
with shadowing effect is assumed except for Di and Ddn runs; $^{b}$isotropic radiation; $^{c}$disc radiation without shadowing effect; $^{d}$Dds run is also called s100, M1e3 and n1e5 runs. We perform a set of simulations to see how the directional dependence of BH irradiation affects the nature of accretion. Table \...
4,096
1,586
2,597
3,911
2,794
0.77692
github_plus_top10pct_by_avg
nd $q_2$ to $\cS_2$. Each server $S_j$ responds with an answer $ans_j=\cA(j,\ba,q_j)$. Finally, $\cU$ computes its output by applying the recovery algorithm $\cR(ans_1,ans_2,i,r)$. The protocol should satisfy the following conditions: - For any n, $\ba\in {{\{0,1\}}}^n$ and $i\in [n]$, the user the outputs the corre...
4,097
4,407
4,159
3,857
983
0.796395
github_plus_top10pct_by_avg
head $\widetilde{S}_c(L_{c}(\mu))$ for each $\mu$. By $\widetilde{S}_c(L_{c}(\lambda))$ is therefore isomorphic to a composition factor of $\Delta_{c+1}(\lambda)$. But, by Corollary \[poono\] and the remark thereafter, the composition factors of $\Delta_{c+1}(\lambda)$, except for the head, are of the form $L_{c+1}(\n...
4,098
3,438
1,266
3,944
4,185
0.767471
github_plus_top10pct_by_avg
rates is negative[@Terry1982]. Without viscosity, the present system does not meet the necessary condition. Note that the time scale for nonlinear energy exchange is very short compared to the time scale of the saturation level increase, strongly suggesting that the nonlinearities of Eqs.  and conserve energy. This ca...
4,099
3,664
5,026
4,066
null
null
github_plus_top10pct_by_avg
_[2E]{}\^[E\_m]{}[1]{}(\_[22,2]{})(x,,E’,E)dE’\ = & -\_2(x,E,E)(x,,E)[1]{} + (\_2(x,,E)(x,,))(E)(E)\ & +\_[2E]{}\^[E\_m]{}[1]{}(\_[22,2]{})(x,,E’,E)dE’\ = & \_2(x,,E)(E)(x,,E) +(K\_[22,2,2]{})(x,,E)\ & +( -\_2(x,E,E)[1]{} +[E]{}(x,E,E)(E))(x,,E), where $$(K_{22,2,2}\psi)(x,\omega,E):= \int_{2E}^{E_m}{1\over{(E'-E)^2}}(...
4,100
1,353
3,127
3,856
null
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github_plus_top10pct_by_avg