text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
|---|---|---|
Alex Chow may refer to:
Alex Chow Wing Hong (born 1990), a social activist in Hong Kong
Alex Chow Tsz-lok (1997–2019), a student of Hong Kong University of Science and Technology who died from injuries during the 2019–20 Hong Kong protests
Alexander Chow, a Chinese American theologian at New College, Edinburgh | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,375 |
Jens Sloth, född 9 september 1982, är en svensk fotbollsspelare som spelade i Trelleborgs FF 1997-2009. Han har därefter påbörjat studier till civilingenjör inom elektroteknik på Lunds tekniska högskola. Under 2010 spelade han i Höörs IF i division 3.
Externa länkar
Svenska fotbollsspelare
Män
Födda 1982
Levande personer
Spelare i Trelleborgs FF | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 169 |
The Peach Belt Conference men's basketball tournament is the annual conference basketball championship tournament for the Peach Belt Conference. The tournament has been held annually since 1992. It is a single-elimination tournament and seeding is based on regular season records.
The winner, declared conference champion, receives the conference's automatic bid to the NCAA Men's Division II Basketball Championship.
Results
Championship records
Georgia Southwestern, North Georgia, USC Beaufort, and Young Harris have not yet won the Peach Belt tournament.
Francis Marion and North Florida never won the tournament as Peach Belt members.
Schools highlighted in pink are former members of the Peach Belt Conference
See also
Peach Belt Conference women's basketball tournament
References
NCAA Division II men's basketball conference tournaments
Tournament
Recurring sporting events established in 1992 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,604 |
{"url":"http:\/\/lambda-the-ultimate.org\/node?from=1810","text":"## Sketchpad: A man-machine graphical communication system\n\nIvan Sutherland's famous thesis has been rereleased in a new electronic edition. This is a freely downloadable and high-quality PDF version created by Alan Blackwell and Kerry Rodden.\n\n## Dynamic Languages Wizards panel videos (rerun)\n\nWe have previously mentioned these videos of a series of panel discussions that were hosted by the MIT Dynamic Languages group in 2001. I just watched them again and I thought they were great, so I'm re-posting them for people who missed them the first time around and as a reminder for anyone who'd like to watch them again.\n\nThere are three separate panels on different topics: compilation, runtime, and language design. The panelists are distinguished people mostly from the Lisp\/Scheme\/MIT world. These panels were a precursor to the Lightweight Languages workshop series.\n\nThe videos are in QuickTime format. To play them on Linux I used VLC. mplayer wasn't able to synchronize the audio and video.\n\n## Slideshow: Functional Presentations\n\nSlideshow: Functional Presentations. Findler, Flatt. ICFP 2004.\n\nNothing earth shattering, but a nice example of DSL design none the less.\n\nMight be useful for teaching (as well as for creating slideshows...)\n\n## More content\n\nI know the type system discussion is taking its toll, but I am sure things would be more interesting around here if we had more news items.\n\nSo all you editors out there: How about sharing?\n\n## Simulators: Virtual Machines of the Past (and Future)\n\nSIMH, the Computer History Simulation system, is a behavioral simulator for obsolete systems of historic interest. Originally intended as an educational project, it is increasingly being used in long-lived production environments as a substitute for real systems. SIMH is continuously being extended to simulate new machines.\n\nThis item isn't directly PL related, but since many LtU regulars are fond of programming language history, I assume there is interest in other apsects of computing history. On top of that, if and when you try to rescue an obsolete language implementation, there's a good chance you are going to need something like SIMH.\n\nThis ACM Queue article describes the design issues invloved in building SIMH, and the problems the arise when simulating old hardware systems.\n\n## Acute: high-level programming language design for distributed computation\n\nThis work is exploring the design space of high-level languages for distributed computation, focussing on typing, naming, and version change. We have designed, formally specified and implemented an experimental language, Acute. This extends an OCaml core to support distributed development, deployment, and execution, allowing type-safe interaction between separately-built programs. It is expressive enough to enable a wide variety of distributed infrastructure layers to be written as simple library code above the byte-string network and persistent store primitives, disentangling the language runtime from communication.\n\nThis requires a synthesis of novel and existing features:\n\n\u2022 type-safe interaction between programs, with marshal and unmarshal primitives;\n\u2022 modules and abstract types with abstraction boundaries that are respected by interaction;\n\u2022 global names, generated either freshly or based on module hashes: at the type level, as runtime names for abstract types; and at the term level, as channel names and other interaction handles;\n\u2022 versions and version constraints, integrated with type identity;\n\u2022 local concurrency and thread thunkification; and\n\u2022 second-order polymorphism with a namecase construct.\nThe language design deals with the interplay among these features and the core. The semantic definition tracks abstraction boundaries, global names, and hashes throughout compilation and execution, but still admits an efficient implementation strategy.\n\nFor more info, see the Main site, from which you can view papers and sample code.\n\n## Dan Sugalski: Implementing an Interpreter\n\nAn annotated set of slides giving the inside story on the implementation details of Parrot.\n\nWell worth checking if you are into this sort of thing.\n\n## Eliminating Array Bound Checking through Non-dependent types\n\nOleg posted this pertinent message on the Haskell mailing list. It's always nice to see cool examples such as this.\n\nHaving saiod that, I must also say that I agree with Conor McBride who wrote that anyone who would argue (and I'm not saying you do) that work to try to make more advanced type systems and stronger static guarantees more convenient and well-supported is not necessary because it happens to be possible to bang out this or that example in Haskell as it stands if you think about it hard enough, is adopting the position of the ostrich.\n\nMaking type systems more expressive is a worthy goal. You want them to remain decidable (i.e., static), of course. Can we at least agree on that? ;-)\n\n## A Visual Environment for Developing Context-Sensitive Term Rewriting Systems\n\n(via an interesting discussion on the types list)\n\nA Visual Environment for Developing Context-Sensitive Term Rewriting Systems. Matthews, Findler, Flatt, Felleisen. International Conference on Rewriting Techniques and Applications (RTA) 2004.\n\nOver the past decade, researchers have found context-sensitive term-rewriting semantics to be powerful and expressive tools for modeling programming languages, particularly in establishing type soundness proofs. Unfortunately, developing such semantics is an error-prone activity. To address that problem, we have designed PLT Redex, an embedded domain-specific language that helps users interactively create and debug context-sensitive term-rewriting systems. We introduce the tool with a series of examples and discuss our experience using it in courses and developing an operational semantics for R5RS Scheme.\n\nSeems like a nice tool (it's DrScheme based, of course). I guess I should try it out.\n\n## TyPiCal: Type-based static analyzer for the Pi-Calculus\n\nTyPiCal is a type-based static analyzer for the pi-calculus. The current version of TyPiCal provides four kinds of program analyses or program transformations: lock-freedom analysis, deadlock-freedom analysis, useless-code elimination, and information flow analysis.\n\nType system is an ordinary type system extended so that channel types carry precise information about how each channel is used. This allows a type inferencer to obtain information about the behavior of a process.","date":"2014-09-18 05:38:38","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.23763597011566162, \"perplexity\": 3634.8735482241655}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-41\/segments\/1410657125654.84\/warc\/CC-MAIN-20140914011205-00294-ip-10-196-40-205.us-west-1.compute.internal.warc.gz\"}"} | null | null |
Combining floral trailing lace with sparkling rhinestone's, Swarovski pearls and a myriad of gemstones to whimsical effect, this gorgeous vintage-inspired bridal sash adds a bohemian accent to your wedding ensemble. Designed to match perfectly to both Amelie and Dorothea and our Isla Cuff.
Detail length approx: 39cm. approx width: 5cm. | {
"redpajama_set_name": "RedPajamaC4"
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\section{Framework for calculation}
The process we have considered here is
\begin{eqnarray}
e(l)+p(P)\rightarrow e(l')+J/\psi (P_h)+X
\end{eqnarray}
Both the scattering electron and target proton are unpolarized. Four momentum of particles is represented within the round
brackets. The dominating subprocess for small $x$ for quarkonium production in $ep$ collision is photon-gluon fusion process, at leading
order this process contributes at $z=1$ \cite{Mukherjee:2016qxa}. In this work, we consider the NLO process
$\gamma^*(q)+g(k)\rightarrow J/\psi(P_h) +g(p_g)$ and the kinematical region $z<1$, which will be accessible at EIC.
The final state gluon is not detected. Here the variable $z$ is defined as $z=P\cdot P_h/P\cdot q$ which is the energy
fraction of $J/\psi$ in the proton rest frame. We use a generalized factorization scheme taking into account the partonic
transverse momenta. We consider the frame in which the virtual photon and proton are moving in $+z$ and $-z$ direction respectively.
The incoming and outgoing electron form a lepton plane, which provides a reference for measuring azimuthal angles of other
particles. The four momenta of proton and virtual photon $q=l-l'$ are given by
\cite{Mukherjee:2016qxa}:
\begin{eqnarray}
P=n_- + \frac{M_p^2}{2}n_+ \approx n_- \\
q=-x_Bn_-+\frac{Q^2}{2x_B}n_+\approx -x_BP+(P\cdot q)n_+
\end{eqnarray}
where $Q^2=-q^2$ and Bjorken variable, $x_B=\frac{Q^2}{2P\cdot q}$. $M_p$ is the mass of proton.
All four momenta are written in terms of light like vectors $n_-=P$ and $n_+=n=(q+x_BP)/P\cdot q$, such that $n_+\cdot n_-=1$ and $n_-^2=n_+^2=0$. The leptonic momenta can be written as
\begin{eqnarray}
l=\frac{1-y}{y}x_BP+\frac{1}{y}\frac{Q^2}{2x_B}n+\frac{\sqrt(1-y)}{y}Q\hat{l}_{\perp}=\frac{1-y}{y}x_BP+\frac{s}{2}n+\frac{\sqrt(1-y)}{y}Q\hat{l}_{\perp}\\
l'=\frac{1}{y}x_BP+\frac{1-y}{y}\frac{Q^2}{2x_B}n+\frac{\sqrt(1-y)}{y}Q\hat{l}_{\perp}=\frac{1}{y}x_BP+(1-y)\frac{s}{2}n+\frac{\sqrt(1-y)}{y}Q\hat{l}_{\perp}
\end{eqnarray}
here, $s=(l+P)^2=2P\cdot l$, is the center of mass energy of electron-proton scattering. $y=P\cdot q/P\cdot l$,
such that the relation $Q^2=sx_By$ hold. The virtual photon and target proton system invariant mass squared is defined as $W^2=(P+q)^2$. In terms of the light-like vectors defined above, the four momenta of initial state gluon is given as
\begin{eqnarray}
k=xP+k_{\perp}+(p\cdot P-xM_p^2)n\approx xP+k_{\perp}
\end{eqnarray}
where, $x=k\cdot n$ is the light-cone momentum fraction. The four momentum of the final state $J/\psi$ and
the final state gluon are give by
\begin{eqnarray}
P_h=z(P\cdot q)n+\frac{M^2+\textbf{P}_{h\perp}^2}{2zP\cdot q}P+P_{h\perp}\\
p_g=(1-z)(P\cdot q)n+\frac{\textbf{p}_{g\perp}^2}{2(1-z)P\cdot q}P+p_{g\perp}
\end{eqnarray}
$P_h^2=-\textbf{P}_{h\perp}^2$. $M$ is the mass of $J/\psi$. \par
For the partonic level process: $\gamma^*(q)+g(k)\rightarrow J/\psi(P_h)+g(p_g)$, we can define the Mandelstam variables as follows
\begin{eqnarray}
\hat{s}=(k+q)^2=q^2+2k\cdot q=\frac{xQ^2}{x_B}-Q^2,
\label{xb}
\end{eqnarray}
\begin{eqnarray}
\hat{t}&=&(k-P_h)^2=M^2-2k\cdot P_h\nonumber\\
&=&M^2-\frac{xzQ^2}{x_B}+2k_{\perp }P_{h\perp}\cos(\phi-\phi_h),
\end{eqnarray}
\begin{eqnarray}
\hat{u}&=&(q-P_h)^2=M^2+q^2-2q\cdot P_h\nonumber\\
&=&M^2-(1-z)Q^2-\frac{M^2+P^2_{h\perp}}{z}.
\end{eqnarray}
The $\phi$ and $\phi_h$ are the azimuthal angles of the initial gluon and $J/\psi$ transverse momentum vector respectively.\\
We use a framework based on generalized parton model approach with the inclusion of intrinsic transverse momentum effects, and assume TMD factorization. The differential cross section for the unpolarized process
is given by \cite{Mukherjee:2016qxa} ;
\begin{eqnarray}
\begin{aligned}
d\sigma=&\frac{1}{2s}\frac{d^3l'}{(2\pi)^32E_{l'}}\frac{d^3P_h}{(2\pi)^32E_{P_h}}\int \frac{d^3p_g}{(2\pi)^32E_g}\int dx
d^2{\bm k}_{\perp}(2\pi)^4\delta(q+k-P_h-p_g)\\
&\times\frac{1}{Q^4}L^{\mu\mu'}(l,q)\Phi^{\nu\nu'}(x,{\bm k}_{\perp})\mathcal{M}^{\gamma^*+g\rightarrow J/\psi +g}_{\mu\nu}\mathcal{M}^{*\gamma^*+g\rightarrow J/\psi +g}_{\mu'\nu'}
\end{aligned}
\end{eqnarray}
where $L^{\mu\mu'}$ is leptonic tensor which is given by
\begin{eqnarray}
L^{\mu\mu'}(l,q)=e^2(-g^{\mu\mu'}Q^2+2(l^{\mu}l'^{\mu'}+l^{\mu'}l'^{\mu}))
\end{eqnarray}
with $e$ is the electric charge of electron. \\
$\Phi^{\nu\nu'}$ is gluon correlator which can be parametrized in terms of gluon TMDs. For unpolarized proton,
at leading twist, gluon correlator can be given as \cite{Mulders:2000sh}:
\begin{eqnarray}
\phi^{\nu\nu'}_g(x,\textbf{k}_{\perp})=\frac{1}{2x}[-g^{\nu\nu'}_{\perp}f_1^g(x,\textbf{k}_{\perp}^2)+(\frac{k_{\perp}^{\nu}k_{\perp}^{\nu'}}{M_p^2}+g_{\perp}^{\nu\nu'}\frac{\textbf{k}_{\perp}^2}{2M_p^2})h_1^{\perp g}(x,\textbf{k}_{\perp}^2)]
\end{eqnarray}
where $f_1^g(x,{\bm k}_{\perp}^2)$ is the unpolarized gluon distribution and
$h_1^{\perp g}(x,{\bm k}_{\perp}^2)$ is the linearly polarized gluon distribution.
$g_{\perp}^{\nu\nu'}=g^{\nu\nu'}-P^{\nu}n^{\nu'}/P\cdot n-P^{\nu'}n^{\nu}/P\cdot n$.
\section*{$J/\psi$ production in NRQCD based color singlet (CS) framework}
The dominating subprocess at is $\gamma^*+g\rightarrow J/\psi +g$. All the tree level Feynman diagrams corresponding to this process are given in Fig. \ref{figure1} .
\begin{figure}[H]
\begin{minipage}[c]{0.99\textwidth}
\hspace{1.5cm}
\includegraphics[width=14cm,height=6.5cm,clip]{fig1.pdf}
\end{minipage}
\caption{\label{fig3} Feynman diagrams for $\gamma^*+g\rightarrow J/\psi +g$ process}
\label{figure1}
\end{figure}
The general expression of the amplitude for the bound state production of $J/\psi$ in NRQCD framework can be written as
\cite{Boer:2012bt, Mukherjee:2016qxa} :
\begin{equation}
\begin{aligned}
\mathcal{M}\left(\gamma^* g\rightarrow Q\bar{Q}[\leftidx{^{2S+1}}{L}{_J}^{(1)}](P_h)+g\right)=\sum_{L_zS_z}\int\frac{d^3\bm{k}^{\prime}}{(2\pi)^3}\Psi_{LL_z}(\bm{k}^\prime) \langle LL_z;SS_z|JJ_z\rangle \\
\times\mathrm{Tr}[O(q,k,P_h,k^\prime)\mathcal{P}_{SS_z}(P_h,k')],
\end{aligned}
\end{equation}
As we have imposed a cutoff on $z$, $ z < 0.9$, we do not need to consider the virtual diagrams as they contribute at $z=1$.
In the above equation, $2k'$ is the relative momentum of heavy quarks and $O(q,k,P_h,k^\prime)$ is calculated from the Feynman diagrams. The spinors of heavy quark, anti-quark legs are absorbed into the bound state wave function. By considering contribution from all the Feynman diagrams, $O(q,k,P_h,k^\prime)$ is given by
\begin{equation}
O(q,k,P_h,k^\prime)=\sum_{m=1}^6 \mathcal{C}_m O_m(q,k,P_h,k^\prime).
\end{equation}
Where, $O_m,\ (m=1,2,...6)$ are corresponding to each Feynman diagrams and $\mathcal{C}_m$ represents
the color factor of corresponding diagram. The expressions for $O_m$ are given below
\begin{equation}\label{ee1}
\begin{aligned}
O_1=
4g^2_s(ee_c)\varepsilon^{\rho\ast}_{\lambda_g}
(p_g)
\gamma_\nu\frac{\slashed{P_h}+2\slashed{k}^\prime-2\slashed{q}+M}{(P_h+2k^\prime-2q)^2-M^2}\gamma_\mu
\frac{-\slashed{P_h}+2\slashed{k}^\prime-2\slashed{p}_g+M}{(P_h-2k^\prime+2p_g)^2-M^2}\gamma_\rho,
\end{aligned}
\end{equation}
\begin{equation}\label{ee2}
\begin{aligned}
O_2=
4g^2_s(ee_c)\varepsilon^{\rho\ast}_{\lambda_g}
(p_g)
\gamma_\rho\frac{\slashed{P_h}+2\slashed{k}^\prime+2\slashed{p}_g+M}{(P_h+2k^\prime+2p_g)^2-M^2}\gamma_\nu
\frac{-\slashed{P_h}+2\slashed{k}^\prime+2\slashed{k}+M}{(P_h-2k^\prime-2k)^2-M^2}\gamma_\mu,
\end{aligned}
\end{equation}
\begin{equation}\label{ee3}
\begin{aligned}
O_3=
4g^2_s(ee_c)\varepsilon^{\rho\ast}_{\lambda_g}
(p_g)
\gamma_\nu\frac{\slashed{P_h}+2\slashed{k}^\prime-2\slashed{q}+M}{(P_h+2k^\prime-2q)^2-M^2}\gamma_\rho
\frac{-\slashed{P_h}+2\slashed{k}^\prime+2\slashed{k}+M}{(P_h-2k^\prime-2k)^2-M^2}\gamma_\mu,
\end{aligned}
\end{equation}
Here, the mass of bound state $M$ is assumed to be twice the mass of charm quark ($m_c$) $i.e.\ M=2m_c$, .The charge conjugation invariance allow us to write the expressions for ($O_4,O_5$ and $O_6$), from the other Feynman diagrams, by reversing the fermion line and replacing $k'$ by $-k'$. Assuming the $Q\bar{Q}$ is formed in color singlet state, the color factor of each diagram is given by
\begin{equation}
\begin{aligned}
\mathcal{C}_1=\mathcal{C}_5=\mathcal{C}_6= \sum_{ij}\langle
3i;\bar{3}j|1\rangle(t_at_b)_{ij},~~~\mathcal{C}_2=\mathcal{C}_3=\mathcal{C}_4= \sum_{ij}\langle
3i;\bar{3}j|1\rangle(t_bt_a)_{ij}
\end{aligned}
\end{equation}
The SU(3) Clebsch-Gordan coefficients for CS are given by
\begin{eqnarray}
\langle 3i;\bar{3}j|1\rangle=\frac{\delta^{ij}}{\sqrt{N_c}}
\end{eqnarray}
where $N_c$ is the number of colors. The generators of the SU(3) group satisfies the relations:
$\mathrm{Tr}(t_a)=0,$ $\mathrm{Tr}(t_at_b)=\delta_{ab}/2$ and
$\mathrm{Tr}(t_at_bt_c)=
\frac14(d_{abc}+if_{abc})$.
From these relations, we get the color factor for the production of $Q\bar{Q}$ pair in CS state as follows;
\begin{eqnarray}
\mathcal{C}_1=\mathcal{C}_2=\mathcal{C}_3=\mathcal{C}_4=\mathcal{C}_5=\mathcal{C}_6=\frac{\delta_{ab}}{2\sqrt{N_c}}.
\end{eqnarray}
The spin projection operator, given in the equation of amplitude of the bound state, includes the spinors of heavy quark
and anti-quark and is given by \cite{Boer:2012bt}:
\begin{eqnarray}
\mathcal{P}_{SS_z}(P_h,k^\prime)&=&\sum_{s_1s_2}\langle\frac12s_1;\frac12s_2|SS_z\rangle v(\frac{P_h}{2}-
k^\prime,s_1)\bar{u}(\frac{P_h}{2}+k^\prime,s_2)\nonumber\\
&=&\frac{1}{4M^{3/2}}(-\slashed{P}_h+2\slashed{k}^\prime+M)\Pi_{SS_z}(\slashed{P}_h+2\slashed{k}^\prime+M)
+\mathcal{O}(k^{\prime 2})
\end{eqnarray}
where $\Pi_{SS_z}=\gamma^{5}$ for singlet ($S=0$) state and $\Pi_{SS_z}=\slashed{\varepsilon}_{s_z}(P_h)$
for triplet ($S=1$) state. $\varepsilon_{s_z}(P_h)$ is the spin polarization vector of $Q\bar{Q}$ pair. Since, $k'<<P_h$, one can perform Taylor expansion of the amplitude around $k'=0$. In that expansion, the first term gives the S-waves(L=0,J=0,1). For the P-waves(l=1,J=0,1,2), we need to consider the linear terms in $k'$ in the expansion as the radial wavefunction $R_1(0)=0$ for $P-$wave. Since, $J/\psi$ is a $^3S_1$ state, in the color singlet model we calculate contribution of the CS state $^3S_1$.
\begin{eqnarray}\label{e8}
\mathcal{M}[\leftidx{^{2S+1}}{S}{_J}^{(1)}](P_h,k)&=&\frac{1}{\sqrt{4\pi}}R_0(0)\mathrm{Tr}[O(q,k,P_h,
k^\prime) \mathcal{P}_{SS_z}(P_h,k^\prime)]\Big\rvert_{k^\prime=0}\nonumber\\
&=&\frac{1}{\sqrt{4\pi}}R_0(0)\mathrm{Tr}[O(0) \mathcal{P}_{SS_z}(0)],
\end{eqnarray}
where,
\begin{eqnarray}
O(0)=O(q,k,P_h,k^\prime)\Big\rvert_{k^\prime=0}~,~~~~~~~~
\mathcal{P}_{SS_z}(0)=\mathcal{P}_{SS_z}(P_h,k^\prime)\Big\rvert_{k^\prime=0}
\end{eqnarray}
We have the following symmetry relations for ${^3}{S}{_1}$ state
\begin{eqnarray}\label{e15}
\mathrm{Tr}[O_1(0)(-\slashed{P}_h+M)\slashed{\varepsilon}_{s_z}]&=&
\mathrm{Tr}[O_4(0)(-\slashed{P}_h+M)\slashed{\varepsilon}_{s_z}]\nonumber\\
\mathrm{Tr}[O_2(0)(-\slashed{P}_h+M)\slashed{\varepsilon}_{s_z}]&=&
\mathrm{Tr}[O_5(0)(-\slashed{P}_h+M)\slashed{\varepsilon}_{s_z}]\nonumber\\
\mathrm{Tr}[O_3(0)(-\slashed{P}_h+M)\slashed{\varepsilon}_{s_z}]&=&
\mathrm{Tr}[O_6(0)(-\slashed{P}_h+M)\slashed{\varepsilon}_{s_z}]\nonumber\\
\end{eqnarray}
The final expression for the amplitude for ${^3}{S}{_1}$ state is given by
\begin{eqnarray}\label{e16}
\begin{aligned}
\mathcal{M}[\leftidx{^{3}}{S}{_1}^{(1)}](P_h,k)=&{}\frac{1}{4\sqrt{\pi M}}R_0(0)\frac{\delta_{ab}}{\sqrt{N_c}}
\mathrm{Tr}\left[\sum_{m=1}^3O_m(0)(-\slashed{P}_h+M)\slashed{\varepsilon}_{s_z}\right],
\end{aligned}
\end{eqnarray}
where
\begin{eqnarray}\label{e17}
\begin{aligned}
\sum_{m=1}^3O_m(0)=&{}g^2_s(ee_c)\varepsilon^{
\rho\ast}_{
\lambda_g}(p_g)\Bigg[\frac{\gamma_\nu(\slashed{P_h}-2\slashed{q}+M)\gamma_\mu
(-\slashed{P_h}-2\slashed{p}_g+M)\gamma_\rho}{(\hat{s}-M^2)(\hat{u}-M^2+q^2)}\\&
\qquad\qquad+\frac{\gamma_\rho(\slashed{P_h}+2\slashed{p}_g+M)\gamma_\nu
(-\slashed{P_h}+2\slashed{k}+M)\gamma_\mu}{(\hat{s}-M^2)(\hat{t}-M^2)}\nonumber\\&\qquad\qquad+
\frac{\gamma_\nu(\slashed{P_h}-2\slashed{q}+M)\gamma_\rho(-\slashed{P_h}+2\slashed{k}+M)\gamma_\mu
}{(\hat{t}-M^2)(\hat{u}-M^2+q^2)}
\Bigg].
\end{aligned}
\end{eqnarray}
\section*{Calculation of the asymmetry}
We use a framework based on generalized parton model, with the
inclusion of intrinsic transverse momentum effects. We assume TMD factorization for
the process considered. We consider a kinematical region in which the transverse momentum
of $J/\psi$ is small compared
to the mass of $J/\psi$, $M$ $i.e. ~~ P_{h\perp}<M$.
The final gluon carries the momenta fraction $(1-z)$, as $z=\frac{P\cdot P_h}{P\cdot q}$, is the energy fraction transferred from the photon to $J/\psi$ in the proton rest frame. So, this means that when $~~z\rightarrow 1$, the outgoing gluon is soft. We consider $z<0.9$ to keep the final gluon hard. Moreover, gluon and heavy quark fragmentation can also contribute to quarkonium production significantly for $P_{h\perp}>4~GeV$. We have imposed an upper limit on $P_{h\perp}$. In order to eliminate the fragmentation of the hard gluon into $J/\psi$ we also use a lower bound on $z$, namely $0.3<z$. \\
In the differential cross section given in Eq.~(12), there is a contraction of four tensors which is written as
\begin{eqnarray}
L^{\mu\mu'}(l,q)\Phi^{\nu\nu'}(x,{\bm k}_{\perp})\mathcal{M}^{\gamma^*+g\rightarrow J/\psi +g}_{\mu\nu}\mathcal{M}^{*\gamma^*+g\rightarrow J/\psi +g}_{\mu'\nu'}
\end{eqnarray}
where the individual components are defined above. The summation over the transverse polarization of the final on-shell gluon is given by
\begin{eqnarray}
\sum_{\lambda_a=1}^2\varepsilon^{\lambda_a}_\mu(p_g)\varepsilon^{\ast\lambda_a}_{\mu^\prime}(p_g)=-g_{
\mu\mu^\prime}+
\frac{p_{g\mu} n_{g\mu^\prime}+p_{g\mu^\prime}n_{g\mu}}{p_g\cdot n_g}-\frac{p_{g\mu} p_{g\mu^\prime}}{(p_g\cdot n_g)^2}
\end{eqnarray}
with $n_g^\mu=\frac{P^\mu_h}{M}$.
We have three amplitudes and their corresponding conjugates, given by Eq.~(27), that will contribute. We use the notation
\begin{eqnarray}
\begin{aligned}
\mathcal{M}_i[\leftidx{^{3}}{S}{_1}^{(1)}](P_h,k)=&{}\frac{1}{4\sqrt{\pi M}}R_0(0)\frac{\delta_{ab}}{\sqrt{N_c}}
\mathrm{Tr}\left[O_i(0)(-\slashed{P}_h+M)\slashed{\varepsilon}_{s_z}\right],
\end{aligned}
\end{eqnarray}
where $i=1,2,3$, corresponds to the contribution from each independent diagram. \\
So, the cross section will get contribution from nine terms $( \mathrm{of~ the~ form} ~ M_iM_j~ ,~ \mathrm{where} ~ i,j=1,2,3)$
\begin{eqnarray}
M_iM_j=L^{\mu\mu'}(l,q)\Phi^{\nu\nu'}(x,{\bm k}_{\perp})\mathcal{M}^{\gamma^*+g\rightarrow J/\psi +g}_{i\mu\nu}\mathcal{M}^{*\gamma^*+g\rightarrow J/\psi +g}_{j\mu'\nu'}
\end{eqnarray}
and hence, the differential cross section can be written as
\begin{eqnarray}
\begin{aligned}
d\sigma=&\frac{1}{2s}\frac{d^3l'}{(2\pi)^32E_{l'}}\frac{d^3P_h}{(2\pi)^32E_{P_h}} \int \frac{d^3p_g}{(2\pi)^32E_g}\int dx
d^2{\bm k}_{\perp}(2\pi)^4\delta(q+k-P_h-p_g)\\
&\times\frac{1}{Q^4} {\mid M \mid }^2;
\end{aligned}
\end{eqnarray}
where $M = \sum_i M_i$. Out of the nine terms in ${\mid M \mid}^2$, six are interference terms with a symmetry $M_iM_j=M_jM_i ~~for~~ i\ne j$.
So, effectively we need to compute six terms.\\
In a frame where the virtual photon and target proton move along the $z$-axis, and the lepton scattering plane defines the azimuthal angles $\phi_l=\phi_{l'}=0$, then we have
\begin{eqnarray}
\frac{d^3l'}{(2\pi)^32E_{l'}}=\frac{1}{16\pi^2}sydx_Bdy, ~~~~ \frac{d^3P_h}{(2\pi)^32E_{h}}=\frac{1}{(2\pi)^3}\frac{1}{2z}dzd^2\textbf{P}_{h\perp}\nonumber\\
\frac{d^3p_g}{(2\pi)^32E_{g}}=\frac{1}{(2\pi)^3}\frac{1}{2z_2}dz_2d^2\textbf{p}_{g\perp}
\end{eqnarray}
and the delta function can be expressed as
\begin{eqnarray}
\begin{split}
\delta^4(q+k-P_h-p_g)=&\delta\Big ( x-\frac{1}{ys}(x_Bys+\frac{M^2+P_{h\perp}^2}{z}+\frac{(k_{\perp}-P_{h\perp})^2}{(1-z)}) \Big )\\
&\times\frac{2}{ys}\delta(1-z-z_2) \times\delta^2(\textbf{k}_{\perp}-\textbf{P}_{h \perp}-\textbf{p}_{g\perp})
\end{split}
\end{eqnarray}
where, the delta function sets $z_2=(1-z)$. Hence, after integrating with respect to $x$, $z_2$ and $p_{g\perp}$,
the final form of the differential cross section can be given by
\begin{eqnarray}
\frac{d\sigma}{dydx_Bdzd^2\textbf{P}_{h\perp}}=\frac{1}{256\pi^4}\frac{1}{x_B^2s^3y^2z(1-z)}\int k_{\perp}dk_{\perp}
{\mid M' \mid }^2
\end{eqnarray}
where, ${\mid M' \mid }^2=\int d\phi{\mid M \mid }^2$, and $k_\perp$ is the
magnitude of ${\bf k_\perp}$.
As we are interested in the small $x$ region, we neglect terms containing higher powers of $x_B$; also as $z<1$, we neglect terms containing higher powers of $z$ and kept up to $z^2$. We also keep terms only up to $({k^2_\perp\over M^2_p})$.
The leading terms in the numerator of the $cos(2\phi_h)$ asymmetry come only from the first Feynman diagram.
These terms are given in the appendix.
The denominator of the $cos(2\phi_h)$ asymmetry, which is defined below, is simply the cross section integrated over the azimuthal angle $\phi_h$. The leading terms in the cross section comes from $f_1^g$ term. All the terms corresponding to $h_1^{\perp g}$ are suppressed by $k_{\perp}^2/M_p^2$. Hence, from the approximations we mentioned above, the leading terms in the cross section in the denominator of $cos(2\phi_h)$ asymmetry are coming from $M_1M_1,~M_1M_2,~M_1M_3$. These contributions are given in the appendix.\\
The differential cross section then can be given as
\begin{align} \label{csf}
\frac{d\sigma}{dydx_Bdzd^2\textbf{P}_{hT}}&=\frac{1}{256\pi^4}\frac{1}{x_B^2s^3y^2z(1-z)}\int k_{\perp}dk_{\perp}\nonumber\\&
\{(A_0+A_1cos\phi_h)f_1^g(x,\textbf{k}_{\perp}^2) \}+
\frac{k_{\perp}^2}{M_p^2}\{(B_0+B_1cos\phi_h+B_2cos2\phi_h)h_1^{\perp g}(x,\textbf{k}_{\perp}^2) \}
\end{align}
The coefficients $A_0, A_1, B_0, B_1$ and $B_2$ are given in the appendix. The $cos(2\phi)$ asymmetry is defined as
\begin{eqnarray}
\langle cos(2\phi_h)\rangle=\frac{\int d\phi_hcos(2\phi_h)d\sigma}{\int d\phi_h d\sigma}
\end{eqnarray}
In order to estimate the $cos(2\phi_h)$ asymmetry, we need to parametrize the TMDs. We discuss two parametrization models, Gaussian parameterization
of the TMDs and McLerran-Venugopalan(MV) model. We also calculate the upper bound of the asymmetry.
\subsection {Gaussian parametrization of the TMDs}
Both for the linearly polarized gluon distribution and the unpolarized gluon TMD, a Gaussian parametrization is
used widely in the literature. The linearly polarized gluon distribution satisfies the model independent positivity bound
\cite{Mulders:2000sh};
\begin{eqnarray}
\frac{\textbf{k}_{\perp}^2}{2M_p^2}\left|h_1^{\perp g}(x,\textbf{k}_{\perp}^2)\right| \leq f_1^g(x,\textbf{k}_{\perp}^2)
\label{positivity}
\end{eqnarray}
The Gaussian parametrizations satisfy the positivity bound but does not saturate it. They are as follows
\cite{Boer:2012bt,Mukherjee:2015smo, Mukherjee:2016cjw};
\begin{eqnarray}
f_1^g(x,\textbf{k}_{\perp}^2)=f_1^g(x,\mu)\frac{1}{\pi\langle k_{\perp}^2\rangle}e^{-k_{\perp}^2/\langle k_{\perp}^2\rangle}
\end{eqnarray}
\begin{eqnarray}
h_1^{\perp g}(x,\textbf{k}_{\perp}^2)=\frac{M_p^2f_1^g(x,\mu)}{\pi\langle k_{\perp}^2\rangle^2}\frac{2(1-r)}{r}e^{1-\frac{k_{\perp}^2}{r\langle k_{\perp}^2\rangle}}
\end{eqnarray}
where, $r(0<r<1)$ is a parameter, in our numerical estimates we took $r=1/3$. $f_1^g(x, \mu)$ is the gluon collinear PDF, which is measured at the scale $\mu=\sqrt{M^2+P_{h\perp}^2}$ and it obeys the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) scale evolution. The width of the Gaussian, $\langle k_\perp^2 \rangle$, depends on the energy scale of the process.
Following \cite{ Boer:2012bt}, we took $\langle k_\perp^2 \rangle=0.25 ~ \mathrm{GeV}^2$.
The asymmetry increases on increasing model parameter $r$, reaches a maximum at $r\approx 0.4$ and then decreases,
but the variation of asymmetry is very small.
\subsection {Upper bound of the asymmetry}
The asymmetry reaches its maximum value when the positivity bound given by Eq. (\ref{positivity}) is saturated.
Using this, we calculate the upper bound of $|\langle cos(2\phi_h)\rangle|$ as below
\cite{Pisano:2013cya};
\begin{align}
|\langle cos(2\phi_h)\rangle|&=\left| \frac{\int d\phi_hcos(2\phi_h)d\sigma}{\int d\phi_h d\sigma}\right|\nonumber\\&
=\frac{\int k_{\perp}dk_{\perp}\textbf{k}_{\perp}^2|h_1^{\perp g}(x,\textbf{k}_{\perp}^2)|}{\int k_{\perp}dk_{\perp}2M_pf_1^g(x,\textbf{k}_{\perp}^2)}\frac{|B_2|}
{A_0}\leq\frac{|B_2|}{A_0}\equiv R
\end{align}
\begin{figure}[H]
\begin{minipage}[c]{0.99\textwidth}
\small{(a)}\includegraphics[width=7cm,height=6.5cm,clip]{fig2a.pdf}
\hspace{0.1cm}
\small{(b)}\includegraphics[width=7cm,height=6.5cm,clip]{fig2b.pdf}
\end{minipage}
\caption{\label{fig3} $cos(2\phi_h)$ asymmetry in $e+p\rightarrow e+ J/\psi +X$
process as function of
(a) $P_{hT}$ (left panel) and (b) $z$ (right panel) at $\sqrt{s}=45$ GeV (EIC) and $x_B=0.01$. The integration ranges are
$0<P_{hT}\leq3$ GeV, $0.3<z<0.9$ and $0.05<y<0.4$. For convention of lines see the legend in the plots.}
\label{figure2}
\end{figure}
\subsection{McLerran-Venugopalan (MV) model}
In the small $x$ region, the Weizs\"{a}cker-Williams (WW) type gluon distribution can be calculated in MV model
\cite{McLerran:1993ni, McLerran:1993ka, McLerran:1994vd}:
Within the nonperturbative McLerran-Venugopalan model, we can define the gluon distribution function inside an unpolarized large nucleus or inside an energetic proton, in the small $x$ limit. In this model, the analytical expression of the WW type unpolarized and linearly polarized gluon distributions are given by
\begin{figure}[H]
\begin{minipage}[c]{0.99\textwidth}
\small{(a)}\includegraphics[width=7cm,height=6.5cm,clip]{fig3a.pdf}
\hspace{0.1cm}
\small{(b)}\includegraphics[width=7cm,height=6.5cm,clip]{fig3b.pdf}
\end{minipage}
\caption{\label{fig3} $cos(2\phi_h)$ asymmetry in $e+p\rightarrow e+ J/\psi +X$
process as function of
(a) $P_{hT}$ (left panel) and (b) $z$ (right panel) at $\sqrt{s}=150$ GeV (EIC) and $x_B=0.01$. The integration ranges are
$0<P_{hT}\leq3$ GeV, $0.3<z<0.9$ and $0.005<y<0.04$. For convention of lines see the legend in the plots.}
\label{figure3}
\end{figure}
\begin{eqnarray}
f_1^g(x,\textbf{k}_{\perp}^2)=\frac{S_{\perp}C_F}{\alpha_s\pi^3}\int dr\frac{J_0(k_{\perp}r)}{r}\left(1-e^{-\frac{r^2}{4}Q^2_{sg}(r)}\right)
\end{eqnarray}
\begin{eqnarray}
h_1^{\perp g}(x,\textbf{k}_{\perp}^2)=\frac{S_{\perp}C_F}{\alpha_s\pi^3}\frac{2M_p^2}{k_{\perp}^2}\int dr\frac{J_2(k_{\perp}r)}{r\log(\frac{1}{r^2\Lambda_{QCD}^2})}\left(1-e^{-\frac{r^2}{4}Q^2_{sg}(r)}\right)
\end{eqnarray}
where $S_{\perp}$ is transverse size of the nucleus or nucleon. $Q_{sg}$ is the saturation scale, which in MV model,
is defined as $Q_{sg}^2=\alpha_sN_c\mu_A\ln\frac{1}{r^2\Lambda_{QCD}^2}$ and $\mu_AS_{\perp}=\alpha_s2\pi A$, where $A=1$ for
the proton. Following the approach of \cite{Bacchetta:2018ivt}, we have used a regularized version of the MV model in our calculation of the asymmetry. The ratio of linearly polarized and unpolarized distribution in MV model can be given by
\begin{eqnarray}
\frac{\textbf{k}_{\perp}^2}{2M_p^2}\frac{h_1^{\perp g}(x,\textbf{k}_{\perp}^2)}{f_1^g(x,\textbf{k}_{\perp}^2)}=\frac{\int dr\frac{J_2(k_{\perp}r)}{r\log(\frac{1}{r^2\Lambda_{QCD}^2})}\left(1-e^{-\frac{r^2}{4}Q^2_{sg0}\log(\frac{1}{r^2\Lambda_{QCD}^2})}\right)}{\int dr\frac{J_0(k_{\perp}r)}{r}\left(1-e^{-\frac{r^2}{4}Q^2_{sg0}\log(\frac{1}{r^2\Lambda_{QCD}^2})}\right)}
\end{eqnarray}
For $Q^2_{sg0}=(N_c/C_F)\times Q^2_{s0}$, where $Q^2_{s0}=0.35~{\mathrm{GeV}}^2$ at $x=0.01$ and $\Lambda_{QCD}=0.2~ {\mathrm{GeV}}$, the ratio is below $1$ for all $k_{\perp}$. Below we give our numerical results.
\section{Numerical Results}
\begin{figure}[H]
\begin{minipage}[c]{0.99\textwidth}
\small{(a)}\includegraphics[width=7cm,height=6.5cm,clip]{fig4a.pdf}
\hspace{0.1cm}
\small{(b)}\includegraphics[width=7cm,height=6.5cm,clip]{fig4b.pdf}
\end{minipage}
\caption{\label{fig3} $cos(2\phi_h)$ asymmetry in $e+p\rightarrow e+ J/\psi +X$
process as function of
(a) $P_{hT}$ (left panel) and (b) $z$ (right panel) at $\sqrt{s}=190$ GeV (EIC) and $x_B=0.005$. The integration ranges are
$0<P_{hT}\leq3$ GeV, $0.3<z<0.9$ and $0.006<y<0.05$. For convention of lines see the legend in the plots.}
\label{figure4}
\end{figure}
We have estimated the $cos(2\phi_h)$ asymmetry in $J/\psi$ production in the kinematics of EIC. MSTW2008 \cite{Martin:2009iq} is used for
collinear PDFs. We have used the DGLAP evolution for the collinear pdfs. We have not included TMD evolution. As stated in the introduction, we have used cuts on $z$, $0.3 < z < 0.9$. As we know, gluon initiated processes are enhanced at small $x$. In fact, small
$x$ values will be accessed at EIC, and this kinematical region will be very important in determining the gluon TMDs including the linearly polarized gluon TMD.
In this work, we have studied the $cos ~2 \phi$ asymmetry for EIC in the small $x$ region. It is to be noted that $x$ is related to the Bjorken variable $x_B$ through
Eq. \ref{xb}. Smaller $x$ values also restrict $Q^2$ to be small, in this
work we took $Q^2$ to be of the same order and bounded by $M^2$ ($1< Q^2 < 9 ~\mathrm{GeV}^2$) , which is the mass of
$J/\psi$. For both the parametrizations used, the asymmetry is negative, which is consistent with the LO calculation \cite{Mukherjee:2016qxa}.
In the plots, we show the magnitude of the asymmetry. CS LDMEs can be found for example in \cite{Chao:2012iv}. As only one state contributes in the
CS model, namely ${^3}{S}{_1}$ the asymmetry does not depend on the specific set of LDME. This is different from the CO model, where even at LO,
contribution comes from several states \cite{Mukherjee:2016qxa}, and the result depends on the choice of LDMEs. However, the unpolarized cross section will depend on the choice of LDMEs in both the models. In our previous work \cite{Mukherjee:2016qxa}, we compared with three set of LDMEs where one sets of LDMEs giving the unpolarized cross section that matches more with the experimental data than the other sets. Figs. \ref{figure2} , \ref{figure3} and \ref{figure4} show the upper bound of the asymmetry as well as an estimate using the Gaussian model,
at $\sqrt{s}=45$~GeV, $150$~GeV and $190$~GeV respectively, as a function of $P_{hT}$ and $z$ .
Corresponding $x_B$ values are $x_B=0.01,~0.01$ and $0.005$ respectively; ranges of $y$ integration are $0.05<y<0.4,~0.005<y<0.04$ and
$0.006<y<0.05$ respectively. $y$ is constrained by the choice of $Q^2$ and $x_B$. The transverse momentum $P_{h\perp}$ of $J/\psi$ is
taken in range $0<P_{h\perp}<3$~ GeV. Energy fraction $z$ is in the range $0.3<z<0.9$ for all these plots.
The upper bound of the asymmetry increases with increase of $\sqrt{s}$ for the same $x_B$, it reaches maximum near $P_{hT}
\approx 3$~ GeV, the maximum is about $4\%$ for $\sqrt{s}=150$~GeV. However, for smaller $x_B$, asymmetry decreases.
The asymmetry reaches a peak near $z=0.6$ for the kinematical cuts chosen. The qualitative behavior of the asymmetry remains the
same for all $\sqrt{s}$. The Gaussian model gives smaller asymmetry. Fig. \ref{figure5} shows a comparison of the upper bound of
the asymmetry with that calculated in Gaussian model as well as MV model, as a function of $P_{hT}$, for two different values of $z$,
(a) $z=0.5$ and (b) $z= 0.7$. For both these plots we have taken fixed value of $x=0.01$, $Q^2=9~{\mathrm{GeV}}^2$ and $0.2 < y <1$. For (a)
$\sqrt{s}$ is in the range $61$ to $181$~ GeV, and for (b) $\sqrt{s}$ is in the range $58$ to $182$~ GeV. Asymmetry in the MV model is
smaller compared to the Gaussian model, and both lie below the upper bound. The asymmetry is higher for higher values of $z$.
\begin{figure}[H]
\begin{minipage}[c]{0.99\textwidth}
\small{(a)}\includegraphics[width=7cm,height=6.5cm,clip]{fig5a.pdf}
\hspace{0.1cm}
\small{(b)}\includegraphics[width=7cm,height=6.5cm,clip]{fig5b.pdf}
\end{minipage}
\caption{\label{fig3} $cos(2\phi_h)$ asymmetry in $e+p\rightarrow e+ J/\psi +X$
process as function of
$P_{hT}$ for (a) fixed $Q^2=9~{\mathrm{GeV}}^2$, $x=0.01$ and $z=0.5$ and (b) fixed $Q^2=9~{\mathrm{GeV}}^2$, $x=0.01$ and $z=0.7$. In both the case integration range on $y$ is $0.2<y<1$. For convention of lines see the legend in the plots.}
\label{figure5}
\end{figure}
\section{conclusion}
In this work, we have calculated the $cos~2 \phi$ asymmetry in electroproduction of $J/\psi$ at EIC, that probes the linearly polarized gluon distribution in the unpolarized proton.
We calculated the asymmetry in the kinematical region $z<1$, where the NLO subprocess $\gamma^* +g \rightarrow J/\psi +g$ gives the leading contribution. The gluon TMDs probed
in this process are of Weizs\"acker-Williams (WW) type. As gluon distributions pay an important role in the small $x$ region, we investigate the asymmetry in the small $x$ kinematical
region, using a Gaussian parametrization of the TMDs as well as in McLerran-Venugopalan model. We also show the upper bound of the asymmetry saturating the inequality for the
linearly polarized gluon distribution. At EIC, low values of $x$ also restrict the $Q^2$ (virtuality of the photon) values. We have calculated the $J/\psi$ production amplitude
in NRQCD based color singlet (CS) approach. The asymmetry in the kinematical region considered is small but sizable. The magnitude of the asymmetry may depend on the production
mechanism of the quarkonium. As shown in \cite{Mukherjee:2016qxa}, CS mechanism underestimates the $J/\psi$ production at HERA, and both CS and CO contributions are needed to describe
the data. In CO formalism contribution will come from several LDMEs in the final state, which may enhance the asymmetry. We plan to see the effect of the CO mechanism on the asymmetry
in a future work. Another interesting study would be the effect of small-$x$ evolution on the asymmetry. In any case, the $cos~2 \phi$ asymmetry in $J/\psi$ production at the EIC will
be an important tool to gain information on the WW type linearly polarized gluon distribution.
\section{Acknowledgement}
We thank P. J. Mulders, E. Petreska and D. Boer for discussion. Part of the work of AM was done at NIKHEF, Amsterdam, the visit was supported by the European Research Council under the "Ideas" program QWORK (contract 320389).
\section{Appendix}
All the amplitude squares and the coefficients are integrated over $\phi$, where $\phi$ and $\phi_h$ are the azimuthal angle of initial gluon and $J/\psi$ respectively.
\begin{eqnarray}
M'_iM'_j=\int d\phi M_iM_j
\end{eqnarray}
\begin{equation}
\begin{split}
M'_1M'_1=&\big\{f_1^g\times 128 \pi M^4 \big\{M^4 (z-1)^3+M^2 \big({P_{h\perp}}^2(z-1) (8 (z-1) z+3)\\
&+s y \big({x_B} \big(z \big((1-6y (y+2)) z^2\\
&+2 y (y+4) z-2 y+z+1\big)-1\big)-x(z-1)^3\big)\big)\\
&+2 {P_{h\perp}} \sqrt{{x_B}}\sqrt{1-y} z \sqrt{s y} \cos ({\phi_h}) \big(M^2 (z(4 z-5)+2)\\
&+{P_{h\perp}}^2 (z (24 z-17)+4)-2 s x y (z (4 z-3)+1)\big)\\
&+{P_{h\perp}}^4 (z (z (11z-23)+13)-3)+{P_{h\perp}}^2 s y \big(x (z (-2 (z-5)z-9)+3)\\
&+{x_B} \left(z \left(-3 (y (5 y+16)-6) z^2+2 (y(y+14)-5) z-6 y+7\right)-3\right)\big)\\
&+s^2 x {x_B}y^2 z (z ((y-2) y (2 z-1)+2 (8 z-7))+4)\big\}\\
&+\frac{k_{\perp}^2h_1^{\perp g}}{M_p^2}\times 64 \pi M^4 \big\{M^4\left(-(z-1)^3\right)+M^2\big({P_{h\perp}}^2 (z (-4 (z-2) z-7)+3)\\
&+s y \big(x(z-1)^3+{x_B} z \big((y (7 y+18)-7) z^2-2 y (2 y+5)z\\
&+2y+z-1\big)+{x_B}\big)\big)+2 {P_{h\perp}}\sqrt{{x_B}} z \big({P_{h\perp}} s \sqrt{{x_B}} (y-1)y (z (5 z-4)+2)\\
&\times\cos (2\phi_h)-\sqrt{1-y} \sqrt{sy} \cos (\phi_h) \big(M^2 (1-3 z)^2+{P_{h\perp}}^2(z (13 z-12)+5)\\
&+s x y (z (6z-5)+2)\big)\big)+{P_{h\perp}}^4 (z ((7-3 z)z-6)+3)\\
&+{P_{h\perp}}^2 s y \big({x_B} \big(z \big((3 y(3 y+8)-22) z^2-2 (y (y+13)-8) z\\
&+10 y-9\big)+3\big)-x(z (2 z (z+1)-5)+3)\big)\\
&-s^2 x y^2 z \big(x \left(6z^2-4 z+1\right)+{x_B} z \big((y-2) y (4 z-3)\\
&+26 z-20\big)-2{x_B} (y-3)\big)\big\}\big\}/\big\{x y^2 (z-1)^2 z \left(M^2+sy ({x_B}-x)\right)^2\\
&\times\left(M^2+{P_{h\perp}}^2-s {x_B}y (z-2) z\right)^2\big\}\\
\end{split}
\end{equation}
\begin{equation}
\begin{split}
M'_1M'_2=&\big\{f_1^g\times 64 \pi M^6 \big\{M^2 (z-1) (2 z-3)+{P_{h\perp}}^2 (2 z (4 z-9)+9)\\
&-2 {P_{h\perp}} \sqrt{{x_B}} \sqrt{1-y} (z-1) z (3 z-8) \sqrt{s y} \cos ({\phi_h})\\
&-s y (z-1) \big(x
(z+1) (2 z-3)+{x_B} z \big(3 (y (y+6)-6) z^2\\
&-6 (y(y+4)-3) z+4 y+3\big)+2 {x_B}y+{x_B}\big)\big\}\\
&-\frac{k_{\perp}^2h_1^{\perp g}}{M_p^2}\times 32 \pi M^6 \big\{M^2 (z-1) (2 z-3)+{P_{h\perp}}^2 (2 z (3 z-7)+7)\\
&-2 {P_{h\perp}} \sqrt{{x_B}} \sqrt{1-y} (z-1) (2 z-3) (3 z+1) \sqrt{s y} \cos ({\phi_h})\\
&-s y (z-1) \big(x (3 z-5)+{x_B} z \big((y (5 y+6)-6) z^2-2 y (5 y+7) z\\
&+2 y (y+2)+6 z+5\big)+{x_B} (4 y-1)\big)\big\}\big\}/\big\{s x^2 y^3 (z-1) z^3\\
&\times \left(M^2+s y ({x_B}-x)\right)^2 \left(M^2+{P_{h\perp}}^2-s {x_B} y (z-2) z\right)\big\}
\end{split}
\end{equation}
\begin{equation}
\begin{split}
M'_1M'_3=&\big\{-f_1^{g}\times 64 \pi M^8 \big\{2 M^2 (z-1)^2 (3 z-5)+4 {P_{h\perp}}^2 (z-1) (z (6 z-13)+8)\\
&-2 {P_{h\perp}} \sqrt{{x_B}} \sqrt{1-y} (z-1)^2 (z (14 z-25)+2) \sqrt{s y} \cos ({\phi_h})\\
&+s y \big(-x (3 z-10) (z-1)^2+{x_B} z \big(y^2 (z (z (31 z-57)+43)-9)\\
&+2 y (z (z (31 z-59)+53)-23)-2 z (5 z (5 z-8)+39)+56\big)\\
&-2 {x_B} ((y-4) y+10)\big)\big\}\\
&+\frac{k_{\perp}^2h_1^{\perp g}}{M_p^2}\times 32 \pi M^8 \big\{2 M^2 (z-1)^2 (7 z-9)+2 {P_{h\perp}}^2 (z-1) (z (14 z-41)+29)\\
&-4 {P_{h\perp}} \sqrt{{x_B}} \sqrt{1-y} (z-1)^2 (7 z (2 z-3)+3) \sqrt{s y} \cos ({\phi_h})\\
&+s y \big({x_B} \big(y^2 (z (z (z (55 z-79)+45)-3)-4)\\
&+2 y (z (z (z (59 z-96)+76)-30)+5)\\
&+2 z (z ((51-43 z) z-44)+37)-30\big)\\
&-x (z-1)^2 (3 z (4 z+1)-14)\big)\big\}\big\}/\big\{s x^2 y^3 (z-1)^2 z^2 \left(M^2+s y ({x_B}-x)\right)^2\\
&\times \left(M^2+{P_{h\perp}}^2-s {x_B} y (z-2) z\right)^2\big\}
\end{split}
\end{equation}
and the coefficients in final expression of cross section, Eq.~(\ref{csf}), are as follows:
\begin{equation}
\begin{split}
A_0=& 64 \pi M^4 \big\{\big\{M^2 (z-1) \left(M^2+{P_{h\perp}}^2-s{x_B} y (z-2) z\right) \big(M^2 (z-1) (2 z-3)\\
&+{P_{h\perp}}^2(2 z (4 z-9)+9)
-s y (z-1) \big(x (z+1) (2 z-3)\\
&+{x_B} z\left(3 (y (y+6)-6) z^2-6 (y (y+4)-3) z+4 y+3\right)+2 {x_B}y+{x_B}\big)\big)\\
&+M^4 z \big(-2 M^2 (z-1)^2(3 z-5)-4 {P_{h\perp}}^2 (z-1) (z (6 z-13)+8)\\
&+s y \big(x (3 z-10)(z-1)^2+{x_B} z \big((50-31 y (y+2)) z^3\\
&+(y (57 y+118)-80)z^2-y (43 y+106) z\\
&+y (9 y+46)+78 z-56\big)+2 {x_B} ((y-4)y+10)\big)\big)\big\}/s\\
&+2 x y z^2 \big(M^4 (z-1)^3+M^2\big({P_{h\perp}}^2 (z-1) (8 (z-1) z+3)\\
&+s y \big({x_B}\left(z \left((1-6 y (y+2)) z^2+2 y (y+4) z-2y+z+1\right)-1\right)\\
&-x (z-1)^3\big)\big)+{P_{h\perp}}^4 (z (z(11 z-23)+13)-3)\\
&+{P_{h\perp}}^2 s y \big(x (z (-2 (z-5)z-9)+3)+{x_B} \big(z \big(-3 (y (5 y+16)-6) z^2\\
&+2 (y(y+14)-5) z-6 y+7\big)-3\big)\big)\\
&+s^2 x {x_B} y^2 z(z ((y-2) y (2 z-1)+2 (8 z-7))+4)\big)\big\}/\big\{x^2 y^3 (z-1)^2
z^3 \\
&\times\left(M^2+s y ({x_B}-x)\right)^2 \left(M^2+{P_{h\perp}}^2-s
{x_B} y (z-2) z\right)^2\big\}
\end{split}
\end{equation}
\begin{equation}
\begin{split}
A_1=&-128 \pi M^4 {P_{h\perp}} \sqrt{{x_B}} \sqrt{1-y} \big\{-2M^4 (z-1)^2 (7 (z-2) z+5)\\
&+M^2 \big({P_{h\perp}}^2 (z-1)^2 (3z-8)-s y z \big(2 x z (z (4 z-5)+2)\\
&+{x_B} (z-2) (3 z-8)(z-1)^2\big)\big)+2 s x y z^2 \big({P_{h\perp}}^2 ((17-24 z)z-4)\\
&+2 s x y (z (4 z-3)+1)\big)\big\}/\big\{x^2 y^2 (z-1)^2 z^2\sqrt{s y} \left(M^2+s y ({x_B}-x)\right)^2\\
&\times\left(M^2+{P_{h\perp}}^2-s {x_B} y (z-2) z\right)^2\big\}
\end{split}
\end{equation}
\begin{equation}
\begin{split}
B_0=& 32 \pi M^4 \big\{\big\{-M^2 (z-1) \big(M^2+{P_{h\perp}}^2-s{x_B} y (z-2) z\big) \big(M^2 (z-1) (2 z-3)\\
&+{P_{h\perp}}^2(2 z (3 z-7)+7)-s y (z-1) \big(x (3 z-5)+{x_B} z \big((y(5 y+6)-6) z^2\\
&-2 y (5 y+7) z+2 y (y+2)+6 z+5\big)+{x_B} (4y-1)\big)\big)\\
&+M^4 z \big(2 M^2 (z-1)^2 (7 z-9)+2{P_{h\perp}}^2 (z-1) (z (14 z-41)+29)\\
&+s y \big({x_B} \big(y^2(z (z (z (55 z-79)+45)-3)-4)\\
&+2 y (z (z (z (59 z-96)+76)-30)+5)\\
&+2z (z ((51-43 z) z-44)+37)-30\big)\\
&-x (z-1)^2 (3 z (4z+1)-14)\big)\big)\big\}/{s}\\
&-2 x y z^2 \big(M^4 (z-1)^3+M^2\big({P_{h\perp}}^2 (z-1) (4 (z-1) z+3)\\
&-s y \big(x(z-1)^3+{x_B} z \big((y (7 y+18)-7) z^2\\
&-2 y (2 y+5) z+2y+z-1\big)+{x_B}\big)\big)\\
&+{P_{h\perp}}^4 (z (z (3z-7)+6)-3)+{P_{h\perp}}^2 s y \big(x (z (2 z (z+1)-5)+3)\\
&+{x_B}\big(z \big((22-3 y (3 y+8)) z^2+2 (y (y+13)-8) z\\
&-10y+9\big)-3\big)\big)+s^2 x y^2 z \big(x \big(6 z^2-4z+1\big)\\
&+{x_B} z ((y-2) y (4 z-3)+26 z-20)-2 {x_B}(y-3)\big)\big)\big\}/\big\{x^2 y^3 (z-1)^2 z^3\\
&\times \left(M^2+s y({x_B}-x)\right)^2 \left(M^2+{P_{h\perp}}^2-s {x_B} y (z-2)z\right)^2\big\}
\end{split}
\end{equation}
\begin{equation}
\begin{split}
B_1=&- 64 \pi M^4 {P_{h\perp}} \sqrt{{x_B}} \sqrt{1-y} \big\{M^4(z-1)^2 (z (4 z (7 z-12)+13)+3)\\
&+M^2 \big(s y z \left(2 x (1-3z)^2 z^2+{x_B} (z-2) (2 z-3) (3 z+1)
(z-1)^2\right)\\
&-{P_{h\perp}}^2 (z-1)^2 (2 z-3) (3 z+1)\big)+2 s xy z^3 \big({P_{h\perp}}^2 (z (13 z-12)+5)\\
&+s x y (z (6
z-5)+2)\big)\big\}/\big\{x^2 y^2 (z-1)^2 z^3 \sqrt{s y}
\left(M^2+s y ({x_B}-x)\right)^2 \\
&\times\left(M^2+{P_{h\perp}}^2-s
{x_B} y (z-2) z\right)^2\big\}
\end{split}
\end{equation}
\begin{equation}
\begin{split}
B_2=&\big\{128 \pi M^4 {P_{h\perp}}^2 s {x_B} (y-1) (z (5 z-4)+2)\big\}/\big\{x y
(z-1)^2 \\
&\times\left(M^2+s y ({x_B}-x)\right)^2\left(M^2+{P_{h\perp}}^2-s {x_B} y (z-2) z\right)^2\big\}
\end{split}
\end{equation}
\bibliographystyle{apsrev}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,484 |
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OH013 UNCG in the 1960s Oral History Collection
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,199 |
{"url":"https:\/\/rao.im\/mathematics\/2018\/04\/10\/computing-normals\/","text":"# Area Forms & Normals\n\nTo compute the area form of $S^3$, I used a general formula for $S^n \\subset \\mathbb{R}^{n+1}$ that I found in Lee\u2019s Introduction to Smooth Manifolds.\n\n$\\begin{equation*} \\Omega = \\sum_{i=1}^{n+1} (-1)^{i+1} x_{i} dx_0 \\wedge \\cdots \\wedge \\widehat{dx_{i}} \\wedge \\cdots \\wedge dx_{n} \\end{equation*}$\n\nis the area form of $S^n$, in terms of its coordinate functions. While trying to understand this formula, I was reminded of the cross product formula, which is an alternating sum of determinants. Well, sure, alternating forms like $$\\Gamma_i = dx_1 \\wedge \\cdots \\wedge \\widehat{dx_{i}} \\wedge \\cdots \\wedge dx_{n+1}$$ are really determinants in disguise. Suppose $v_1, \\ldots,v_n$ are tangent vectors at some point on $S^n$. Individually, 1-forms $dx_{j}(v)$ are linear functionals and act on tangent vectors $v \\in T_{p}S^n$. Essentially, $dx_{j}(v_k )$ is a portion of the derivative $Dx_j$ in the $v_k$ direction; the directional derivative. Alternatively, it is the action of $v_k$ on coordinate $x_j$. I summarize these two descriptions below.\n\n\\begin{align*} dx_{j}(v_k) &= v_k \\star x_j = v_k \\cdot Dx_j \\end{align*}\n\nThe action of a vector on a function is denoted $\\star$. Also here $v \\in T_p S^n$ and $Dx_j$ are n-dimensional vectors. Implicitly, coordinates $x_i$ are functions of some local parameters $\\theta_1, \\cdots, \\theta_n$. $n$ is the dimension of $S^n$. Then explicitly,\n\n$\\begin{gather*} v = \\sum_{k=1}^{n} c_k \\frac{\\partial}{\\partial \\theta_k} \\in T_p S^n, \\end{gather*}$\n\nand $Dx_j$ is just a row in the derivative of $x$, $Dx : T_pS^n \\rightarrow T_q\\mathbb{R}^{n+1}$. In matrix form\n\n$Dx = \\begin{pmatrix} \\frac{\\partial x_1}{\\partial \\theta_1} & \\frac{\\partial x_1}{\\partial \\theta_2} & \\cdots & \\frac{\\partial x_1}{\\partial \\theta_n} \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ \\frac{\\partial x_{n+1}}{\\partial \\theta_1} & \\frac{\\partial x_{n+1}}{\\partial \\theta_2} & \\cdots & \\frac{\\partial x_{n+1}}{\\partial \\theta_n} \\\\ \\end{pmatrix}.$\n\nSince ${x_i}$ are coordinates, $Dx$ is full rank and embeds $T_pS^n \\hookrightarrow T_q\\mathbb{R}^{n+1}$, as vector space.\n\nAs an $n$-form evaluated on $v_1, \\ldots, v_n$\n\n$\\begin{equation*} \\Gamma_i(v_1, \\ldots,v_n) = \\frac{1}{n!}\\det\\Big(\\Big[v_k \\star x_j\\Big]_{j \\neq i}\\Big). \\\\ \\end{equation*}$\n\nContinuing by substituting $\\Gamma_i$ into the formula for $\\Omega$ yields\n\n\\begin{align*} \\Omega(v_1, \\ldots,v_n) &= \\sum_{i=1}^{n+1} (-1)^{i+1} x_{i} \\Gamma_i(v_1, \\ldots,v_n) \\\\ &= \\sum_{i=1}^{n+1} (-1)^{i+1} x_{i} \\frac{1}{n!}\\det\\Big(\\Big[v_k \\cdot Dx_j\\Big]_{j \\neq i}\\Big). \\\\ \\end{align*}\n\nThe last expression is exactly the recursive formula for the determinant of a yet larger matrix that contains all the $v_k \\cdot Dx_j$ and $x_i$ terms.\n\n\\begin{align*} \\Omega(v_1, \\ldots,v_n) &= \\frac{1}{n!} \\det \\begin{pmatrix} x_1 & x_2 & \\cdots & x_{n+1} \\\\ v_1 \\star x_1 & v_1 \\star x_1 & \\cdots & v_1 \\star x_{n+1} \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ v_n \\star x_1 & v_n \\star x_1 & \\cdots & v_n \\star x_{n+1} \\\\ \\end{pmatrix} \\\\ &= \\frac{1}{n!} \\det \\begin{pmatrix} x_1 \\ x_2 \\ \\cdots x_{n+1} \\\\ \\begin{bmatrix} v_1 \\\\ v_2 \\\\ \\vdots \\\\ v_n \\\\ \\end{bmatrix} \\begin{bmatrix} Dx_1 & Dx_2 & \\ldots & Dx_{n+1} \\\\ \\end{bmatrix} \\end{pmatrix} \\end{align*}\n\nThe final $n+1 \\times n+1$ matrix description above I think shows more clearly that the rows are $n+1$ vectors, $$\\{\\tilde{v_1},\\ \\tilde{v_2}, \\cdots, \\tilde{v_n}, \\ x \\}$$, where the $\\tilde{v_k} = Dx \\cdot v_k$ represent $T_pS^n$ as a co-dimension $1$ plane\/subspace of $T_q\\mathbb{R}^{n+1}$. To be a proper area-form $\\Omega_p(\\tilde{v_1},\\ \\tilde{v_2}, \\cdots, \\tilde{v_n})$ must always be positive, which, in particular means\n\n$\\Omega_p(\\tilde{v_1},\\ \\tilde{v_2}, \\ldots, \\tilde{v_n}) = \\frac{1}{n!} \\det \\begin{bmatrix} x \\\\ \\tilde{v_1} \\\\ \\tilde{v_2} \\\\ \\vdots \\\\ \\tilde{v_n} \\\\ \\end{bmatrix} > 0.$\n\nFor clarity I have written $\\Omega$ as a form on a subspace $V^n \\subset \\mathbb{R}^{n+1}$. The $\\det > 0$ condition implies that $$\\{\\tilde{v_1},\\ \\tilde{v_2}, \\cdots, \\tilde{v_n}, \\ x \\}$$ are mutually independent. Great! This $\\det > 0$ condition forces $x$ to at least have a normal component. Though it\u2019s easy to see that $x$ is orthogonal to $T_pS^n$; I prove this in an appendix at the end of this post. However, the cross product makes this connection between the normal of $T_pS^n$ and $\\Omega$ explicit.\n\n## Cross Products\n\nI mentioned the cross product formula above because in computing a determinant one can also compute a normal vector. Lets review. Take a distinguished vector $a \\in \\mathbb{R}^{n+1}$, and vectors $v_1, v_2, \\cdots, v_n$ which form a basis of $V^n \\subset \\mathbb{R}^{n+1}$, a codimension $1$ subspace\/plane. So basically the situation we have above for tangent spaces of $S^n$. Arranging these vectors into a matrix we can relate the determinant of the matrix to the inner product of $a$ and a special vector that is only dependent on the $\\lbrace v_k\\rbrace$.\n\n\\begin{align*} \\det \\begin{bmatrix} a \\\\ v_1 \\\\ v_2 \\\\ \\vdots \\\\ v_n \\end{bmatrix} & = \\sum^{n+1}_{i=1}a_i (-1)^{i+1}M_{1,i} = \\langle a, \\eta \\rangle,\\\\ \\end{align*}\n\nwhere $\\eta = ( M_{1,1}, \\ -M_{1,2}, \\cdots, (-1)^{n+1}M_{1,n+1})$. The $M_{1,i}$ are called $(1,i)$-minors, they are determinants of submatrices, which only involve terms from the $v_k$. Okay so we\u2019ve converted a determinant ( or rather rewritten ) it as an inner product which is very helpful. Simply take $a = v_k$; then vectors $v_k, v_1, v_2, \\cdots, v_n$ are no longer mutually independent and\n\n\\begin{align*} 0 = \\det \\begin{bmatrix} v_k \\\\ v_1 \\\\ v_2 \\\\ \\vdots \\\\ v_n \\end{bmatrix} & = \\sum^{n+1}_{i=1}a_i (-1)^{i+1}M_{1,i} = \\langle v_k, \\eta \\rangle \\\\ \\end{align*}\n\nBoom!! $\\langle v, \\eta \\rangle = 0$ for any $v \\in V^n$. $\\eta$ is the normal we seek\u2013the cross product. With this in mind, lets return to $\\Omega$ by noting that $\\Omega$ evaluated on $V^n \\subset \\mathbb{R}^{n+1}$ has the same expression as the left hand side of the equation above that relates $V^n$ to the cross product; therefore\n\n\\begin{align*} \\Omega_p(\\tilde{v_1},\\ \\tilde{v_2}, \\ldots, \\tilde{v_n}) = \\frac{1}{n!} \\det \\begin{bmatrix} x \\\\ \\tilde{v_1} \\\\ \\tilde{v_2} \\\\ \\vdots \\\\ \\tilde{v_n} \\\\ \\end{bmatrix} &= \\frac{1}{n!} \\langle x, \\eta \\rangle > 0 \\end{align*}.\n\n$x$ must have a positive normal component\u2013which we knew. I think it\u2019s clearer from the above expression that $\\eta$ and the $\\Omega$ are dual. For me, this duality reinforces the picture of $\\Omega$ as a density, and its relationship with $\\eta$ gives a way to graph this density in the ambient space.\n\n## Appendix: Computing the Normal to $S^n$\n\nTo make things easy take coordinates $x = (x_1, x_2, \\ldots, x_n, \\sqrt{1 - r^2} )$ where $r^2 = x^2_1 + x^2_2 + \\cdots + x^2_n$. The cross product formula for these coordinates yields the normal $\\eta = (\\eta_i)$ where\n\n$\\eta_i = (-1)^{i+1}\\det \\begin{bmatrix} - & - & \\cdots & - & \\cdots & - & - \\\\ 1 & 0 & \\cdots & \\bf{0} & \\cdots & 0 & -\\frac{x_1}{x_{n+1}} \\\\ 0 & 1 & \\cdots & \\bf{0} & \\cdots & 0 & -\\frac{x_2}{x_{n+1}} \\\\ \\vdots & \\vdots & \\ddots & \\bf{\\vdots} & \\ddots & 0 & \\vdots \\\\ 0 & 0 & \\cdots & \\bf{1} & \\cdots & 0 & -\\frac{x_i}{x_{n+1}} \\\\ \\vdots & \\vdots & \\ddots & \\bf{\\vdots} & \\ddots & 0 & \\vdots \\\\ 0 & 0 & \\cdots & \\underbrace{\\bf{0}}_{\\bf{i-th\\ column}} & \\cdots & 1 & -\\frac{x_n}{x_{n+1}} \\\\ \\end{bmatrix}.$\n\nHopefully it\u2019s clear the matrix above, let\u2019s call it $A_i$, is $n \\times n$. The $i$-th column and first row are distinguished because they are missing. When $i \\leq n$ it\u2019s easier to compute the determinant of $A_i$ if the $i$-th row and first row are swapped, by say permutation $P_{1i}$. The bulk of\n\n$P_{1i} A_i = \\begin{bmatrix} 0 & 0 & \\cdots & 0 & 0 & \\cdots & 0 & -\\frac{x_i}{x_{n+1}} \\\\ 1 & 0 & \\cdots & 0 & 0 & \\cdots & 0 & -\\frac{x_1}{x_{n+1}} \\\\ 0 & 1 & \\cdots & 0 & 0 & \\cdots & 0 & -\\frac{x_2}{x_{n+1}} \\\\ \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\ddots & 0 & \\vdots \\\\ 0 & 0 & \\cdots & 1 & 0 & \\cdots & 0 & -\\frac{x_{i-1}}{x_{n+1}} \\\\ 0 & 0 & \\cdots & 0 & 1 & \\cdots & 0 & -\\frac{x_{i+1}}{x_{n+1}} \\\\ \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\ddots & 0 & \\vdots \\\\ 0 & 0 & \\cdots & 0 & 0 & \\cdots & 1 & -\\frac{x_n}{x_{n+1}} \\\\ \\end{bmatrix}$\n\nis an $n-1 \\times n-1$ identity matrix, in the lower left. Which makes our life easy. Knowing $\\det(P_{1i}) = \\det(P_{1i}^T) = (-1)^{i+1}$ and using the recursive formula for the determinant,\n\n\\begin{align*} \\det(P_{1i} A_i) = (-1)^{n}\\frac{x_i}{x_{n+1}} & \\Longrightarrow \\det(A_i) = (-1)^{i+1}(-1)^{n}\\frac{x_i}{x_{n+1}} \\\\ & \\Longrightarrow \\eta_i = (-1)^{i+1}(-1)^{i+1}(-1)^{n}\\frac{x_i}{x_{n+1}} \\\\ \\end{align*}\n\nfor $i \\leq n$ and $\\eta_{n+1} = (-1)^n$.\n\n$\\eta = \\Big((-1)^n \\frac{x_1}{x^{n+1}}, \\cdots ,(-1)^n \\frac{x_n}{x^{n+1}}, (-1)^n\\Big)$\n\nlooks like it\u2019s in homogeneous coordinates. Anyway, it\u2019s easy to see that $x = (-1)^n x_{n+1} \\eta$. I wonder why for these coordinates the orientation of $\\eta$, the normal, alternates depending on the parity of dimension.","date":"2022-08-09 22:24:39","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 1.0000085830688477, \"perplexity\": 344.32880376801137}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-33\/segments\/1659882571090.80\/warc\/CC-MAIN-20220809215803-20220810005803-00229.warc.gz\"}"} | null | null |
Q: Do people tend to be more hostile toward users with default gravatars? When I signed up, I encountered some hostility, but it seems to have gone down since I added a personalized image. Do people on here tend to be more hostile toward users who have a default gravatar?
A: No, I don't think so. There are plenty of regular users on various sites I've used who still use the default avatar, and they don't cop hostility just because of that.
You may be mistaking correlation for causation: you might have changed your profile picture around the same time something else changed. Your behaviour might have changed, for instance, or you've simply been interacting with people who are being less hostile.
Ultimately, it's your behaviour that determines peoples' hostility or lack thereof. If you have 1 rep and the default avatar or you're totally new, you'll receive respect if you're engaging with people constructive. If you notice correlation between those factors and hostility, it probably isn't because they have 1 rep and the default answer - it might be because the person is new to the community, unaware of how it works, and grating against the expectations of the members of the community. The fact they have only 1 rep and the default avatar is an incidental and unimportant detail compared to their behaviour.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,518 |
MoviesTech
November 21, 2015 | Conrad Schafman
Totally Dope
Ten years ago this month a movie about Johnny Cash named Walk the Line opened across America to the tune of $22 million. It quadrupled its budget, won Reese Witherspoon an Oscar, launched Joaquin Phoenix briefly into the stratosphere (before … Read More
November 25, 2014 | Michelle
The Windows 8 platform is a "large reason" why consumers are hesitant to buy 2-in-1 tablets, according to a report out Tuesday by the International Data Corporation.
The report also stated that worldwide sales of tablets will take a tumble in … Read More
Microsoft announced Tuesday that its dropping the price of its Xbox One- special edition bundles included- to the all-time low of $329 for Black Friday and Cyber Monday. This comes just a few weeks after Microsoft slashed the price to $349 and … Read More
In a surprise move last week, Microsoft announced that it will allow iOS and Android users free access to its Office software.
Yes, that's right. The entire Microsoft Office Suite is available to iOS and Android users. That means that … Read More
November 3, 2014 | Michelle
So it's not exactly the science fiction do-it-all device we were hoping it would be, but Microsoft's new wearable device, Microsoft Band, is pretty darn close. It's spiffy, too.
Experts are giving it rave reviews and touting it as the … Read More
October 27, 2014 | Michelle 1
Starting Nov. 2, the price of the Xbox One will go down to $349 from its original price of $399.
Looks like Microsoft is hitting Sony harder than ever just in time for the holiday shopping season. Microsoft is trying … Read More
Microsoft is planning to release a smartwatch to compete with Google's Galaxy Gear and Apple's planned Watch just in time for the holiday season, according to Forbes.The watch will have a battery life of two days and will track a … Read More
If you've been following football season this year, you might have noticed that all the NFL sportscasters and announcers are fiddling around with Microsoft Surface Pro tablets. The only problem is that they may not even realize that the Microsoft … Read More
Plex is coming to Xbox and here's what you need to know!
October 6, 2014 | Michelle
Plex announced this weekend that its streaming services will make their way to Microsoft's Xbox One and Xbox 360. The software will be compatible with Xbox One's voice command and hand gestures making use incredibly easy, according to the Plex … Read More
Will Microsoft's Wireless Display Adapter kill Chromecast?
September 25, 2014 | Michelle
Microsoft this week introduced the Microsoft Wireless Display adapter, which appears to be a direct competitor to Google's Chromecast. The device works on both Windows and Android platforms.
The Microsoft Wireless Display adapter enables users to see what's on their … Read More
September 17, 2014 | Michelle 2
By now you may have heard about Microsoft's recent decision to acquire Minecraft developer, Mojang. But if you haven't, here's the gist: Microsoft will soon own the Minecraft brand, and the Mojang team will join Microsoft Studios. Microsoft has agreed to buy … Read More
Apple's October Event 2013
October 22, 2013 | Dionicios
Apple held its fall event today to unveil new iPads, Macbook Pros, Mac Pros, as well as to release its new operating system update, OS X Mavericks.
CEO Tim Cook took center stage in Cupertino, CA and began the event by touting the success … Read More | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,963 |
module NewRelic
module Agent
module Datastores
module MetricHelper
ROLLUP_METRIC = "Datastore/all".freeze
WEB_ROLLUP_METRIC = "Datastore/allWeb".freeze
OTHER_ROLLUP_METRIC = "Datastore/allOther".freeze
DEFAULT_PRODUCT_NAME = "ActiveRecord".freeze
OTHER = "Other".freeze
ALL = "all".freeze
ALL_WEB = "allWeb".freeze
ALL_OTHER = "allOther".freeze
def self.statement_metric_for(product, collection, operation)
"Datastore/statement/#{product}/#{collection}/#{operation}"
end
def self.operation_metric_for(product, operation)
"Datastore/operation/#{product}/#{operation}"
end
def self.product_suffixed_rollup(product, suffix)
"Datastore/#{product}/#{suffix}"
end
def self.product_rollup(product)
"Datastore/#{product}/all"
end
def self.suffixed_rollup(suffix)
"Datastore/#{suffix}"
end
def self.all_suffix
if NewRelic::Agent::Transaction.recording_web_transaction?
ALL_WEB
else
ALL_OTHER
end
end
def self.metrics_for(product, operation, collection = nil, generic_product = nil)
if overrides = overridden_operation_and_collection
if should_override?(overrides, product, generic_product)
operation = overrides[0] || operation
collection = overrides[1] || collection
end
end
suffix = all_suffix
# Order of these metrics matters--the first metric in the list will
# be treated as the scoped metric in a bunch of different cases.
metrics = [
operation_metric_for(product, operation),
product_suffixed_rollup(product, suffix),
product_rollup(product),
suffixed_rollup(suffix),
ROLLUP_METRIC
]
metrics.unshift statement_metric_for(product, collection, operation) if collection
metrics
end
def self.metrics_from_sql(product, sql)
operation = NewRelic::Agent::Database.parse_operation_from_query(sql) || OTHER
metrics_for(product, operation)
end
# Allow Transaction#with_database_metric_name to override our
# collection and operation
def self.overridden_operation_and_collection #THREAD_LOCAL_ACCESS
state = NewRelic::Agent::TransactionState.tl_get
txn = state.current_transaction
txn ? txn.instrumentation_state[:datastore_override] : nil
end
# If the override declared a product affiliation, abide by that
# ActiveRecord has database-specific product names, so we recognize
# it by the generic_product it passes.
def self.should_override?(overrides, product, generic_product)
override_product = overrides[2]
override_product.nil? ||
override_product == product ||
override_product == generic_product
end
end
end
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,049 |
// Tag.java
//
package de.ppi.samples.fuwesta.model;
import java.util.List;
import javax.persistence.Column;
import javax.persistence.Entity;
import javax.persistence.ManyToMany;
import de.ppi.fuwesta.jpa.helper.VersionedModel;
/**
* A tag which is used to mark a posting.
*
*/
@Entity
public class Tag extends VersionedModel {
/** The name of the Tag. */
@Column(nullable = false, unique = true)
private String name;
/**
* Flag if the tag is active.
*/
private boolean active = true;
/**
* The list of postings which have this tag.
*/
@ManyToMany()
private List<Post> postings;
/**
* Gets the name of the Tag.
*
* @return the name of the Tag
*/
public String getName() {
return name;
}
/**
* Sets the name of the Tag.
*
* @param name the new name of the Tag
*/
public void setName(final String name) {
this.name = name;
}
/**
* Checks if is flag if the tag is active.
*
* @return the flag if the tag is active
*/
public boolean isActive() {
return active;
}
/**
* Sets the flag if the tag is active.
*
* @param active the new flag if the tag is active
*/
public void setActive(boolean active) {
this.active = active;
}
/**
* Gets the list of postings which have this tag.
*
* @return the list of postings which have this tag
*/
public List<Post> getPostings() {
return postings;
}
/**
* Sets the list of postings which have this tag.
*
* @param postings the new list of postings which have this tag
*/
public void setPostings(final List<Post> postings) {
this.postings = postings;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,375 |
[jvm]
Content
@[JvmStatic](https://kotlinlang.org/api/latest/jvm/stdlib/kotlin.jvm/-jvm-static/index.html)()
fun [toJavaModifier](to-java-modifier.md)(modifiers: [Collection](https://kotlinlang.org/api/latest/jvm/stdlib/kotlin.collections/-collection/index.html)<[KoresModifier](../index.md)>): [Int](https://kotlinlang.org/api/latest/jvm/stdlib/kotlin/-int/index.html)
More info
Convert [KoresModifier](../index.md)s to Java Modifiers flags.
#### Return
Java modifiers flags ([Modifier](https://docs.oracle.com/javase/8/docs/api/java/lang/reflect/Modifier.html))
## Parameters
jvm
| Name| Summary|
|---|---|
| <a name="com.github.jonathanxd.kores.base/KoresModifier.Companion/toJavaModifier/#kotlin.collections.Collection[com.github.jonathanxd.kores.base.KoresModifier]/PointingToDeclaration/"></a>modifiers| <a name="com.github.jonathanxd.kores.base/KoresModifier.Companion/toJavaModifier/#kotlin.collections.Collection[com.github.jonathanxd.kores.base.KoresModifier]/PointingToDeclaration/"></a><br><br>Modifiers<br><br>
[jvm]
Content
@[JvmStatic](https://kotlinlang.org/api/latest/jvm/stdlib/kotlin.jvm/-jvm-static/index.html)()
fun [toJavaModifier](to-java-modifier.md)(codeModifier: [KoresModifier](../index.md)): [Int](https://kotlinlang.org/api/latest/jvm/stdlib/kotlin/-int/index.html)
More info
Convert a [KoresModifier](../index.md) to Java Modifiers flags.
#### Return
Java modifiers flags ([Modifier](https://docs.oracle.com/javase/8/docs/api/java/lang/reflect/Modifier.html))
## Parameters
jvm
| Name| Summary|
|---|---|
| <a name="com.github.jonathanxd.kores.base/KoresModifier.Companion/toJavaModifier/#com.github.jonathanxd.kores.base.KoresModifier/PointingToDeclaration/"></a>codeModifier| <a name="com.github.jonathanxd.kores.base/KoresModifier.Companion/toJavaModifier/#com.github.jonathanxd.kores.base.KoresModifier/PointingToDeclaration/"></a><br><br>Modifier to convert<br><br>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,716 |
Dendropsophus triangulum (common name: triangle treefrog) is a species of frog in the family Hylidae.
It is found in the upper Amazon Basin in Bolivia, western Brazil, Colombia, Ecuador, and Peru.
Dendropsophus triangulum is widespread but generally uncommon. It is most commonly found around temporary ponds in clearings near forest, but can be also found in forests. Breeding takes place in temporary ponds, where the tadpoles develop.
References
triangulum
Amphibians of Bolivia
Amphibians of Brazil
Amphibians of Colombia
Amphibians of Ecuador
Amphibians of Peru
Amphibians described in 1869
Taxa named by Albert Günther
Taxonomy articles created by Polbot | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,802 |
Q: Python3 - Pipenv install mysqlclient? Trying to install from pipenv with:
pipenv install mysqlclient
will reseult in:
Installing mysqlclient… Collecting mysqlclient Using cached
https://files.pythonhosted.org/packages/6f/86/bad31f1c1bb0cc99e88ca2adb7cb5c71f7a6540c1bb001480513de76a931/mysqlclient-1.3.12.tar.gz
Complete output from command python setup.py egg_info:
/bin/sh: 1: mysql_config: not found
Traceback (most recent call last):
File "", line 1, in
File "/tmp/pip-install-5vhtqgve/mysqlclient/setup.py", line 17, in
metadata, options = get_config()
File "/tmp/pip-install-5vhtqgve/mysqlclient/setup_posix.py", line 44, in get_config
libs = mysql_config("libs_r")
File "/tmp/pip-install-5vhtqgve/mysqlclient/setup_posix.py", line 26, in mysql_config
raise EnvironmentError("%s not found" % (mysql_config.path,))
OSError: mysql_config not found
----------------------------------------
Error: An error occurred while installing mysqlclient! Command
"python setup.py egg_info" failed with error code 1 in
/tmp/pip-install-5vhtqgve/mysqlclient/
This is likely caused by a bug in mysqlclient. Report this to its
maintainers.
I'm using a Debian and with another virtualenv it get the system package
python-mysqldb/testing,now 1.3.10-1 amd64
Pipenv won't use this one and won't install the other.
How can I solve this?
Thanks,BR
A: I fixed that problem with the following command:
brew install mysql
A: You probably need the mysql client lib for the OS.
sudo apt install libmysqlclient-dev
Then you should be able to:
pipenv install mysqlclient
A: First install python-dev
sudo apt-get install python3-dev
and then install mysqlclient-dev version
sudo apt-get install python3-dev libmysqlclient-dev
A: I would recommend you to install the file first.
On windows I used
pip install "mysqlclient-1.3.13-cp35-cp35m-win_amd64.whl"
and the tried:
pip install mysqlclient.
It worked well.
A: if you are on Centos
Try: yum install mariadb-devel
this package includes the missing mysql-config
A: Try:
sudo apt-get install libmysqlclient-dev
and then:
sudo apt-get install libmariadbclient-dev
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,443 |
{"url":"https:\/\/open.oregonstate.education\/intermediatemicroeconomics\/chapter\/module-3\/","text":"# 3 Budget Constraints\n\n## The Policy QuestionHybrid Car Purchase Tax Credit\u2014Is It the Government\u2019s Best Choice to Reduce Fuel Consumption and Carbon Emissions?\n\nThe US government policy of extending tax credits toward the purchase of electric and hybrid cars can have consequences beyond decreasing carbon emissions. For instance, a consumer that purchases a hybrid car could spend less money on gas and have more money to spend on other things. This has implications for both the individual consumer and the larger economy.\n\nEven the richest people\u2014from Bill Gates to Oprah Winfrey\u2014can\u2019t afford to own everything in the world. Each of us has a budget that limits the extent of our consumption. Economists call this limit a budget constraint. In our policy example, an individual\u2019s choice between consuming gasoline and everything else is constrained by their current income. Any additional money spent on gasoline is money that is not available for other goods and services and vice versa. This is why the budget constraint is called a constraint.\n\nThe budget constraint is governed by income on the one hand\u2014how much money a consumer has available to spend on consumption\u2014and the prices of the goods the consumer purchases on the other.\n\n## Exploring the Policy Question\n\n1. What are some of the budget implications for a consumer who owns a hybrid car? What purchase decisions might this consumer make given their savings on gas, and how does this, in turn, affect the goals of the tax subsidy policy?\n\n## Learning Objectives\n\n### 3.1 Description of the Budget Constraint\n\nLearning Objective 3.1: Define a budget constraint conceptually, mathematically, and graphically.\n\n### 3.2 The Slope of the Budget Line\n\nLearning Objective 3.2: Interpret the slope of the budget line.\n\n### 3.3 Changes in Prices and Income\n\nLearning Objective 3.3: Illustrate how changes in prices and income alter the budget constraint and budget line.\n\n### 3.4 Coupons, Vouchers, and Taxes\n\nLearning Objective 3.4: Illustrate how coupons, vouchers, and taxes alter the budget constraint and budget line.\n\n### 3.5 Policy ExampleHybrid Car Purchase Tax Credit\u2014Is It the Government\u2019s Best Choice to Reduce Fuel Consumption and Carbon Emissions?\n\nLearning Objective 3.5: The Hybrid Car Tax Credit and Consumers\u2019 Budgets\n\n## 3.1 Description of the Budget Constraint\n\nLearning Objective 3.1: Define a budget constraint conceptually, mathematically, and graphically.\n\nThe is the set of all the bundles a consumer can afford given that consumer\u2019s income. We assume that the consumer has a budget\u2014an amount of money available to spend on bundles. For now, we do not worry about where this money or income comes from; we just assume a consumer has a budget.\n\nSo what can a consumer afford? Answering this depends on the prices of the goods in question. Suppose you go to the campus store to purchase energy bars and vitamin water. If you have $5 to spend, energy bars cost fifty cents each, and vitamin water costs$1 a bottle, then you could buy ten bars and no vitamin water, no bars and five bottles of vitamin water, four bars and two vitamin waters, and so on.\n\nThis table shows the possible combinations of energy bars and vitamin water the student can buy for exactly $5: Table 3.1.1 Combinations of energy bars and vitamin water Number of Energy bars Bottles of vitamin water 10 0 8 1 6 2 4 3 2 4 0 5 It is also true that you could spend less than$5 and have money left over. So we have to consider all possible bundles\u2014including consuming none at all.\n\nNote that we are focusing on bundles of two goods so that we maintain tractability (as explained in chapter 1), but it is simple to think beyond two goods by defining one of the goods as \u201cmoney spent on everything else.\u201d\n\nMathematically, the total amount the consumer spends on two goods, $A$ and $B$, is\n\n$P_{A}A+P_{B}B$(3.1)\n\nwhere $P_{A}$ is the price of good$A$ and $P_{B}$ is the price of good $B$. If the money the consumer has to spend on the two goods, their income, is given as $I$, then the budget constraint is\n\n$P_{A}A+P_{B}B\\leq I$(3.2)\n\nNote the inequality: this equation states that the consumer cannot spend more than their income but can spend less. We can simplify this assumption by restricting the consumer from spending all of their income on the two goods. This will allow us to focus on the frontier of the budget constraint. As we shall see in chapter 4, this assumption is consistent with the assumption\u2014if you can consume more (if your income allows it), you should because you will make yourself better off. With this assumption in place, we can write the budget constraint as\n\n$P_{A}A+P_{B}B=I$(3.3)\n\nGraphically, we can represent this budget constraint as in figure 3.1.1. We call this the : the line that indicates the possible bundles the consumer can buy when spending all their income.\n\n## 3.2 The Slope of the Budget Line\n\nLearning Objective 3.2: Interpret the slope of the budget line.\n\nFrom the graph of the budget constraint in section 3.1, we can see that the budget line slopes downward and has a constant slope along its entire length. This makes intuitive sense: if you buy more of one good, you are going to have to buy less of the other good. The rate at which you can trade one for the other is determined by the prices of the two goods, and they don\u2019t change.\n\nWe can see these details in figure 3.2.1.\n\nWe can find the slope of the budget line easily by rearranging so that we isolate $B$ on one side. Note that in our graph, B is the good on the vertical axis, so we will rearrange our equation to look like a standard function, with B as the dependent variable:\n\n$B=\\frac{I}{P_{B}}-\\frac{P_{A}}{P_{B}}A$(3.4)\n\nNow we have our budget line represented in point-slope form, where the first part, $\\frac{I}{P_{B}}$, is the vertical intercept, and the second part, $-\\frac{P_{A}}{P_{B}}$, is the slope coefficient on A.\n\nNote that the slope of the budget line is simply the ratio of the prices, also known as the price ratio. This is the rate at which you can trade one good for the other in the marketplace. To see this, let\u2019s return to the campus store with $5 to spend on energy bars and vitamin water. Suppose you originally decided to buy five bottles of vitamin water and placed them in a basket. After some thought, you decided to trade one bottle for two energy bars. Now you have four bottles of vitamin water and two energy bars in the basket. If you want even more bars, the same trade-off is available: two more bars can be had if you give up one bottle of vitamin water and so on. The slope of the budget line is also called the . The slope of the budget line also represents the of consuming more of good A because it describes how much of good B the consumer has to give up to consume one more unit of good A. The opportunity cost of something is the value of the next best alternative given up in order to get it. For example, if you decide to buy one more bottle of vitamin water, you have to give up two energy bars. Note that opportunity cost is not limited to the consumption of material goods. For example, the opportunity cost of an hour-long nap might be the hour of studying microeconomics that did not happen because of it. ## 3.3 Changes in Prices and Income Learning Objective 3.3: Illustrate how changes in prices and income alter the budget constraint and budget line. From our mathematical description of the budget line, we can easily see how changes in prices and income affect the budget line and a consumer\u2019s choice set\u2014the set of all the bundles available to them at current prices and income. Let\u2019s go back to equation 3.3: $P_{A}A+P_{B}B=I$ We know from the previous figure that the vertical intercept for is $\\frac{I}{P_{B}}$ and the horizontal intercept is $\\frac{I}{P_{A}}$. Now consider an increase in the price of good $A$. Notice that this increase does not affect the vertical intercept, only the horizontal intercept. As $P_{A}$ increases, $\\frac{I}{P_{A}}$ decreases, moving closer to the origin. This change makes the budget line \u201csteeper\u201d or more negatively sloped, as we can see from the slope coefficient: $-\\frac{P_{A}}{P_{B}}$. As $P_{A}$ increases, this ratio increases in absolute value, so the slope becomes more negative or steeper. What this means intuitively is that the trade-off or opportunity cost has risen. Now the consumer has to give up more of good $B$ to consume one more unit of good $A$. Next, consider a change in income. Suppose the consumer gets an additional amount of money to spend, so $I$ increases. $I$ affects both intercept terms positively, so as I increases, both $\\frac{I}{P_{B}}$ and $\\frac{I}{P_{A}}$ increase or move away from the origin. But $I$ does not affect the slope: $-\\frac{P_{A}}{P_{B}}$. Thus the shift in the budget line is a parallel shift outward\u2014the consumer with the additional income can afford more of both (as displayed in figure 3.3.2). ## 3.4 Coupons, Vouchers, and Taxes Learning Objective 3.4: Illustrate how coupons, vouchers, and taxes alter the budget constraint and budget line. Budget constraints can change due to changes in prices and income, but let\u2019s now consider other common features of the real-world market that can affect the budget constraint. We start with coupons or other methods firms use to give discounts to consumers. Consider a coupon or a sale that gives consumers a discount on the price of one item in our budget constraint problem. A coupon that entitles the bearer to a percentage off in price is essentially a reduction in price and has precisely the same effect. For example, a 20 percent off coupon on a good that normally costs$10 is the same as reducing the price to $8. More complicated is a coupon that gives a percentage off the entire purchase. In this case, the percentage is taken from the price of both items A and B in our budget constraint problem. In this case, the price ratio, or the slope of the budget constraint, does not change. For example, if the price of $A$ is regularly$10 and the price of $B$ is regularly $20, then with 20 percent off the entire purchase, the new prices are$8 and $16, respectively. Intuitively, we can see that this is equivalent to increasing the income and achieves the same result: by expanding the budget set, the consumer can now afford bundles with more of both goods. Table 3.4.1 The effect of a 20 percent discount on price Product Regular price ($) New price with 20 percent discount on entire purchase ($) Good A 10 8 Good B 20 16 Another common discount is on a maximum number of items. For example, you might see an advertisement for 20 percent off up to three units of good $A$. This discount lowers the opportunity cost of $A$ in terms of $B$ for the first three units but reverts back to the original opportunity cost thereafter. Figure 3.4.1 illustrates this. Taxes have the same effects as coupons but in the opposite direction. An is a tax based on the value of a good, such as a percentage sales tax. In terms of the budget constraint, an ad valorem tax on a specific good is equivalent to an increase in price, as shown in figure 3.4.2. A general sales tax on all goods has the effect of a parallel shift of the budget line inward. Note also that income taxes are, in this case, functionally equivalent to a general sales tax; they cause a parallel shift inward of the budget line. Vouchers that entitle the bearer to a certain quantity of a good (either value or quantity) are slightly more complicated. Let\u2019s return to your purchase of vitamin water and energy bars. Suppose you have a voucher for two free energy bars. You have$5.\n\nThe price of one energy bar is $0.50. The price of one bottle of vitamin water is$1.\n\nHow would we now draw your budget line?\n\nOne place to start is to consider the simple bundle that contains 2 energy bars and two bottles of vitamin water. Note that giving up one or two bars does not allow the student to consume any more vitamin water. The opportunity cost of these two bars is 0, and so the budget line in this part has a zero slope. After using the voucher, if the student wants more than two bars, the opportunity cost is the same as before\u2014.05 for a bottle of vitamin water\u2014and so the budget line from this point on is the same as before. The new budget line with the voucher has a kink.\n\n## 3.5 THE Policy ExampleHybrid Car Purchase Tax Credit\u2014Is It the Government\u2019s Best Choice to Reduce Fuel Consumption and Carbon Emissions?\n\nLearning Objective 3.5: The Hybrid Car Tax Credit and Consumers\u2019 Budgets\n\nFor several chapters, we have considered the policy of a hybrid car tax credit. In chapter 1, we thought about the various driving preferences of a typical consumer. In chapter 2, we translated these preferences into a type of utility function and corresponding indifference curve. Now let\u2019s think about the appropriate budget line for our policy example.\n\n### Graphs\n\nNormal budget constraint\nBudget constraint with coupon\nBudget constraint with voucher\n\n### Equations\n\nBudget constraint\n\n$P_{A}A+P_{B}B=I$\n\nGraphically produces a line that indicates the possible bundles the consumer can buy when spending all their income.\n\n$P_{A}A+P_{B}B$\n\nThe total amount a consumer spends on two goods, $A$ and $B$.\n\n$P_{A}A+P_{B}B\\leq I$\n\nAn inequality that states that the consumer cannot spend more than their income but can spend less.\n\n$B=\\frac{I}{P_{B}}-\\frac{P_{A}}{P_{B}}A$\n\nThe budget line represented in form, where the first part, $\\frac{I}{P_{B}}$, is the vertical intercept, and the second part, $-\\frac{P_{A}}{P_{B}}$, is the slope coefficient on A. The slope of this equation is the .","date":"2023-01-28 23:50:59","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.31880128383636475, \"perplexity\": 1006.6221811753582}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764499695.59\/warc\/CC-MAIN-20230128220716-20230129010716-00283.warc.gz\"}"} | null | null |
Наталія Максимова (наст. Наталія Євгенівна Порожнякова, нар. ) — українська художниця.
Біографія
Н. Є. Порожнякова народилася 13 березня 1971 року в місті Умань. У 1987 році закінчила Тираспіль художню школу. У 1989 році після закінчення Тираспольської загальноосвітньої школи вступила на художньо-графічний факультет Одеського державного педагогічного інституту ім. К. Д. Ушинського, який закінчила 1994 року. У 1994-1998 роках працювала викладачем образотворчого мистецтва в школі мистецтв Тирасполя.
У 1999 році — початок творчої діяльності — брала участь у виставках «Через Мистецтво маєте Світло» (Білгород-Дністровський краєзнавчий музей), «Індія очима одеситів» (виставка батика в Одеському Будинку вчених). У 1999—2000 роках працювала керівником гуртка «Юний художник» Центру позашкільної роботи Ленінський район (Одеса) Ленінського району Одеси.
У 2000-2003 роках навчалася в аспірантурі Південноукраїнського державного педагогічного університету ім. К.Д.Ушинського. З 2000 року — перші публікації статей у журналах та збірниках. У 2005-2006 роках
Художники Одеси
Члени Національної спілки художників України
Посилання
[Місто Умань]
[]
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Q: Total cost function in javascript i am having issues (very lost) in making a code that me and my friend were given to create.
So I am suppose to compute and return the average of all values in a given array named customerBalance, the array holds the amount of "what customers owe my business" (I dont own a business) and each item in the array holds the "customers balance", i also have to use a for() to process the array and calculate the average and divide by customerBalance length, and finally return the average.
Here is my code so far
function average() {
customerBalance
for(i=0,i++)
sum(customerBalance)
total=sum/5
return average;
I know that this is COMPLETELY wrong, I am not sure on how i start typing the array, please don't be harsh I would really like to know how to do this.
Thank you and have a great day
A: function average(customerBalance) {
if (customerBalance.length == 0) { // Prevent division by zero later
return 0;
}
var total = 0;
for (var i = 0; i < customerBalance.length; i++) {
total += customerBalance[i];
}
var average = total/customerBalance.length;
return average;
}
You have many problems:
*
*The parameter to a function goes in the parenthese after the function name, not the next line.
*Your for() syntax is all wrong. You need to put the initialization, repetition test, and increment separated by semicolons.
*There's no sum() function in Javascript. And even if there were, you would need to assign the result to a variable.
*When you calculate the average, you're putting it in total, but then you're returning average, which is the variable that contains the function, not the average you calculated.
Other recommendations:
*
*Don't hard-code the array size, use array.length to get it.
*Always put braces around the body of for, if, while, etc. even if they're just one line.
*Local variables should be declared with var.
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Your Source for Real Estate, Insurance and Appraisals in Olean, NY and across WNY. | {
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{"url":"https:\/\/gmatclub.com\/forum\/on-a-map-1-centimeter-represents-4-kilometers-a-circle-on-the-map-254117.html","text":"GMAT Question of the Day - Daily to your Mailbox; hard ones only\n\n It is currently 16 Jul 2018, 03:50\n\n### GMAT Club Daily Prep\n\n#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.\n\nCustomized\nfor You\n\nwe will pick new questions that match your level based on your Timer History\n\nTrack\nYour Progress\n\nevery week, we\u2019ll send you an estimated GMAT score based on your performance\n\nPractice\nPays\n\nwe will pick new questions that match your level based on your Timer History\n\n# On a map, 1 centimeter represents 4 kilometers. A circle on the map\n\n new topic post reply Question banks Downloads My Bookmarks Reviews Important topics\nAuthor Message\nTAGS:\n\n### Hide Tags\n\nMath Expert\nJoined: 02 Sep 2009\nPosts: 47015\nOn a map, 1 centimeter represents 4 kilometers. A circle on the map\u00a0[#permalink]\n\n### Show Tags\n\n23 Nov 2017, 05:41\n00:00\n\nDifficulty:\n\n(N\/A)\n\nQuestion Stats:\n\n84% (01:01) correct 16% (00:09) wrong based on 19 sessions\n\n### HideShow timer Statistics\n\nOn a map, 1 centimeter represents 4 kilometers. A circle on the map with a circumference of 3\u03c0 centimeters represents a circular region of what area?\n\n(A) 6\u03c0 km^2\n(B) 12\u03c0 km^2\n(C) 36\u03c0 km^2\n(D) 72\u03c0 km^2\n(E) 144\u03c0 km^2\n\n_________________\nSC Moderator\nJoined: 22 May 2016\nPosts: 1825\nOn a map, 1 centimeter represents 4 kilometers. A circle on the map\u00a0[#permalink]\n\n### Show Tags\n\n23 Nov 2017, 07:02\nBunuel wrote:\nOn a map, 1 centimeter represents 4 kilometers. A circle on the map with a circumference of 3\u03c0 centimeters represents a circular region of what area?\n\n(A) 6\u03c0 km^2\n(B) 12\u03c0 km^2\n(C) 36\u03c0 km^2\n(D) 72\u03c0 km^2\n(E) 144\u03c0 km^2\n\nAnswer C\n\nCircumference, 2\u03c0r, of circle on the map, means radius equals:\n$$2\u03c0r = 3\u03c0$$ cm\n$$r = \\frac{3}{2}$$ cm\n\nActual radius of the circular region?\n\n$$\\frac{Scale}{Actual} = \\frac{1cm}{4km}=\\frac{(\\frac{3}{2}cm)}{Xkm}$$\n\n$$x = (4) * (\\frac{3}{2}cm) = 6 km$$\n\nThat is, r = $$\\frac{3}{2}$$ cm on the map = actual length of r = $$6$$ km\n\nActual area of circular region in km, where actual $$r = 6$$ km:\n\n$$\u03c0r^2 = (6 km)^2* \u03c0 = 36\u03c0 km^2$$\n\nAnswer C\n_________________\n\nIn the depths of winter, I finally learned\nthat within me there lay an invincible summer.\n\n-- Albert Camus, \"Return to Tipasa\"\n\nGMAT Club Legend\nJoined: 16 Oct 2010\nPosts: 8121\nLocation: Pune, India\nRe: On a map, 1 centimeter represents 4 kilometers. A circle on the map\u00a0[#permalink]\n\n### Show Tags\n\n23 Nov 2017, 22:42\n1\nBunuel wrote:\nOn a map, 1 centimeter represents 4 kilometers. A circle on the map with a circumference of 3\u03c0 centimeters represents a circular region of what area?\n\n(A) 6\u03c0 km^2\n(B) 12\u03c0 km^2\n(C) 36\u03c0 km^2\n(D) 72\u03c0 km^2\n(E) 144\u03c0 km^2\n\nCircumference = 2\u03c0r = 3\u03c0 cm\n\nr = 3\/2 cm\n\n$$Area = \u03c0r^2 = 9 \u03c0\/4 cm^2$$\n\nSince 1 cm = 4 km, $$1 cm^2 = 16 km^2$$\n\n$$Area = 9 \u03c0\/4 * 16 km^2 = 36\u03c0 km^2$$\n\nAnswer (C)\n_________________\n\nKarishma\nPrivate Tutor for GMAT\nContact: bansal.karishma@gmail.com\n\nRe: On a map, 1 centimeter represents 4 kilometers. A circle on the map \u00a0 [#permalink] 23 Nov 2017, 22:42\nDisplay posts from previous: Sort by\n\n# On a map, 1 centimeter represents 4 kilometers. A circle on the map\n\n new topic post reply Question banks Downloads My Bookmarks Reviews Important topics\n\n# Events & Promotions\n\n Powered by phpBB \u00a9 phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT\u00ae test is a registered trademark of the Graduate Management Admission Council\u00ae, and this site has neither been reviewed nor endorsed by GMAC\u00ae.","date":"2018-07-16 10:50:16","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.48228558897972107, \"perplexity\": 13811.191911257085}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-30\/segments\/1531676589251.7\/warc\/CC-MAIN-20180716095945-20180716115945-00281.warc.gz\"}"} | null | null |
Binge drinking is on the rise
Sermo Team · March 30, 2021
As the world turned upside down, people in every country were forced to grapple with unprecedented isolation, fear, anxiety, loss of work, illness, children learning at-home, and more. According to studies published in JAMA Network, binge drinking quickly became a coping mechanism for many:
"As stay-at-home orders began in some US states as a mitigation strategy for coronavirus disease 2019 (COVID-19) transmission, Nielsen reported a 54% increase in national sales of alcohol for the week ending March 21, 2020, compared with 1 year before; online sales increased 262% from 2019. Three weeks later, the World Health Organization warned that alcohol use during the pandemic may potentially exacerbate health concerns and risk-taking behaviors…
Comparisons before and during the COVID-19 pandemic were made on number of days of any alcohol use and heavy drinking (defined as 5 or more drinks for men and 4 or more drinks for women within a couple of hours), and average number of drinks consumed over the past 30 days. The 15-item Short Inventory of Problems assessed adverse consequences associated with alcohol use in the past 3 months (eg, "I have taken foolish risks when I have been drinking"). Comparisons were made overall, and across self-reported sex, age, and race/ethnicity. Significant changes were assessed based on whether the 95% CI around change from wave 1 to wave 2 included 0. Analyses include weights…
On average, alcohol was consumed 1 day more per month by 3 of 4 adults. For women, there was also a significant increase of 0.18 days of heavy drinking (95% CI, 0.04-0.32 days), from a 2019 baseline of 0.44 days, which represents an increase of 41% over baseline. This equates to an increase of 1 day for 1 in 5 women. For women there was an average increase in the Short Inventory of Problems scale of 0.09 (95% CI, 0.01-0.17 items), over the 2019 average baseline of 0.23, representing a 39% increase, which is indicative of increased alcohol-related problems independent of consumption level for nearly 1 in 10 women…
In addition to a range of negative physical health associations, excessive alcohol use may lead to or worsen existing mental health problems, such as anxiety or depression, which may themselves be increasing during COVID-19. The population level changes for women, younger, and non-Hispanic White individuals highlight that health systems may need to educate consumers through print or online media about increased alcohol use during the pandemic and identify factors associated with susceptibility and resilience to the impacts of COVID-19…"
A poll of 200+ Sermo physicians revealed similar findings.
When asked which substances they have seen an increase of use among patients, this is how the physicians responded:
52% said Alcohol
26% Benzodiazepines, such as Xanax
13% said Marijuana
5% said Prescription opioids
2% Prescription stimulants, such as Adderall
0% Cocaine
Regarding the long-term health health effects of increased alcohol and drug use, 69% of physicians said the biggest burden on physicians and hospitals will be emotional and mental health issues; and 25% said diseases rising from abuse (heart, liver, kidney etc.)
In addition, 77% said healthcare systems do not offer sufficient educational information and resources to help patients cope with the increase in stress and anxiety that the pandemic has caused. And 63% believe there has also been an increase of alcohol and drug use among healthcare workers.
Even when the pandemic is behind us, 66% of physicians believe that unhealthy increases in alcohol and drug use will persist as long-term coping mechanisms. See below for a quick recap of our findings:
Below, Sermo physicians from around the world share their professional insights, perspectives, and opinions on this important topic—in their own words:
Alcohol excess could increase domestic violence, falls + fractures, drunk driving, hypertensive crisis, foster overweight, noncompliance in treatment for chronic diseases (like diabetes/hypertension), in some individuals suicide increase, etc. (etc)
Health systems do not face the reality representing the consequences of confinement by the pandemic. Depression, psychosis, anxiety, dependence to alcohol and drugs. It is necessary to implement a system of care for affected patients from the psychological point of view.
Easy access and addiction behind closed doors. Also financial stress from job loss, increased domestic violence, limited socialization opportunities in lockdown.
Pediatrics (excluding surgery)
Alcohol consumption, especially among women of child-bearing age may increase the incidence of 'Feta-alcohol syndrome and 'Feta-alcohol effect' These are preventable cause of mental handicaps in children, and the latter is difficult to diagnose without history, often resulting in anti-social behavior in these children. This is in addition to an increase in automobile accidents, & other illnesses!
Pediatrics (excluding surgery) – Neonatal & Perinatal Medicine
In Germany alcohol is drug no. 1.
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Off-label use of Ozempic impacts drug supply and availability for diabetes patients | {
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Minister of Finance to reveal three-year plan for budget cuts
Detailed plans to cut spending and increase taxes over the next three years are to be announced by the government this autumn.
The decision to announce the multi-year programme is designed to show the markets how Ireland will reduce its deficit and to give certainty to consumers about what lies ahead.
The move by Michael Noonan, The Minister for Finance, to include the details in the pre-budget outlook document – probably in October – would provide clarity about what will happen, according to senior sources.
It will also be seen as a measure to bolster confidence in the country's determination to deliver on its pledges under the EU/ IMF bailout.
While the precise level of detail to be included in the three-year programme remains to be finalised, it will include a new spending plan to emerge after the comprehensive spending review in all areas, now nearing completion.
The government also hopes that details of its tax strategy, while sure to provoke controversy, will give consumers a clear view of what they will face and thus help restore some level of confidence.
Final projections for 2012, to be completed in the early autumn, will show the exact outlook for 2012.The existing plan is for €3.6 billion in spending cuts and tax increases next year.
But the government is not ruling out the need for an increased adjustment of up to €4 billion, if this is required to reduce the 2012 budget deficit to 8.6 per cent, the level promised in the EU/IMF programme.
Sources said a clearer picture on the level of adjustment required in next year's budget would come when full-year figures for growth rates, taxes, job creation and unemployment had been evaluated in November.
This weekend, the government's projected adjustment of €3.6 billion was described as ''the working target'' by junior minister Brian Hayes.
But he warned that ''this may go up because the bigger question is getting the deficit down to 8.6 per cent''. Fears of a global double-dip recession have raised serious concerns about Ireland's tentative return to growth on the basis that export growth is driven primarily by foreign direct investment, particularly from the US companies.
''In the second half of the year there are ominous signs on the world economic stage in relation to the entire question of national debt and where economies are going," the minister said. ''Our task is to navigate our way through this as a small, open economy. If the world economy takes a hit, we take a hit."
The government's strategy would see the bulk of adjustments in the public expenditure rather than in taxation, but household and other charges will form part of the budget.
The public expenditure savings to be introduced by Brendan Howlin, the Minister for Public Expenditure and Reform, were described as ''critical in financing the budget for next year'', according to Hayes.
All departments have been participating in a detailed review of all their spending programmes, and reforms and money-saving measures are to be finalised in the weeks ahead in final negotiations between the departments and the Department of Finance
Source Sunday Business Post
By McCarthy Accountants|2011-08-22T11:32:20+00:00August 22nd, 2011|News|0 Comments | {
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Barcelona Confirm Neymar To Make Return After International Break
Barcelona have confirmed that Neymar will return to the club following the international break after captaining Brazil to gold at the Rio Olympics.
In a statement, the Liga champions said he would return on Sep. 8, meaning he will miss the game against Athletic Bilbao this weekend.
Neymar scored in normal time of the 1-1 draw against Germany before converting the winning penalty as Brazil triumphed 5-4 in the shootout.
The 24-year-old forward, who stood down as captain of the national side after the win over Germany, will look to help his side to victories in the forthcoming World Cup qualifiers against Ecuador and Colombia before returning to his club.
RELATED: Chelsea's Fabregas Disappointed To Be Left Out Of FA Cup Starting Lineup
"Off the back of winning Olympic gold with Brazil, Neymar Jr has been called up to the full national team and, with the permission of Luis Enrique, will return to the squad after the international break," the Barcelona statement said.
Neymar — who signed a new five-year contract with Barcelona this summer — will return to a Barca side that began the Liga season in blistering fashion with a 6-2 home win over Real Betis.
He is expected to be ready to play against Alaves at the the Camp Nou on Sep. 10.
Barca said midfielder Rafinha, also part of Brazil's Olympic success, would return to training this week.
"Rafinha has not been selected for the national team's latest squad and will therefore return to Barca training on Wednesday," the statement added.
Conte Tells Costa To Remain Steadfast Amid Criticism From Media
AC Milan Reject Chelsea offers For Defender Alessio Romagnoli | {
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WHO warns: Government policies will make half of Europeans catch COVID-19
Alex Lantier, Johannes Stern
Yesterday, the World Health Organization-Europe bluntly warned of the catastrophic consequences of European governments' policy of loosening health protocols and self-isolation guidelines, amid a massive surge of COVID-19 driven by the Omicron variant.
WHO-Europe Director Dr. Hans Kluge said the Omicron variant "represents a new west-to-east tidal wave" spreading across Europe. The first week of 2022, he noted, saw 7 million cases in the 53 countries in the WHO's European region: the British Isles, Scandinavia, the European Union (EU) and the countries of the former Soviet Union. He added, "As of 10 January, 26 countries report that over 1 percent of their population is catching COVID-19 each week. … [Omicron is] quickly becoming the dominant virus in western Europe and is now spreading in the Balkans.
"At this rate, the Institute for Health Metrics and Evaluation (IHME) forecasts that more than 50 percent of the population in the region will be infected in the next 6 to 8 weeks," Kluge warned. With the WHO-Europe region having well over 800 million people, this means a staggering 400 million cases of COVID-19 in Europe alone.
Shoppers walk down Oxford Street, Europe's busiest shopping street, in London, Dec. 23, 2021. (AP Photo/Frank Augstein, File)
The working class faces a cataclysmic health emergency, driven by an irresponsible ruling class that opposes any attempt to control the pandemic as an intolerable restriction on profits. Already, over 1.6 million people have died of COVID-19, and millions are suffering from Long COVID in the WHO-Europe region. Yet European governments are preparing a catastrophe, with a new wave of mass death and debilitating disease flowing from an unprecedented surge in infection.
To date, Europe has seen approximately 100 million confirmed cases of COVID-19. Now, the WHO is warning that in just the next two months, there will be four times more cases than in the entire pandemic until now.
These figures are so vast that they almost defy understanding. With between 10 and 50 percent of COVID-19 patients suffering from Long COVID, depending on the definition used for it, this means tens or hundreds of millions of people in Europe will be suffering debilitating long-term illness requiring labor intensive care. This would stagger society, as vast numbers of people could not work due to illness, and lead to widespread severe illness and death.
European governments falsely claim that vaccinations have "broken the correlation," in the words of French Health Minister Olivier Véran, between infections and serious illness and death.
In fact, such a massive Omicron wave would swamp hospitals that already are stretched to the breaking point. Now, even before the most recently infected cases arrive in hospitals, 23,371 of 3.4 million active cases are hospitalized, and 3,969 are on life support in France, a country with a relatively high vaccination rate of 74.9 percent. If similar proportions applied to the WHO's projections, this would mean nearly 3 million patients requiring hospitalization and 500,000 on life support in the next two months in Europe.
This alone would likely be beyond the capacity of European hospitals, leading to a surge in deaths as COVID-19 or other patients could not obtain care in overburdened facilities. However, everything indicates that the crisis would in fact be even more serious.
Polish medical adviser Andrzej Horban warned in the Rzeczpospolita newspaper of a "tsunami of infected people." The 12 million unvaccinated Poles will "all be infected with the new variant," he said, and with 5 to 10 percent of them needing hospital care, Poland would have "to treat around 1 million people." Even if they did not all come in at once but "over the course of a few months," he added, this would hopelessly overburden hospitals. "We probably would need 50-60,000 COVID beds. And I'm not even talking about where we would find doctors and other medical personnel."
Similarly, the WHO's Kluge warned: "I am also deeply concerned that as the variant moves east, we have yet to see its full impact in countries where levels of vaccination uptake are lower, and where we will see more severe disease in the unvaccinated." He also expressed his concern for the impact on the health care staff, calling "for more support for their mental health and well-being."
WHO-Europe Senior Emergency Officer Dr. Catherine Smallwood warned against the relaxing of health measures now underway. She said, "We're yet to see how Omicron will pan out in a situation where there are more people [unvaccinated against] SARS-CoV-2. And that's where we need to hold our guns, be very cautious and not jump to any conclusions about changing the strategy and letting COVID spread."
The WHO's horrific projections do not have to come to pass. A strict lockdown to halt transmission, followed by vaccinations and contact tracing to isolate the sick and prevent the virus from spreading, can eliminate transmission of the virus. However, imposing such a policy requires the independent political mobilization of the working class against the utterly reckless policies of Europe's capitalist governments.
The ruling class is responding to the explosive spread of Omicron by doubling down on its contagion policy that openly puts capitalist profit interests ahead of the health and lives of millions.
Governments across Europe are shortening quarantine periods for people infected with or exposed to the virus. A week ago Sunday, the French government announced that COVID-19 patients would be isolated for at most seven days and could return to work after five days if their viral load escapes detection in unreliable antigen tests. The UK and Spain previously launched similar regulations.
Denmark no longer has even a minimum number of quarantine days after infection. After 48 symptom-free hours, people can return to work. This anti-scientific policy results in vast numbers of sick, infectious people returning to infect their colleagues.
On Friday, the German government announced that it was reducing the quarantine period in Germany to just 5-7 days (previously 14). Acting Berlin Mayor Franziska Giffey (SPD) said: "We have committed to keeping schools open. … People need good child care so they can go about their business, and that's why it's important that we keep schools open."
European governments are responding to Omicron by dropping even the last pretense that they want to prevent the spread of the virus. On Monday, French Prime Minister Jean Castex announced a simplification of school health protocols: If a positive case is reported in a class, parents will no longer have to pick children up at the middle of the day, but only at the end. Castex baldly stated that his government will keep schools and nonessential production open, whatever the cost in lives. He said, "We are not closing the schools or the country."
The Spanish government has called for a change reporting and self-isolating protocols so as to treat COVID-19 like the flu. "It's a necessary debate. Science has given us the answer to protect ourselves," Prime Minister Pedro Sanchez told radio station Cadena Ser on Tuesday. "We have to evaluate the evolution of COVID-19 from pandemic to an endemic illness."
Such statements testify to a toxic political atmosphere that prevails in a ruling class that is callously indifferent to the deaths of millions. It is urgent to mobilize growing opposition in the working class internationally in a movement to impose a scientific policy to eliminate the spread of the virus and take control of the resources of the world economy out of the hands of an irresponsible financial aristocracy.
An open letter to the working class: The pandemic must be ended and lives saved in 2022!
UK campaigner Lisa Diaz subject to concerted media attack for demanding COVID safe schools
As Omicron infections soar, Europe's governments force the sick back to work
The coronavirus pandemicEuropeMedical science | {
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{"url":"https:\/\/answers.opencv.org\/question\/3996\/cannot-do-anything-with-opencv-anymore-on-windows-7-64-bit\/?sort=votes","text":"# Cannot Do Anything With OpenCV Anymore on Windows 7 64-bit\n\nHi,\n\nI have tried to work with OpenCV 2.2, 2.3, 2.4.0, 2.4.2 and none of them gave my any luck at all. I have Windows 7 64-bit installed in my i5 machine with L3 cache, 8 GB RAM, and 500 GB Hard Drive. I do this to integrate OpenCV:\n\n3) Add C:\\OpenCV\\build\\x86\\vc10\\bin folder to SYSTEM PATH.\n\n4) Make OpenCV files in a folder called \"vs2010build\" in OpenCV installation folder.\n\n5) Open the opencv solution in \"vs2010build\" folder and then build all the libraries again.\n\nWhen I am at step 5. My windows become really and phenomenally slow like the a browser window, file explorer window, or even the simply volume control menu in the task bar takes nearly a minute to pop-up. Ironically, it is only with OpenCV and no other Visual C++ Express 2010 solution or project will cause this mess! The problem was the same when I tried to install with Code::Blocks IDE and MingGW compiler.\n\nI have been trying to draw attention to people of OpenCV community to actually investigate whether or not they have the same problem and if no, how do you go about doing it. People simply point me towards the OpenCV's own website but I am finding it really misleading. I want a solution to this problem by people who actually did it themselves rather than blinding pointing me towards OpenCV's installation guideline (outdated anyway). Most importantly, some of the important documentations and guidelines are not even quality controlled i.e. no feedbacks or productive comments that it actually does or doesn't work!\n\nI have been following posts from <answers.opencv.org>, <code.opencv.org>, <www.stackoverflow.com>, and other possible Google Search Results but no one is addressing this issue. This is really serious for me I cannot work because of this problem now! I would really appreciate if someone can verify what I am talking about. Most importantly, I would be grateful if someone has pretty much the same setup of Visual Studio\/Visual C++ Express 2010, OpenCV, and Windows 7 64-bit as mine, but DO NOT HAVE THIS PROBLEM!!! PLEASE I NEED HELP!!!\n\nN.B. I believe pointing to x86 library files is correct because my Visual C++ Express 2010 ACTUALLY gets registered in the process list as a 32-bit application running on Windows 7 64-bit. However, I changed it also to x64 library files but SAME RESULT!!! JUST SO YOU KNOW THAT WE ALL ARE GOOD PEOPLE TRYING TO SORT OUT ERRORS\/FAILURES\/BUGS by considering any\/every possible combination of solutions.\n\nJust to tell you what I am on about, If you have OpenCV and Windows 7 64-bit, take my source code (below) and use it to build a simple project and see if your PC is dying slowly.\n\n #include <opencv2\/core\/core.hpp>\n#include <opencv2\/highgui\/highgui ...\nedit retag close merge delete\n\n1\n\nWe have the same problem on installation on the new OpenCV but I'm using Eclipse. I think OpenCV must create a new guide for OpenCV installation. I also have problems building the libraries. My sympathy.\n\n( 2012-11-10 10:32:05 -0500 )edit\n\nKarl...thanks a lot for confirming that...I have also tried itvwith Dev C++, code::blocks, eclipse, and visual studio...nothing...are your symptoms same as mine?\n\n( 2012-11-10 10:43:11 -0500 )edit\n1\n\nYes i have the same Issue, but I have managed to fix some basic functionality like image loading but image comparison just didn;t want to compile SURF or FANN neither.\n\n( 2012-11-10 10:49:31 -0500 )edit\n\n@Szippy I have wasted 10 weekends tried to fix this but still not anywhere!!!! I have to ask a colleague in the office whom I saw yesterday doing some hankey pankey with OpenCV and (possibly) with Windows 7 64-bit. If he has managed to fix it, which will be great, I would be posting updates on Monday, 1st or 2nd thing :P...But once again, +1 for your contribution Szippy and I am pleased that you have confirmed this issue in a way I expected. Ta\n\nBtw...Any chance EmguCV (although it is a wrapper to Windows-based development) can make our lives better? or is it even worse?\n\n( 2012-11-10 10:55:32 -0500 )edit\n( 2012-11-10 19:03:33 -0500 )edit\n\nDid you actually check if you can create 64-bit programs with Visual Studio Express? I doubt that but I am not sure.\n\n( 2012-11-11 13:49:39 -0500 )edit\n\n@SR I am pretty sure about 32-bit stuff...which is my only concern for the time being...personally I couldn't care less about the 64-bit support in visual C++ express 2010...more b importantly as I did before...even if you had the full version OpenCV just doesn't work with anything on Windows 7 64-bit......aaaaaargh...\n\n( 2012-11-11 14:06:52 -0500 )edit\n\n@manmedia. That is not true for me. I used OpenCV 2.1, 2.2, 2.3 with Visual Studio 2008 SP1 on Windows 7 in 64-bit mode extensively and I never experienced such problems.\n\n( 2012-11-11 14:46:12 -0500 )edit\n\n@SR so what is it that you think you have and I don't have? This is my original question. And I am glad to know that you have a working version of OpenCV without any problem on Windows 7 64-bit. Could you please tell me how you got about setting up your OpenCV? What exactly did you do with them? This is what I really want to know that if I am missing something, I need to UNMISS it so that I can do the same as you.....It involves any Windows Update too. I just want to fix this problem because it only creates problems when I start using OpenCV\n\n( 2012-11-11 14:50:09 -0500 )edit\n\nI did not do anything special. I used both pre-compiled and self-compiled versions with success. See also my answer below.\n\n( 2012-11-11 15:03:54 -0500 )edit\n\nSort by \u00bb oldest newest most voted\n1. Unfortunately you do not provide a specific error message or describe a specific behaviour. The description is rather unclear as you keep complaining about the effect. Are there any reproducable steps to get \"that effect\"?\n2. It does not matter which kind of process (32-bit, 64-bit) Visual Studio or Windows is. It only matters whether you compile your program with the x86 or the x64 toolchain. You must link against the corresponding OpenCV DLLs.\n3. Double-check that you only link against debug DLLs in debug mode and you only link against release DLLs in release mode.\n4. Your step 3: \"Add C:\\OpenCV\\build\\x86\\vc10\\bin folder to SYSTEM PATH.\" sounds dangerous to me. Not by itself (that's fairly standard) but only because of the described behaviour. You might override some important DLLs with those within that folder. Omit that step. Compile OpenCV with your desired architecture and copy the resulting OpenCV Dlls in that folder where your program's exe is.\n5. If the problem persists: Copy your Project, the entire solution, the code and the OpenCV DLLs to another machine. Check (recompile if necessary) if the problem is present there too. If not, you might want to get a fresh reinstall of your OS.\nmore\n\n@SR Last night I was bored and did \"Brute Force\" attack on my own machine....and yes, even the Windows Update install\/search is slowing down my machine like this!!! I realised that after SP1 installation Windows 7 64-bit troubled a millions of PCs. I tried to download Microsoft's Hotfix but it complains that \"Please insert the last disk which is the part of this compressed package\"??? What on earth? And then I went to Lenovo's service centre online (My model is V470 Ideapad) to download hotfix from them. And it still doesn't do any good after installation. I know this is OT for here now, so I am happy to conclude that My Windows got CORRUPTED SOMEHOW!!! I raised an issue both in MS Support site and poweruser.com...any suggestions..Thnx for your help..really can't ask for more!! :)\n\n( 2012-11-12 03:03:08 -0500 )edit\nmore\n\n@Hodali I apologise, but I think I have REPEATEDLY said IN MY ORIGINAL QUESTION that all those things that you are posting are bit \"useless\" for me as I HAVE TRIED all of them almost 10 times with based on different IDEs. I want a solution that is by someone who manually installed and found a problem. If you haven't had any problem, you wouldn't understand what I am trying to get across to other user here. Please see @Karl's and @Szippy's comments after the original question. Thanks for your effort, but please read my original question before you suggest anything that I have been trying since last month!\n\n( 2012-11-11 04:12:49 -0500 )edit\n\nThis Can be helpful for installation in windows with visual studio. http:\/\/blogcenter22.blogspot.in\/\n\nmore\n\nI have Visual Studio 2012 installed on Windows 7 64-bit and it works well except debugging. I installed OpenCV in the root directory C:.\n\nI added C:\\opencv\\build\\x86\\vc10\\bin to the system variable Path. To each project you have to create a PropertySheet. The include directory are C:\\opencv\\build\\include and c:\\opencv\\include. The library directory is C:\\opencv\\build\\x86\\vc10\\lib. Add the following libs to the Linker (Debug):\n\nopencv_calib3d243d.lib opencv_contrib243d.lib opencv_core243d.lib opencv_features2d243d.lib opencv_flann243d.lib opencv_gpu243d.lib opencv_haartraining_engined.lib opencv_highgui243d.lib opencv_imgproc243d.lib opencv_legacy243d.lib opencv_ml243d.lib opencv_nonfree243d.lib opencv_objdetect243d.lib opencv_photo243d.lib opencv_stitching243d.lib opencv_ts243d.lib opencv_video243d.lib opencv_videostab243d.lib\n\nFor the Release (Linker) the same except the follwing libs have to be added:\n\nopencv_calib3d243.lib opencv_contrib243.lib opencv_core243.lib opencv_features2d243.lib opencv_flann243.lib opencv_gpu243.lib opencv_haartraining_engine.lib opencv_highgui243.lib opencv_imgproc243.lib opencv_legacy243.lib opencv_ml243.lib opencv_nonfree243.lib opencv_objdetect243.lib opencv_photo243.lib opencv_stitching243.lib opencv_ts243.lib opencv_video243.lib opencv_videostab243.lib\n\nThat all! You can compile and run the applications. But I cannot debug because the following message is always appeared:\n\nThe program can't start because MSVCP100D.DLL is missing from your computer. Try reinstalling the program to fix this problem\n\nI couldn't find MSVCP100D.DLL on my system and the internet. Does anyone knows this problem?\n\nmore\n\nThanks for that I will try it out! I am using Visual C++ 2010 Express so it should be fine. But we have tried with different IDEs and compilers and OpenCV has got a problem, not our PC or IDEs. Nevertheless, I will try your fix.\n\nHey you can check what target it is for your project i.e. is it a JUST console application or Windows Console application. And also, did you generate precompiled header and then deleted it? I remember it has something to do with they way you configure your projects. I am pretty certain that I had this but I fixed it by playing with the property sheet. Apologies I cannot remember anymore :( Please look forward to further comments as I have to include C:\\opencv\\include as well. Last time I didn't add it. However, My problem was with 2010 and you are using 2012.\n\n( 2012-11-10 12:27:40 -0500 )edit\n( 2012-11-10 12:36:01 -0500 )edit\n\n@Hodali Nada!! Your solution seems to be working in Visual Studio 2012 but not Visual Studio 2010. I cannot get it to work with Windows 7 64-bit after following what you told me. It is slowing down my machine just like everything else. The last hope is that I can use the event logger to check what is going on as soon as I call the OpenCV stuff from Visual Studio.\n\n( 2012-11-10 18:22:32 -0500 )edit\n( 2012-11-10 19:14:29 -0500 )edit\n\nMSVCP100D.DLL is a debug DLL of the Visual C++ 10.0 (VS2010) Runtime. While you can download and install the redistributable (i.e. the release DLLs) for any Visual C++ version, AFAIK the debug DLLs are only shipped with the respective Visual Studio version. Apparently you can run the program because you have the respective runtime dlls installed. But you cannot even run the debug version of your program because the debug DLLs you have are these of Visual Studio 2012.\n\n( 2012-11-11 13:37:27 -0500 )edit\n\nI solved that problem by copying the DLLs from Visual Studio 2010 Express to the working directory. Actually the OpenCV team should provide libraries which work with Visual Studio 2012. By the way I rebuilt the binary from scratch in Visual Studio 2012. But it it hasn't helped (same problem).\n\n( 2012-11-11 14:04:57 -0500 )edit\n\n@SR\n@Hodali I apolgise for not seeing you guys solving the MSVCP100D.dll issue...copying the .dll to the working (debug\/release) is always A FIX....However, has anyone except @Hodali has solved the crucial isse of OpenCV and Windows 7 64-bit?\n\n( 2012-11-11 14:24:30 -0500 )edit\n\nMy Windows 7 64-bit was totally messed up due to some updates\/virus\/something that was not supposed to be there! Funny enough that I had Kaspersky Anti-Virus and usually Anti-Virus is the one that causes all these trouble, but it didn't. Restored the original build image of my laptop and now it is running okay.\n\nTnanks to all for contributing! I take my word back that OpenCV doesn't have any problem on Windows 7 64-bt.\n\nmore\n\nCongratulations. Good for you. :)\n\n( 2012-11-13 01:43:50 -0500 )edit\n\nThis Can be helpful to install in windows with Visual Studio. http:\/\/blogcenter22.blogspot.in\/\n\nmore\n\nTry Visual Studio 2012 Express! It is avaiable on http:\/\/www.microsoft.com\/visualstudio\/eng\/downloads#d-2012-express for free. Debugging is also possible. I found out that one have to copy some DLLs from Visual Studio 10 or Visual Studio 2010 Express.\n\nmore\n\nOfficial site\n\nGitHub\n\nWiki\n\nDocumentation","date":"2022-12-09 05:26:58","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2172696441411972, \"perplexity\": 2627.277885961945}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446711390.55\/warc\/CC-MAIN-20221209043931-20221209073931-00740.warc.gz\"}"} | null | null |
NGC 2931 ist eine Spiralgalaxie mit ausgedehnten Sternentstehungsgebieten vom Hubble-Typ Sbc im Sternbild Löwe auf der Ekliptik. Sie ist schätzungsweise 332 Millionen Lichtjahre von der Milchstraße entfernt und hat einen Durchmesser von etwa 80.000 Lj. Gemeinsam mit NGC 2929 und NGC 2930 bildet sie das gravitativ gebundene Galaxientrio Holm 134.
Das Objekt wurde am 21. Februar 1863 von Heinrich d'Arrest entdeckt.
Weblinks
SIMBAD Astronomical Database
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Earned the Cheers to Independent U.S. Craft Breweries (Level 68) badge! Earned the Riding Steady (Level 65) badge! Earned the Pale as the Moon (Level 31) badge!
Clean, refreshing and quite tasty!
Light wheat beer. Good Friday night beer! | {
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{"url":"https:\/\/pub.uni-bielefeld.de\/publication\/2907033","text":"# In-medium P-wave quarkonium from the complex lattice QCD potential\n\nBurnier Y, Kaczmarek O, Rothkopf A (2016)\nJournal of High Energy Physics (10): 032.\n\nNo fulltext has been uploaded. References only!\nJournal Article | Original Article | Published | English\n\nAuthor\nAbstract\nWe extend our lattice QCD potential based study [1] of the in-medium properties of heavy quark bound states to P-wave bottomonium and charmonium. Similar to the behavior found in the S-wave channel their spectra show a characteristic broadening, as well as mass shifts to lower energy with increasing temperature. In contrast to the S-wave states, finite angular momentum leads to the survival of spectral peaks even at temperatures, where the continuum threshold reaches below the bound state remnant mass. We elaborate on the ensuing challenges in de fining quarkonium dissolution and present estimates of melting temperatures for the spin averaged chi(b) and chi(c) states. As an application to heavy-ion collisions we further estimate the contribution of feed down to S-wave quarkonium through the P-wave states after freezeout.\nKeywords\nPublishing Year\nISSN\nFinancial disclosure\nOpen Access publishing charge funded by SCOAP$^3$ \u2013 Sponsoring Consortium for Open Access Publishing in Particle Physics and Bielefeld University.\nPUB-ID\n\n### Cite this\n\nBurnier Y, Kaczmarek O, Rothkopf A. In-medium P-wave quarkonium from the complex lattice QCD potential. Journal of High Energy Physics. 2016;(10): 032.\nBurnier, Y., Kaczmarek, O., & Rothkopf, A. (2016). In-medium P-wave quarkonium from the complex lattice QCD potential. Journal of High Energy Physics(10), 032. doi:10.1007\/JHEP10(2016)032\nBurnier, Y., Kaczmarek, O., and Rothkopf, A. (2016). In-medium P-wave quarkonium from the complex lattice QCD potential. Journal of High Energy Physics:032.\nBurnier, Y., Kaczmarek, O., & Rothkopf, A., 2016. In-medium P-wave quarkonium from the complex lattice QCD potential. Journal of High Energy Physics, (10): 032.\nY. Burnier, O. Kaczmarek, and A. Rothkopf, \u201cIn-medium P-wave quarkonium from the complex lattice QCD potential\u201d, Journal of High Energy Physics, 2016, : 032.\nBurnier, Y., Kaczmarek, O., Rothkopf, A.: In-medium P-wave quarkonium from the complex lattice QCD potential. Journal of High Energy Physics. : 032 (2016).\nBurnier, Yunnis, Kaczmarek, Olaf, and Rothkopf, Alexander. \u201cIn-medium P-wave quarkonium from the complex lattice QCD potential\u201d. Journal of High Energy Physics 10 (2016): 032.\nThis data publication is cited in the following publications:\nThis publication cites the following data publications:\n\n### Export\n\n0 Marked Publications\n\nOpen Data PUB\n\n### Web of Science\n\nView record in Web of Science\u00ae\n\narXiv 1606.06211\n\nInspire 1471291\n\nSCOAP3 17454","date":"2018-05-21 07:18:31","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6696996092796326, \"perplexity\": 14842.64913536579}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-22\/segments\/1526794863967.46\/warc\/CC-MAIN-20180521063331-20180521083331-00175.warc.gz\"}"} | null | null |
\section{Introduction}
\label{chap: Introduction}
With the ever-increasing popularity of the Web and subsequent increasing abundance of reviews on products or services available, a wealth of interesting information is available to businesses and consumers alike. But due to this increased quantity of reviews available, it becomes more and more infeasible or even impossible to analyse them by hand.
As such, sentiment analysis,
concerned with the algorithmic analysis of expressed sentiment, can be of great value. In this research, we are interested in Aspect-Based Sentiment Analysis (ABSA), which entails determining the sentiment with respect to a certain aspect\cite{SchoutenSurvey}. Specifically, we perform this task at the sentence level. In the sentence ``The soup was delicious but we sat in a poorly-lit room" for example, a positive sentiment is expressed with regard to the aspect ``Food quality'', but the sentiment towards ``Ambience" is negative.
\cite{wallaart2019hybrid} approaches this problem using a hybrid model, where first an ontology is used to assign a positive or negative sentiment towards an aspect in a rule-based manner. When this method delivers contradicting or no results, an LCR-Rot neural network as described in \cite{zheng2018left}, extended using representation iterations and called LCR-Rot-hop, is used. \cite{trusca2020hybrid} further develops this LCR-Rot-hop model by incorporating contextual word embeddings and hierarchical attention. This new model, called LCR-Rot-hop++, delivers state-of-the-art results.
Research into neural networks is rapidly advancing, and novel techniques are developed continuously. One such technique proposed in \cite{goodfellow2014generative} is Generative Adversarial Network (GAN). Here, two networks are simultaneously trained: a generator tries to generate new input samples, whereas a discriminator tries to discern between real and generated samples. These conflicting objectives converge to a situation where the generator produces samples indiscernible from real data. Furthermore, training a neural network as the discriminator in an adversarial network can increase the robustness of the trained model.
\cite{han2019adversarial} gives an overview of contributions of GANs to the domains of affective computing and sentiment analysis. These mostly fall into the field of image generation, however, which has the benefit that input data is of fixed size. This is not the case in text analysis, as sentences can be of any length. This problem has been worked around in the, so far (to the best of our knowledge), only research where GAN is applied to ABSA in \cite{karimi2020adversarial}. In this paper, not entire new instances are generated, but rather perturbations are made to real data aimed at increasing loss. These are then used to train a BERT Encoder \cite{xu2019bert}, leading to increased accuracy with respect to the baseline model.
This research contributes to the literature in two ways. First, we will develop a method where adversarial samples are fully generated, rather than obtained from perturbing existing samples as in \cite{karimi2020adversarial}. Second, HAABSA++ is a more sophisticated methodology with respect to the specifics of the ABSA task than the BERT Encoder used in \cite{karimi2020adversarial}, making it interesting to investigate whether we can achieve a similar increase in accuracy when applying adversarial to HAABSA++.
This research is structured as follows. First, Sect. \ref{chap: Related Work} gives a brief overview of the related works on ABSA and adversarial training. In Sect. \ref{chap: Data} the datasets used are described. We discuss the HAABSA++ framework in Sect. \ref{chap: Methodology}, as well as how we apply adversarial training to it. Then, Sect. \ref{chap: Results} presents the results of the proposed methods. Last, in Sect. \ref{chap: conclusion} we draw conclusions and give suggestions for further research.
\section{Related Work}\label{chap: Related Work}
\cite{SchoutenSurvey} provides a comprehensive survey on Aspect-Based Sentiment Analysis (ABSA) based on three types of methods: knowledge-based, machine learning, or hybrid approaches. In ABSA, one tries to find the sentiment expressed towards a given or extracted aspect in a sentence or full review (in this research we focus on sentences). Whereas ABSA also comprises tasks like target extraction (i.e., the selection of a target word indicative of a certain aspect) and aspect detection (i.e., the detection of aspects towards which a sentiment is expressed in a text), in this research we follow \cite{trusca2020hybrid} and \cite{wallaart2019hybrid} in focusing on the sentiment classification of sentences in which aspects are explicitly stated in so-called targets. For example, in the sentence ``The food was bland but at least the waiter was allright.", ``food" is a target for the aspect ``Food Quality", whereas ``waiter" serves as a target for the aspect ``Service". Towards the former, a negative aspect is expressed, and towards the latter the sentiment is neutral.
In \cite{wallaart2019hybrid}, the sentiment classification task of ABSA is addressed by means of a hybrid approach. Here, first a knowledge-based ontology method is used to classify the sentiment towards a target, and a neural network based on \cite{zheng2018left} is used as back-up when this fails. \cite{trusca2020hybrid} extends upon this work by adding two features to the neural network part: contextual word embeddings are used rather than non-contextual ones, and a hierarchical attention mechanism is applied. Compared to other methods for ABSA, HAABSA++ is found to provide state-of-the-art results when applied to the SemEval 2015 \cite{semeval2015} and SemEval 2016 \cite{semeval2016} datasets.
The field of machine learning is in rapid development, and one particular advancement sparking great interest was proposed in \cite{goodfellow2014generative}. GANs are trained by pitting a generative model against a discriminator. The generator's task is to generate realistic samples when compared to an empirical dataset. At the same time, the discriminator is trained to discern between generated and real samples. These conflicting objectives lead to a minimax game which \cite{goodfellow2014generative} shows to converge to a situation where generated samples are indistinguishable from real samples.
\cite{han2019adversarial} provides an overview of applications of adversarial training to the field of sentiment analysis. Here, the authors note four benefits of adversarial training. First, it allows for generated emotions to feel more natural than those generated through other techniques. Second, it aids in overcoming the sparse availability of labeled sentiment data. Although plenty of images, speech, and text samples exist, only a small fraction of these are labeled and thus suitable for supervised learning. Third, GANs have the potential to learn in a robust manner, reducing the problems occurring when samples are gathered from different contexts. For example, the word ``greasy" related to the domain of restaurant reviews can be understood as positive in a fast-food restaurant, but not in a fine dining establishment. Last, GANs allow for easy quality evaluation of the generated samples. Whereas in prior methods for sample generation, humans needed to assess the quality of the samples, the discriminator built into the GAN framework automates this task. Most of the advancements to GANs listed in \cite{han2019adversarial} focus on generating as realistic as possible samples which are highly relevant for, e.g., image generation, but not as much for the analysis of written reviews.
\cite{Odena} proposes a semi-supervised GAN, where the discriminator simultaneously acts as a classifier. Namely, whereas a regular discriminator is only given the task to discern between `Fake' and `Real' data, in this application the `Real' class is divided into the different classes of the original task. Such a model is commonly referred to as a Categorical Generative Adversarial Network (CatGAN). When applied to the MNIST dataset (where the discriminator discerns between `Fake', `0', `1', ... , `8' and `9'), this provided a significant improvement in performance compared to a non-adversarially trained convolutional neural network. Applications of CatGANs are also found in \cite{springenberg2015unsupervised} and \cite{salimans2016improved}, where again the MNIST dataset is used for testing. In the former, the semi-supervised CatGAN was found to outperform most competing models, only marginally lagging behind the best performing model. Furthermore, CatGAN outperformed competing GAN-based models by great margins, a fact also revealed in the study of \cite{salimans2016improved}.
An application of CatGAN to ABSA is found only recently in \cite{karimi2020adversarial}, but it is not applied in the traditional sense with an explicit generator and discriminator. Rather, real samples are classified by a BERT Encoder (the network intended to train adversarially). The gradient of the loss is then computed with respect to the initial input data, and based on this the original samples are perturbed. These samples are then again fed to the BERT Encoder, and the total loss is computed based on the combined loss of the perturbed and original samples. Although there is no explicit generator or discriminator here, the BERT Encoder is thus adversarially trained in the sense that samples generated with the explicit aim of being difficult to classify, are fed to it. This methodology outperforms the (non-adversarially trained) BERT-PT model \cite{xu2019bert} when applied to the SemEval 2014 dataset.
\section{Data}
\label{chap: Data}
For our research, we use data posed for the SemEval 2015 and SemEval 2016 contests. Intended to evaluate methods developed for ABSA, these sets contain English review sentences for restaurants. For each of these sentences, one or multiple aspect categories are denoted together with a negative, neutral or positive sentiment.
\begin{center}
\begin{threeparttable}[h!]
\small
\vspace{-6mm}
\caption{Sentiment frequencies in the used datasets}
\label{tab: sentiment frequencies}
\begin{tabular}{cccccccccc}
\toprule
& \multicolumn{4}{c}{\textbf{SemEval 2015}} & & \multicolumn{4}{c}{\textbf{SemEval 2016}} \\ \cline{2-5} \cline{7-10}
& \textit{Negative} & \textit{Neutral} & \textit{Positive} & Total & & \textit{Negative} & \textit{Neutral} & \textit{Positive} & Total \\ \cline{1-5} \cline{7-10}
Train Data & 3.2\% & 24.4\% & 72.4\% & 1278 & & 26.0\% & 3.8\% & 70.2\% & 1879 \\
Test Data & 5.3\% & 41.0\% & 53.7\% & 597 & & 20.8\% & 4.9\% & 74.3\% & 650\\ \bottomrule
\end{tabular}
\end{threeparttable}
\end{center}
\noindent Table \ref{tab: sentiment frequencies} shows the distribution over sentiment polarities in the considered datasets. Here, we note that for both data sets, `Positive' polarities are most abundant. Both data sets have a clear minority class. For SemEval 2015, this is the `Negative' class, whereas for SemEval 2016 this is `Neutral'. For the SemEval 2015 data set, a larger disparity between the relative frequencies among the polarities can be noted between the train and test data compared to SemEval 2016. Furthermore, we did not notice any remarkable discrepancies between the aspect category frequencies in the train and test sets.
We directly apply the datasets as obtained in \cite{wallaart2019hybrid} after preprosessing. First, the authors deleted all sentences where sentiment is implicit, as the applied methodology requires an explicitly mentioned target. For 2015, this amounted to 22.7\% of the train data, and 29.3\% of the test data. For 2016, this was 25.0\% and 24.3\%, respectively\footnote{All values in Table \ref{tab: sentiment frequencies} are excluding implicit targets.}. They then processed the remaining sentences using the NLTK toolkit \cite{bird2009natural}, and, last, tokenized the data and lemmatized the words with the WordNet English lexical database \cite{miller1995wordnet}.
\section{Methodology}
\label{chap: Methodology}
In this section, the methodology we employ for sentiment classification of restaurant reviews is discussed. First, we will describe the original HAABSA++ algorithm in Sect. \ref{sec: metho-haabsa++}. Then, Sect. \ref{sec: catGan} puts forward the methodology for the CatGAN and elaborates on how to adapt the standard HAABSA++ algorithm to serve as the discriminator in this methodology. Furthermore, this section describes the training procedure.
\subsection{HAABSA++}
\label{sec: metho-haabsa++}
HAABSA++ is a hybrid approach to aspect-based sentiment analysis where, as proposed in \cite{wallaart2019hybrid}, first an ontology is used to determine the sentiment expressed towards a given aspect. If this proves inconclusive, a neural network proposed in \cite{wallaart2019hybrid} and improved upon in \cite{trusca2020hybrid} is used as back-up.
\subsubsection{Ontology.}
\label{subsec: metho-ontology}
The ontology is based upon \cite{schouten2018ontology} and consists of three classes. First, \textit{SentimentMention} contains the expressions of sentiment. It consists of three subclasses, the first of which contains words always expressing the same sentiment value regardless of the aspect, the second containing words always expressing the same sentiment that only adhere to specific aspects, and the third containing words for which the sentiment they express depends on the associated aspect. The \textit{AspectMention} class governs the aspect to which a word adheres, and the \textit{SentimentValue} class labels words as expressing either a positive or negative sentiment. For example, the word `expensive' could fall into the \textit{Price Negative Sentiment} subclass of the \textit{SentimentMention} class, the \textit{Price Mention} subclass of the \textit{AspectMention} class, and the \textit{Negative} subclass of the \textit{SentimentValue} class. Aspect sentiment is then determined by assessing whether in a given sentence, a word falls into the \textit{AspectMention} class of a given aspect, and if so, in what \textit{SentimentValue} subclass it falls.
The ontology-based method is powerful but might prove inconclusive whenever both negative and positive sentiment are detected for an aspect, or whenever the ontology does not cover the lexicalizations present in a sentence. In these cases, we resort to a back-up neural network approach.
\subsubsection{Multi-Hop LCR-Rot Neural Network with Hierarchical Attention and Contextual Word Embeddings.}
\label{subsec: metho-neural network}
\cite{trusca2020hybrid} further develops the Multi-Hop LCR-Rot-hop neural network used as back-up in \cite{wallaart2019hybrid} into LCR-Rot-hop++ by adding contextual word embeddings and a hierarchical attention mechanism. Although they compare multiple ways of implementing these additions, we only consider the BERT contextual word embeddings \cite{BERT} as these are found to perform best out-of-sample in our datasets. Furthermore, we use the last method out of the four methods for hierarchical attention introduced in \cite{trusca2020hybrid}, as it performs best on average. According to the fourth method, the last layer of attention is applied repetitively and separately for contexts and targets.
First, the words in a sentence are turned into word embeddings using the contextual BERT model. Here, first token vectors that are unique for each word, position embeddings showing the word's location in the sentence, and segment embeddings discerning between multiple sentences present, are averaged. The newly computed embeddings feed into a Transformer Encoder. The entire network is pre-trained on the Masked Language Model and Next Sentence Prediction tasks. This method ensures that a word's embedding depends on how it is used in the sentence. For example, the word `light' could refer to an object's mass or to the visible light coming from the sun or a lamp, depending on the context.
Then, the embedded sentences are split into three parts: Left (with respect to the target), Target, and Right (with respect to the target). Each of these feeds a bi-directional LSTM layer. These outputs are then used to create four attention vectors: a target2context and a context2target for both the left and right contexts. This is done using a two-step rotary attention mechanism, where in each iteration the intermediate context and target vectors are weighted using an attention score computed at the sentence level. This weighting is done separately for the two target vectors and the two context vectors. The four resulting vectors are then concatenated and subjected to another attention layer, which computes attention weights separately for contexts and targets. This process is repeated for a specified number of hops, the final output of which is used as input for a multi-layer perceptron determining the final sentiment classification.
\subsection{Classifying Generative Adversarial Network}
\label{sec: catGan}
As described before, a promising advancement in the field of deep learning is the Generative Adversarial Network. First proposed in \cite{goodfellow2014generative}, a GAN generates new data samples by simultaneously training a generative and a discriminative model. While the generative model produces new samples based on a random input vector, the discriminative model tries to discern between the generated samples and real data.
This section first describes how to adapt the neural network in HAABSA++ so as to constitute both a classifier and a discriminator (i.e., a CatGAN). This added objective should increase the robustness of the model, as it is forced to more clearly recognize what input characteristics determine the class to which an instance belongs. This can be made more apparent through an example. Imagine a child tasked with labeling images of vehicles as either `plane', `train', or `car'. It might then be fairly easy for the child to recognize cars, as only they have tires, but such a strategy will lead him to wrongly characterize planes on the ground (with their landing gear out) as cars. If, however, every now and then an image of a bicycle is given to the child, this challenges him to notice that it is not the characteristic ``having tires" by which cars can be recognized, but rather ``having four tires". This realization will in turn lead him to not label grounded planes as cars anymore, as they have more than four tires.
In the first subsection, we describe the model, and the second subsection gives its implementation details. Then, we present the training procedure and discuss convergence in GAN training. The last subsection describes the procedure for hyperparameter optimization.
\subsubsection{Model Formulation.}
\label{subseb: model formulaion}
\cite{salimans2016improved} shows how the loss function of the regular GAN model can be adapted so the discriminator simultaneously serves as a classifier, as such constituting a Categorical GAN (CatGAN). Instead of discriminating between real or fake data, the discriminator now discriminates between K+1 classes. In our case, K=3 and the first three classes are `Negative', `Neutral' and `Positive'. The K+1$^{\text{th}}$ class is `Fake'. This yields the loss function:
\begin{equation}
\label{eq: implicit loss function}
\begin{aligned}
L_{G,D} = &-\mathbb{E}_{\Vec{x},y \sim p_{\text{data}}(\Vec{x},y) }\text{log}[p_{\text{model}}(y|\Vec{x},y<\text{K}+1)] + \lambda(||\Theta_G||^2 + ||\Theta_D||^2) \\
&- \mathbb{E}_{\Vec{z}\sim P(\vec{z})}\text{log}[p_{\text{model}}(y=\text{K}+1|\Vec{z})],
\end{aligned}
\end{equation}
\noindent resulting in the following optimization problem to solve:
\begin{equation}
\label{eq: minimax problem}
\max_G \min_{D} L_{G,D}.
\end{equation}
\noindent In Equation \ref{eq: implicit loss function}, the first two terms correspond to the loss term as posed in \cite{wallaart2019hybrid}\footnote{Note that $\lambda||\Theta_G||^2$ and $\lambda||\Theta_D||^2$ correspond to L$_2$-regularization terms and are not included in \cite{salimans2016improved}.}. The last term corresponds to the the samples generated by the generator, which are labeled to the new, `Fake' class ($y = K+1 = 4$). Furthermore, $y=1$ means `Negative', $y=2$ is `Neutral' and $y=3$ is `Positive'. This loss function can be split into loss functions for the generator and discriminator, respectively, as follows:
\begin{subequations}
\begin{align}
L_{G} = &- \mathbb{E}_{\Vec{z}\sim P(\vec{z})}\text{log}[p_{\text{model}}(y=\text{K}+1|\Vec{z})] + \lambda||\Theta_G||^2\\
L_{D} = &-\mathbb{E}_{\Vec{x},y \sim p_{\text{data}}(\Vec{x},y) }\text{log}[p_{\text{model}}(y|\Vec{x},y<\text{K}+1)] + \lambda ||\Theta_D||^2 \\
&- \mathbb{E}_{\Vec{z}\sim P(\vec{z})}\text{log}[p_{\text{model}}(y=\text{K}+1|\Vec{z})]\nonumber.
\end{align}
\end{subequations}
\noindent Note here that the last term of Equation \ref{eq: implicit loss function} is included in both the generator and discriminator loss functions, as fake samples are first processed by the generator and then labeled by the discriminator. Furthermore, one could rewrite $\text{log}[p_{\text{model}}(y=\text{K}+1|\Vec{z})]$ as $\text{log}[1-D(G(\vec{z}))]$ and $\text{log}[p_{\text{model}}(y|\Vec{x},y<\text{K}+1)]$ as $\text{log}[D_y(\vec{x})]$, where $D(\vec{x})=\sum\limits_{y=1,2,3}D_y(\vec{x})$ represents the probability that the argument $\vec{x}$ stems from the real data. $D_y(\vec{x})$ in turn represents the probability that the argument stems from the real data and has label $y$.
Written explicitly as in \cite{wallaart2019hybrid}, Equation \ref{eq: implicit loss function} becomes:
\begin{equation}
\label{eq: explicit loss function}
L_{G,D} = -\sum_{j \in \mathbb{J}} \vec{y}_j \times \text{log}(\hat{p}_j) - \sum_{i \in \mathbb{I}} \vec{y}_i \times \text{log}(\hat{p}_i) + \lambda(||\Theta_G||^2 + ||\Theta_D||^2).
\end{equation}
\noindent Here, $j \in \mathbb{J}$ is the batch of real data samples. $\vec{y}_j$ is the real sentiment of the $j^{th}$ sample written in vector form, i.e., when $y_j=1$, $\vec{y}_j=[1,0,0,0]$, when $y_j=2$, $\vec{y}_j=[0,1,0,0]$ etc. $\hat{p}_j$ is the predicted sentiment of the $j^{th}$ sample. $i \in \mathbb{I}$ are the generated samples, and $\hat{p}_i$ is the predicted sentiment for the $i^{th}$ generated sample. Note furthermore that $\vec{y}_i$ is always equal to $[0,0,0,1]$. $\Theta_G$ and $\Theta_D$ contain the parameters for the generator and discriminator, respectively.
A problem occurs, however, when a generator is tasked with forming sentences. Constituted by a neural network, the generator can only output vectors and thus sentences of fixed length. This poses no problem in classical applications of GANs, as for example images generated always have the same resolution and thus output length. Sentences have variable length, however, and the discriminator can therefore possibly distinguish between generated and real samples based on their length. As such, we here only generate the four LCR-Rot-hop++ representation vectors of length $2d$ each, where $d$ is the dimensionality of the embedding. Then, we use the final MultiLayer Perceptron (MLP) of the LCR-Rot-hop++ network simultaneously as classifier and discriminator. The only modifications necessary are then to adapt the loss function to Equation \ref{eq: explicit loss function}, and let the MLP output a vector of probabilities of length $K+1$ rather than $K$.
The generator is constituted by a fully connected, 4-layer MLP. It uses an $r$-dimensional random vector as input, the first hidden layer will have $2 \times d$ neurons and the second hidden layer will have $6 \times d$ neurons. It then outputs a vector of length $8d$ (according to the LCR-Rot-hop++ model, the four vectors of length 2d are concatenated, resulting a vector of length 8d). This choice of architecture is the result of a trade-off between model complexity and speed of training. Then, the discriminator is constituted by the final MLP layer of the Multi-Hop LCR-Rot++ network in HAABSA++. A schematic of this new algorithm, called HAABSA*, is given in Figure \ref{Figure: HAABSA* Schematic}.
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.8\textwidth]{schematic.png}%
\end{center}
\caption{HAABSA* structure}
\label{Figure: HAABSA* Schematic}
\vspace{-6mm}
\end{figure}
\subsubsection{Implementation Details.}
\label{subsec: implementation details}
Following \cite{wallaart2019hybrid} and \cite{trusca2020hybrid}, we run the optimization algorithm for 200 iterations. For each iteration, a batch of $m=20$ real samples, as well as 20 fake samples, is selected. We initialize all weights randomly following a U(-0.01,0.01) distribution, and all biases are initialized as zero. To ensure all parameters are included in the regularization terms, $\Theta_D$ includes both the parameters in the final MLP layer and the parameters in the LCR-Rot-hop++ network w/o MLP. $\Theta_G$ includes the parameters of the generator. The random input for the generator follows a U(0,1) distribution and is of dimension $r=100$. As in \cite{trusca2020hybrid}, the dimensionality of the word embedding $d=768$. Last, it is important to note that that, like \cite{wallaart2019hybrid} and \cite{trusca2020hybrid}, we always train the adversarial network on the full training set. This may result in bias, as for the test set, only samples not classified by the ontology are classified by the neural network. However, the increased performance due to the larger training set size outweighs this downside.
Our methods are implemented in \verb+Python+ using the \verb+TensorFlow+ platform. All code can be found at \url{https://github.com/RonHochstenbach/HAABSAStar}.
\subsubsection{Training Procedure and GAN Convergence.}
\label{subsec: Training procedure and GAN convergence}
The training procedure for HAABSA*, based on the one put forward in \cite{goodfellow2014generative}, is shown in Algorithm \ref{Algorithm: HAABSA*}. In our implementation, the discriminator is updated every iteration, whereas the generator is updated only every $k^{th}$ iteration \cite{goodfellow2014generative}.
\begin{algorithm}[h!]
\small
\SetAlgoLined
\For{number of training iterations}{
\eIf{iteration number divisible by k}{
\begin{itemize}
\item Sample minibatch of $m$ noise samples $\{\Vec{z}^{(1)},\ldots,\Vec{z}^{(m)}\}$ from noise
\\prior $p_{\text{noise}}(\Vec{z})$
\item Sample minibatch of $m$ examples with their associated labels $\{(\Vec{x}^{(1)},y^{(1)}),\ldots,(\Vec{x}^{(m)},y^{(m)})\}$ from dataset $\mathcal{X}$
\item Update the generator by ascending the stochastic gradient of the
\\loss function with respect to $\Theta_G$:
\begin{equation*}
\nabla_ {\Theta_G}-\frac{1}{m}\sum_{i=1}^m[\text{log}(1-D(G(\vec{z}^i)))].
\end{equation*}
\item Update the discriminator by descending the stochastic gradient
\\of the loss function with respect to $\Theta_D$:
\begin{equation*}
\nabla_ {\Theta_D}-\frac{1}{m}\sum_{i=1}^m[\text{log}(D_y(\vec{x}^i))+\text{log}(1-D(G(\vec{z}^i)))].
\end{equation*}
\end{itemize}
}{
\begin{itemize}
\item Sample minibatch of $m$ noise samples $\{\Vec{z}^{(1)},\ldots,\Vec{z}^{(m)}\}$ from noise
\\prior $p_{\text{noise}}(\Vec{z})$
\item Sample minibatch of $m$ examples with their associated labels $\{(\Vec{x}^{(1)},y^{(1)}),\ldots,(\Vec{x}^{(m)},y^{(m)})\}$ from dataset $\mathcal{X}$
\item Update the discriminator by descending the stochastic gradient
\\of the loss function with respect to $\Theta_D$
\end{itemize}
}
}
\caption{HAABSA* training procedure}
\label{Algorithm: HAABSA*}
\end{algorithm}
\cite{goodfellow2014generative} proves the minimax game given in Equation \ref{eq: minimax problem} has a theoretical optimum under two conditions. First of all, the generator and discriminator need enough capacity to, respectively, generate realistic samples and discern them effectively. No formal method to ascertain sufficient capacity is given, however. Second, the discriminator should be allowed to reach its optimum given an instance of the generator, before the generator is updated again. In Algorithm \ref{Algorithm: HAABSA*}, this can be (amongst other later to be discussed options) controlled by the factor $k$.
However, in \cite{goodfellowNonConverge}, it is explained that this only holds true for the convex case. Due to the minimax nature of the game in which a saddle-point is the optimum, convergence is not guaranteed. Namely, the updating procedures for both networks have conflicting aims, and updates with respect to, for example, $\Theta_G$ might counteract gains made in prior updates to $\Theta_D$. This means it could also occur that the generator, instead of increasing the loss function, makes the bound in which the discriminator can update looser. This results in the algorithm oscillating instead of converging.
\cite{salimans2016improved} describes this problem as well, and further notes that when either the generator or discriminator becomes too good at its task, this prevents the other from learning further. For example, when the discriminator perfectly identifies all fake samples, the generator has no reference for how to change its tactic in order to make samples capable of being misclassified as real by the discriminator.
\subsubsection{Hyperparameter Optimization.}
\label{subsec: hyperparam optim}
\cite{salimans2016improved} mentions several intricate possible techniques that could increase the probability of convergence, but careful selection of hyperparameters could also at least prevent divergence. \cite{trusca2020hybrid} considers multiple hyperparameters, two of which could aid in preventing divergence.
First, the learning rate of the employed momentum optimizer governs the pace at which descent takes place in the gradient direction. Whereas too small values might prevent reaching of the optimum in the given number of iterations, smaller values prevent one of the networks from becoming too good too quickly for the other to keep up. Second, the momentum term governs the extent to which gradient values of previous iterations are considered \cite{sutskever}. Lower values for this might, in a similar manner as with the learning rate, prevent divergence.
\cite{trusca2020hybrid} also considers the L$_2$-regularization term and the dropout probability (which has been applied to all hidden layers of the network to prevent overfitting) as hyperparameters. Since, however, the optimal value for these was not found to differ much compared to \cite{wallaart2019hybrid}, and they do not directly affect the convergence of the minimax game, we leave them at the values found in \cite{trusca2020hybrid} (i.e. 0.0001 and 0.3 for the L$_2$-regularization term and keep probability, respectively).
Preliminary trial runs showed that higher values for the learning rate and momentum term led the generator to cause divergence. However, lower values impeded the discriminator from learning. As such, we use different values for the learning rate and momentum term for the generator and discriminator, writing the learning rate and momentum term for the generator as a function of those terms for the discriminator as follows: $lr_{gen} = \mu_{lr} \times lr_{dis}$ and $mom_{gen} = \mu_{mom} \times mom_{dis}$. Here, $\mu_{lr}$ and $\mu_{mom}$ are multiplier terms for the learning rate and momentum, respectively. We will then consider $lr_{dis}$, $mom_{dis}$, $\mu_{lr}$ and $\mu_{mom}$ as hyperparameters for optimization.
Last, we treat the value of $k$ as a hyperparameter. As this value determines how much more often the discriminator is updated then the generator, it can be of great importance in ensuring one of the networks does not learn too much more quickly than the other.
For the hyperparameter optimization, we use a Tree-structured Parzen Estimator (TPE) approach \cite{bergstra2011}. This method has a higher convergence speed than other methods like grid search. It optimizes by, for each run, selecting hyperparameters from the options given by maximizing the ratio of fit values of the best set of hyperparameters to the fit values of the previously unconsidered options for hyperparameters.
We run the hyperparameter optimization for the 2015 and 2016 datasets separately. The considered options for the learning rate and momentum term of the discriminator are based upon the found values in \cite{trusca2020hybrid}. To ensure a manageable runtime, we limit the algorithm to 20 runs. The algorithm is run on datasets obtained by randomly splitting the training set of the given year into 80\% train and 20\% test data.
\section{Results}
\label{chap: Results}
In this section, we discuss the results obtained from the adversarial training of HAABSA++. First, we provide a brief discussion of the results of hyperparameter optimization in Sect. \ref{sec: Results hyperpar optim}. Then, Sect. \ref{sec: performance analysis} puts forward the obtained accuracies using HAABSA*. Furthermore, we compare these with the accuracies of HAABSA++ and other competing models for ABSA.
\subsection{Results Hyperparameter Optimization}
\label{sec: Results hyperpar optim}
To decrease the risk of divergence, we include different values for the learning rate and momentum term of the generator and discriminator. Whereas trial runs with equal learning rates or momentum terms for the generator and discriminator diverged on numerous occasions, for different learning rates and momentum terms the hyperparameter optimization only one out of the total of 40 runs (20 for each dataset) diverged. The results of the hyperparameter optimization are shown in Table \ref{tab: hyperparam}.
\begin{center}
\begin{threeparttable}[h!]
\small
\caption{Hyperparameter optimization results }
\label{tab: hyperparam}
\begin{tabular}{llcc}
\toprule
\multicolumn{1}{c}{\textbf{Hyperparameter}} & \multicolumn{1}{c}{\textbf{Considered Values}} & \multicolumn{2}{l}{\textbf{Optimal Value}} \\
\multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \textbf{2015} & \textbf{2016} \\ \hline
$lr_{dis}$ & [0.007, 0.01, 0.02, 0.03, 0.05, 0.09] & 0.02 & 0.03 \\
$mom_{dis}$ & [0.7, 0.8, 0.9] & 0.9 & 0.7 \\
$\mu_{lr}$ & [0.1, 0.15, 0.2, 0.4] & 0.1 & 0.15 \\
$\mu_{mom}$ & [0.4, 0.6, 0.8, 1.6] & 0.4 & 0.6 \\
$k$ & [3, 4, 5] & 3 & 3 \\ \bottomrule
\end{tabular}
\end{threeparttable}
\vspace{-3mm}
\end{center}
\begin{center}
\begin{threeparttable}[h!]
\small
\caption{Accuracies of HAABSA++ and HAABSA*}
\label{table: accuracies}
\begin{tabular}{clccccc}
\toprule
\multicolumn{1}{l}{} & & \multicolumn{2}{c}{\textbf{SemEval 2015}} & & \multicolumn{2}{c}{\textbf{SemEval 2016}} \\ \cline{3-4} \cline{6-7}
\multicolumn{1}{l}{} & & \textit{in-sample} & \textit{out-of-sample} & & \textit{in-sample} & \textit{out-of-sample} \\ \hline
\multirow{2}{*}{\textbf{w ontology}} & HAABSA++ & 88.8\% & 81.7\% & & 91.0\% & 84.4\% \\
& HAABSA* & 89.7\% & \textbf{82.5\%} & & 91.5\% & 87.3\% \\
\multirow{2}{*}{\textbf{w/o ontology}} & HAABSA++ & 94.9\% & 80.7\% & & 95.1\% & 80.6\% \\
& HAABSA* & \textbf{96.6\%} & 82.2\% & & \textbf{96.2\%} & \textbf{88.2\%} \\ \bottomrule
\end{tabular}
\begin{tablenotes}[flushleft]
\small
\item
Note that the accuracies found for HAABSA++ differ slightly from those reported in \cite{trusca2020hybrid}. This might be due to the stochastic nature of batch selection during training, which was not seeded in the implementation.
Best result per dataset is shown in bold.
\end{tablenotes}
\end{threeparttable}
\vspace{-2mm}
\end{center}
\subsection{Performance Analysis}
\label{sec: performance analysis}
We ran our algorithm using the hyperparameters with the values discussed in the previous section. The results are displayed in Table \ref{table: accuracies}. A few considerations must be made when interpreting these results. HAABSA++ was developed as a hybrid approach, since the ontology accuracy for the cases that it was able to predict was found to be higher than the neural network accuracy out-of-sample (82.8\% versus 81.7\% and 86.8\% versus 84.4\% for the SemEval 2015 and 2016, respectively). To get a better understanding of how the neural network parts of HAABSA++ and HAABSA* perform, we also report the accuracies without ontology. Furthermore, training the HAABSA* assumes the classification of data in four classes, whereas HAABSA++ only has three classes to discern between. This hinders direct comparison between the in-sample accuracies of the two models. However, the evaluation of the testing accuracy is more straightforward as we consider only three sentiment options `Negative', `Neutral' and `Positive' for both HAABSA ++ and HAABSA*.
For our comparison between HAABSA++ and HAABSA*, we will thus focus on out-of-sample accuracy. Here, we find HAABSA* to outperform HAABSA++ by a considerable margin. Specifically, when only comparing the neural network parts of both algorithms (i.e., accuracy without ontology), a large increase in accuracy of 7.6 percentage points is found to be achieved by the adversarial training procedure for 2016. For 2015, a smaller but still substantial increase in accuracy of 1.5 percentage points is found.
It is interesting to note that for the SemEval 2016 task, a higher accuracy is obtained when not using the ontology compared to when the ontology is used. For SemEval 2015, using the ontology does yield an increase in accuracy still, but with 0.3 percentage points, the margin is small. After further development of the adversarial training method for the LCR-Rot-hop++ method for ABSA, it might be worthwhile to opt out of using the ontology (and thus, the hybrid approach), instead only using the neural network part.
\begin{center}
\begin{threeparttable}[b]
\small
\caption{Comparison with competing models}
\label{tab: comparison models}
\begin{tabular}{lcllc}
\toprule
\multicolumn{2}{c}{\textbf{SemEval 2015}} & & \multicolumn{2}{c}{\textbf{SemEval 2016}} \\ \cline{1-2} \cline{4-5}
HAABSA* (w/o ontology) & \textbf{82.2\%} & & HAABSA* (w/o ontology) & \textbf{88.2\%} \\
HAABSA++ \cite{trusca2020hybrid} & 81.7\% & & XRCE \cite{pontiki-etal-2014-semeval} & 88.1\% \\
LSTM+SynATT+TarRep \cite{He-effectiveattentionmodeling} & 81.7\% & & HAABSA++ \cite{trusca2020hybrid} & 87.0\% \\
PRET+MULT \cite{pretMult} & 81.3\% & & BBLSTM-SL \cite{BBLSTM} & 85.8\% \\
BBLSTM-SL \cite{BBLSTM} & 81.2\% & & PRET+MULT \cite{pretMult} & 85.6\% \\\bottomrule
\end{tabular}
\begin{tablenotes}[flushleft]
\small
\ite
Values shown are out-of-sample accuracies as reported in the respective research.
Best result per dataset is shown in bold.
\end{tablenotes}
\end{threeparttable}
\end{center}
As can be seen in Table \ref{tab: comparison models}, this increase in accuracy leads to HAABSA* outperforming LSTM+SynATT+TarRep (81.7\%) for the SemEval 2015 task. Furthermore, when the ontology is not used, HAABSA* outperforms XRCE (88.1\%) for the SemEval 2016 task. As such, it performs best among those models considered for the SemEval 2015 and 2016 tasks in \cite{trusca2020hybrid}.
It is also of interest to compare our obtained increase in accuracy from adversarial training with the results of \cite{karimi2020adversarial}.
Although they differ from the original implementation of GANs, instead opting for adversarial perturbations, this is, to the best of our knowledge, the only other research in which a form of adversarial training is applied to ABSA. Whereas direct comparison is not possible since they consider different datasets and a different benchmark model, we note that \cite{karimi2020adversarial} reports increases in accuracy with a maximum of 1 percentage point for all considered datasets and tasks with respect to the non-adversarially trained benchmark model. We, however, obtain an increase of 7.6 percentage points by training our neural network adversarially on the SemEval 2016 task, while an increase of 1.5 percentage points is found for the 2015 task. This could indicate that the classic implementation of GANs
\cite{goodfellow2014generative} with explicit generator and discriminator delivers better results than the approach with adversarial perturbations.
\section{Conclusion}
\label{chap: conclusion}
In this work, we applied adversarial training to the neural network part of the method devised for ABSA in \cite{trusca2020hybrid}. Although convergence might prove troublesome for adversarial networks, we found enabling differing learning rates and momentum terms for the generator and discriminator to reduce the problem of divergence. As such, we achieved an increase overall performance from 81.7\% to 82.5\% and from 84.4\% to 87.3\% for the SemEval 2015 and 2016 tasks, respectively. When only using the neural network part, adversarial training increased accuracy from 80.6\% to 88.2\% for the 2016 task, thus outperforming the hybrid approach with ontology. For the 2015 task, accuracy increased from 80.7\% to 82.2\%.
These increases in accuracy are considerably higher than those found in \cite{karimi2020adversarial}: the, so far, only other application of adversarial training to ABSA, where the authors opted for adversarial perturbations rather than the classical implementation with explicit generator and discriminator.
In future work, we would like to investigate other methods ensuring stability in GAN training, such as feature matching
\cite{featurematching1},
, minibatch discrimination \cite{salimans2016improved}, and historical averaging \cite{salimans2016improved}. Furthermore, we wish to explore whether the generator network can be improved by producing full sentences rather than attention vectors, and experiment with other architectures for the generator. Last, we plan a more direct comparison to adversarial perturbation method of \cite{karimi2020adversarial} by using the same datasets and benchmark model.
\bibliographystyle{splncs04}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,910 |
{"url":"https:\/\/zbmath.org\/0694.42017","text":"# zbMATH \u2014 the first resource for mathematics\n\nTables of Fourier transforms and Fourier transforms of distributions. Transl. from the German. Rev. and enlarged ed. (English) Zbl\u00a00694.42017\nBerlin etc.: Springer-Verlag. viii, 259 p. DM 64.00 (1990).\nThese tables represent a new, revised and enlarged version of the previously published book by this author, entitled \u201cTabellen zur Fourier-Transformation\u201d (1957; Zbl 0077.120). Known errors have been corrected, apart from the addition of a considerable number of new results, which involve almost exclusively higher functions. Again, the following tables contain a collection of integrals of the form $$(A)\\quad g_ c(y)=\\int^{\\infty}_{0}f(x)\\cos (xy)dx$$ Fourier Cosine Transform, $$(B)\\quad g_ s(y)=\\int^{\\infty}_{0}f(x)\\sin (xy)dx$$ Fourier Sine Transform, $$(C)\\quad g_ e(y)=\\int^{\\infty}_{- \\infty}f(x)e^{ixy}dx$$ Exponential Fourier Transform.\nClearly, (A) and (B) are special cases of (C) if f(x) is respectively an even or an odd function. The transform parameter y in (A) and (B) is assumed to be positive, while in (C) negative values are also included. A possible analytic continuation to complex parameters $$y^*$$ should present no difficulties. In some cases the result function g(y) is given over a partial range of y only. This means that g(y) for the remaining part of y cannot be given in a reasonably simple form. Under certain conditions the following inversion formulas for (A), (B), (C) hold: $$(A')\\quad f(x)=\\frac{2}{\\pi}\\int^{\\infty}_{0}g_ c(y)\\cos (xy)dy,$$ $$(B')\\quad f(x)=\\frac{2}{\\pi}\\int^{\\infty}_{0}g_ s(y)\\sin (xy)dy,$$ $$(C')\\quad f(x)=(2\\pi)^{-1}\\int^{\\infty}_{-\\infty}g_ e(y)e^{- ixy}dy.$$\nIn the following parts I, II, III tables for the transforms (A), (B) and (C) are given. The parts I and II are subdivided into 23 sections each involving the same class of functions. The first and the second column (in parenthesis) refers to the location of the correspondent page number for the cosine- and sine-transform respectively.\nCompared with the before-mentioned previous edition, a new part IV titled \u201cFourier Transforms of Distributions\u201d has been added. In this, those functions f(x) occurring in the parts I-III have been singled out which represent so-called probability density (or frequency distribution) functions. The corresponding normalization factors are likewise listed.\n\n##### MSC:\n 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 42-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces\n##### Keywords:\nDistributions; probability density; normalization factors\nZbl 0077.120","date":"2022-01-17 21:35:33","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7692821621894836, \"perplexity\": 856.292319628472}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-05\/segments\/1642320300624.10\/warc\/CC-MAIN-20220117212242-20220118002242-00660.warc.gz\"}"} | null | null |
\section{Introduction}
Multiple access in 5G mobile networks is an emerging research topic, since it is key for the next generation network to keep pace with the exponential growth of mobile data and multimedia traffic \cite{Li5G} and \cite{Huawei5g}. Non-orthogonal multiple access (NOMA) has recently received considerable attention as a promising candidate for 5G multiple access \cite{NOMAPIMRC,6933459,Nomading,6708131}. Particularly, NOMA uses the power domain for multiple access, where different users are served at different power levels. The users with better channel conditions employ successive interference cancellation (SIC) to remove the messages intended for other users before decoding their own \cite{Cover1991}. The benefit of using NOMA can be illustrated by the following example. Consider that there is a user close to the edge of its cell, denoted by $A$, whose channel condition is very poor. For conventional MA, an orthogonal bandwidth channel, e.g., a time slot, will be allocated to this user, and the other users cannot use this time slot. The key idea of NOMA is to squeeze another user with better channel condition, denoted by $B$, into this time slot. Since $A$'s channel condition is very poor, the interference from $B$ will not cause much performance degradation to $A$, but the overall system throughput can be significantly improved since additional information can be delivered between the base station (BS) and $B$. The design of NOMA for uplink transmissions has been proposed in \cite{6933459}, and the performance of NOMA with randomly deployed mobile stations has been characterized in \cite{Nomading}. The combination of cooperative diversity with NOMA has been considered in \cite{Zhiguo_conoma}.
Since multiple users are admitted at the same time, frequency and spreading code, co-channel interference will be strong in NOMA systems, i.e., a NOMA system is interference limited. As a result, it may not be realistic to ask all the users in the system to perform NOMA jointly. A promising alternative is to build a hybrid MA system, in which NOMA is combined with conventional MA. In particular, the users in the system can be divided into multiple groups, where NOMA is implemented within each group and different groups are allocated with orthogonal bandwidth resources. Obviously the performance of this hybrid MA scheme is very dependent on which users are grouped together, and the aim of this paper is to investigate the effect of this grouping. Particularly, tn this paper, we focus on a downlink communication scenario with one BS and multiple users, where the users are ordered according to their connections to the BS, i.e., the $m$-th user has the $m$-th worst connection to the BS. Consider that two users, the $m$-th user and the $n$-th user, are selected for performing NOMA jointly, where $m<n$. The impact of user pairing on the performance of NOMA will be characterized in this paper, where two types of NOMA will be considered. One is based on fixed power allocation, termed F-NOMA, and the other is cognitive radio inspired NOMA, termed CR-NOMA.
For the F-NOMA scheme, the probability that F-NOMA can achieve a larger sum rate than conventional MA is first studied, where an exact expression for this probability as well as its high signal-to-noise ratio (SNR) approximation are obtained. These developed analytical results demonstrate that it is almost certain for F-NOMA to outperform conventional MA, and the channel quality of the $n$-th user is critical to this probability. In addition, the gap between the sum rates achieved by F-NOMA and conventional MA is also studied, and it is shown that this gap is determined by how different the two users' channel conditions are, as initially reported in \cite{Zhiguo_conoma}. For example, if $n=M$, it is preferable to choose $m=1$, i.e., pairing the user with the best channel condition with the user with the worst channel condition. The reason for this phenomenon can be explained as follows. When $m$ is small, the $m$-th user's channel condition is poor, and the data rate supported by this user's channel is also small. Therefore the spectral efficiency of conventional MA is low, since the bandwidth allocated to this user cannot be accessed by other users. The use of F-NOMA ensures that the $n$-th user will have access to the resource allocated to the $m$-th user. If $(n-m)$ is small, the $n$-th user's channel quality is similar to the $m$-th user's, and the benefit to use NOMA is limited. But if $n>>m$, the $n$-th user can use the bandwidth resource much more efficiently than the $m$-th user, i.e., a larger $(n-m)$ will result in a larger performance gap between F-NOMA and conventional MA.
The key idea of CR-NOMA is to opportunistically serve the $n$-th user on the condition that the $m$-th user's quality of service (QoS) is guaranteed. Particularly the transmit power allocated to the $n$-th user is constrained by the $m$-th user's signal-to-interference-noise ratio (SINR), whereas F-NOMA uses a fixed set of power allocation coefficients. Since the $m$-th user's QoS can be guaranteed, we mainly focus on the performance of the $n$-th user offered by CR-NOMA. An exact expression for the outage probability achieved by CR-NOMA is obtained first, and then used for the study of the diversity order. In particular, we show that the diversity order experienced by the $n$-th user is $m$, which means that the $m$-th user's channel quality is critical to the performance of CR-NOMA. This is mainly because of the imposed SINR constraint, where the $n$-th user can be admitted into the bandwidth channel occupied by the $m$-th user, only if the $m$-th user's SINR is guaranteed. As a result, with a fixed $m$, increasing $n$ does not bring much improvement to the $n$-th user's outage probability, which is different from F-NOMA. If the ergodic rate is used as the criterion, a similar difference between F-NOMA and CR-NOMA can be observed. Again take the scenario described in the last paragraph as an example. If $n=M$, in order to yield a large gain over conventional MA, F-NOMA prefers the choice of $m=1$, but CR-NOMA prefers the choice of $m=M-1$ , i.e., pairing the user with the best channel condition with the user with the second best channel condition.
\section{NOMA With Fixed Power Allocation }\label{section noma}
Consider a downlink communication scenario with one BS and $M$ mobile users. Without loss of generality, assume that the users' channels have been ordered as $|h_1|^2\leq \cdots \leq |h_M|^2$, where $h_m$ denotes the Rayleigh fading channel gain between the BS and the ordered $m$-th user. Consider that the $m$-th user and the $n$-th user, $m<n$, are paired to perform NOMA.
In this section, we focus on F-NOMA, where the BS allocates a fixed amount of transmit power to each user. In particular, denote $a_m$ and $a_n$ as the power allocation coefficients for the two users, where these coefficients are fixed and $a_m^2+a^2_n=1$. According to the principle of NOMA, $a_m\geq a_n$ since $|h_m|^2\leq |h_n|^2$. The rates achievable to the two users are given by
\begin{eqnarray}
R_m = \log \left( 1+\frac{|h_m|^2a_m^2}{|h_m|^2a_n^2+\frac{1}{\rho}} \right),
\end{eqnarray}
and
\begin{eqnarray}
R_n = \log \left( 1+ \rho a^2_n |h_n|^2\right),
\end{eqnarray}
respectively, where $\rho$ denotes the transmit SNR. Note that the $n$-th user can decode the message intended for the $m$-th user successfully and $R_n$ is always achievable at the $n$-th user,
since $R_m\leq \log \left( 1+\frac{|h_n|^2a_m^2}{|h_n|^2a_n^2+\frac{1}{\rho}} \right)$.
On the other hand, an orthogonal MA scheme, such as time-division multiple-access (TDMA), can support the following data rate:
\begin{eqnarray}
\bar{R}_i = \frac{1}{2}\log \left( 1+ \rho |h_i|^2\right),
\end{eqnarray}
where $i\in\{m,n\}$. In the following subsections, the impact of user pairing on the sum rate and the individual user rates achieved by F-NOMA is investigated.
\subsection{Impact of user pairing on the sum rate}
In this subsection, we focus on how user pairing affects the probability that NOMA achieves a lower sum rate than conventional MA schemes, which is given by
\begin{eqnarray}
\mathrm{P}(R_m+R_n<\bar{R}_m+\bar{R}_n).
\end{eqnarray}
The following theorem provides an exact expression for the above probability as well as its high SNR approximation.
\begin{theorem}\label{lemma1}
Suppose that the $m$-th and $n$-th ordered users are paired to perform NOMA. The probability that F-NOMA achieves a lower sum rate than conventional MA is given by
\begin{align}
&\mathrm{P}(R_m+R_n<\bar{R}_m+\bar{R}_n)=\\\nonumber &1- \sum^{n-1-m}_{i=0}{n-1-m \choose i} \frac{(-1)^i\varpi_1}{m+i} \int^{\varpi_2}_{\varpi_4} f(y)(F(y))^{n-1-m-i} \\\nonumber &\times \left(1-F(y)\right)^{M-n} \left(\left[F\left(y\right)\right]^{m+i}-\left[F\left(\frac{\varpi_2-y}{1+y}\right)\right]^{m+i}\right)dy\\ \nonumber &-\frac{\varpi_3}{\rho}\sum^{n-1}_{j=0}{n-1 \choose j}(-1)^j \frac{\rho}{M-n+j+1} e^{-\frac{(M-n+j+1)\varpi_2}{\rho}},
\end{align}
where $f(x)=\frac{1}{\rho}e^{-\frac{x}{\rho}}$, $F(x) = 1-e^{-\frac{x}{\rho}}$,
$\varpi_1=\frac{M!}{(m-1)!(n-1-m)!(M-n)!}$, $\varpi_2=\frac{1-2a_n^2}{a_n^4}$, $\varpi_3=\frac{M!}{(n-1)!(M-n)!}$ and $\varpi_4=\sqrt{1+\varpi_2}-1$.
At high SNR, this probability can be approximated as follows:
\begin{align}
&\mathrm{P}(R_m+R_n<\bar{R}_m+\bar{R}_n) \approx\frac{1}{\rho^n}\left(
\frac{ \varpi_3\varpi_2^n}{n} - \varpi_1\varpi\right),
\end{align}
where $\varpi=\sum^{n-1-m}_{i=0}{n-1-m \choose i} \frac{(-1)^i}{m+i} \int^{\varpi_2}_{\varpi_4} y^{n-1-m-i} $ $\times \left( y^{m+i}-\left[\frac{\varpi_2-y}{(1+y)}\right]^{m+i}\right)dy$, i.e., $\varpi$ is a constant and not a function of $\rho$.
\end{theorem}
\begin{proof}
See the appendix.
\end{proof}
Theorem \ref{lemma1} demonstrates that it is almost certain for F-NOMA to outperform conventional MA, particularly at high SNR. Furthermore, the decay rate of the probability $\mathrm{P}(R_m+R_n<\bar{R}_m+\bar{R}_n)$ is approximately $\frac{1}{\rho^n}$, i.e., the quality of the $n$-th user's channel determines the decay rate of this probability.
\subsection{Asymptotic studies of the sum rate achieved by NOMA}
In addition to the probability $\mathrm{P}(R_m+R_n<\bar{R}_m+\bar{R}_n)$, it is also of interest to study how large of a performance gain F-NOMA offers over conventional MA, i.e.,
\[
\mathrm{P}(R_m+R_n-\bar{R}_m-\bar{R}_n<R),
\]
where $R$ is a targeted performance gain. The probability studied in the previous subsection can be viewed as a special case by setting $R=0$. An interesting observation for the cases with $R>0$ is that there will be an error floor for $\mathrm{P}(R_m+R_n-\bar{R}_m-\bar{R}_n<R)$, regardless of how large the SNR is. This can be shown by studying the following asymptotic expression of the sum rate gap:
\begin{align}
&R_m+R_n-\bar{R}_m-\bar{R}_n\\ \nonumber \underset{\rho\rightarrow \infty}{\rightarrow} &
\log \left( \frac{1}{a_n^2} \right)+ \log \left( \rho a^2_n |h_n|^2\right) - \log \left( \rho|h_m| |h_n|\right)
\\ \nonumber =& \log |h_n| - \log |h_m| ,
\end{align}
which is not a function of SNR.
Hence the probability can be expressed asymptotically as follows:
\begin{align}\label{asym}
&\mathrm{P}\left(R_m+R_n-\bar{R}_m-\bar{R}_n<R\right)\\ \nonumber \underset{\rho\rightarrow \infty}{\rightarrow} &\mathrm{P}\left( \log |h_n| - \log |h_m| <R \right) .
\end{align}
When $R=0$, $\mathrm{P}\left(R_m+R_n-\bar{R}_m-\bar{R}_n<R\right)\rightarrow 0$, which is consistent with Theorem \ref{lemma1}, since $$\mathrm{P}\left(R_m+R_n<\bar{R}_m+\bar{R}_n\right)\sim \frac{1}{\rho^n}\underset{\rho\rightarrow \infty}{\rightarrow}0.$$
When $R\neq 0$, \eqref{asym} implies that the probability $\mathrm{P}\left(R_m+R_n-\bar{R}_m-\bar{R}_n<R\right)$ can be expressed asymptotically as follows:
\begin{align}
\mathrm{P}\left( \log |h_n| - \log |h_m| <R \right) \rightarrow
\mathrm{P}\left( \frac{|h_n|^2}{ |h_m|^2} <2^{2R} \right).
\end{align}
Directly applying the joint probability density function (pdf) of the users' channels shown in \eqref{joint pdf}, the probability can be rewritten as follows:
\begin{align}
&\mathrm{P}\left( \log |h_n| - \log |h_m| <R \right) \\ \nonumber & =
\int^{\infty}_{0}\int^{y}_{2^{-2R}y}\varpi_1 f(x) f(y)[F(x)]^{m-1} \\\nonumber &\times \left(F(y)-F(x)\right)^{n-1-m} \left(1-F(y)\right)^{M-n}dx dy ,
\end{align}
which is quite complicated to evaluate.
In \cite{Subranhmaniam}, a simpler pdf for the ratio of two order statistics has been provided as follows:
\begin{align}\nonumber
f_{ \frac{|h_m|^2}{ |h_n|^2} }(z) = \frac{M!}{(m-1)!(n-m-1)!(M-n)!} \sum^{m-1}_{j_1=0}\sum^{n-m-1}_{j_2=0}\\ \nonumber (-1)^{j_1+j_2} {m-1 \choose j_1} {n-m-1 \choose j_2} (\tau_2+\tau_1 z)^{-2},
\end{align}
where $\tau_1=j_1-j_2+n-m$ and $\tau_2=M-n+1+j_2$. By using this pdf, the addressed probability can be calculated as follows:
\begin{align}\label{sum rate gap}
&\mathrm{P}\left( \log |h_n| - \log |h_m| <R \right) \\ \nonumber & \rightarrow
\frac{M!}{(m-1)!(n-m-1)!(M-n)!} \sum^{m-1}_{j_1=0}\sum^{n-m-1}_{j_2=0}\\ \nonumber & \frac{(-1)^{j_1+j_2}}{\tau_1} {m-1 \choose j_1} {n-m-1 \choose j_2} \left(\frac{1}{\tau_2+2^{-2R}\tau_1} - \frac{1}{\tau_2+\tau_1} \right) .
\end{align}
\subsection{Impact of user pairing on individual user rates}
Careful user pairing not only improves the sum rate, but also has the potential to improve the individual user rates, as shown in this section. We first focus on the probability that F-NOMA can achieve a larger rate than orthogonal MA for the $m$-th user which is given by
\begin{align}
&\mathrm{P}(R_m>\bar{R}_m) \\ \nonumber =& \mathrm{P}\left( \left( 1+\frac{|h_m|^2a_m^2}{|h_m|^2a_n^2+\frac{1}{\rho}} \right)^2> (1+\rho|h_m|^2)\right).
\end{align}
After some algebraic manipulations, the above probability can be further rewritten as follows:
\begin{align}\label{user m}
&\mathrm{P}(R_m>\bar{R}_m) = \mathrm{P}\left( |h_m|^2<\frac{1-2a_n^2}{\rho a_n^4}\right)\\ \nonumber &= \int^{\frac{1-2a_n^2}{\rho a_n^4}}_{0} \frac{\varpi_5 }{\rho}e^{-\frac{(M-m+1)y}{\rho}} \left(1- e^{-\frac{y}{\rho}}\right)^{m-1} dy
\\ \nonumber &= \sum^{m-1}_{i=0} {m-1 \choose i} \frac{(-1)^i\varpi_5}{M-m+i+1}\left(1-e^{-\frac{(1-2a_n^2)(M-m+i+1)}{\rho a_n^4}}\right) , \end{align}
where $\varpi_5=\frac{M!}{(m-1)!(M-m)!}$.
By applying a series expansion, the above probability can be rewritten as follows:
\begin{align}\label{indvidtual 1}
\mathrm{P}(R_m>\bar{R}_m)
&= \sum^{m-1}_{i=0} {m-1 \choose i} (-1)^{i+1}\varpi_5 \\ \nonumber&\times \sum^{\infty}_{k=1}(-1)^k \frac{(1-2a_n^2)^{k}(M-m+i+1)^{k-1}}{k!\rho^{k} a_n^{4k}}.
\end{align}
Again applying the results in \eqref{property1} and \eqref{property2}, the above equation can be approximated as follows:
\begin{align}\label{user m high}
\mathrm{P}(R_m>\bar{R}_m)
&\approx \varpi_5 \frac{(1-2a_n^2)^{m}}{m\rho^{m} a_n^{4m}},
\end{align}
which means that $\mathrm{P}(R_m>\bar{R}_m)$ decays at a rate of $\frac{1}{\rho^m}$.
On the other hand, the probability that the $n$-th user can experience better performance in a NOMA system than in orthogonal MA systems is given by
\begin{eqnarray}\nonumber
\mathrm{P}(R_n>\bar{R}_n) = \mathrm{P}\left(\log \left( 1+ \rho a^2_n |h_n|^2\right)> \frac{1}{2}\log (1+\rho|h_n|^2 \right).
\end{eqnarray}
Following similar steps as previously, we obtain the following:
\begin{eqnarray} \label{user n}
\mathrm{P}(R_n>\bar{R}_n) = \mathrm{P}\left( |h_n|^2>\frac{1-2a_n^2}{\rho a_n^4}\right).
\end{eqnarray}
Interestingly $\mathrm{P}(R_n>\bar{R}_n)$ in \eqref{user n} is very much similar to $\mathrm{P}(R_m>\bar{R}_m)$ in \eqref{user m}, which yields the following:
\begin{align}\label{individutal 2}
&\mathrm{P}(R_n>\bar{R}_n) = 1- \sum^{n-1}_{i=0} {n-1 \choose i} \frac{(-1)^i\varpi_3}{M-n+i+1}\\ \nonumber &\times \left(1-e^{-\frac{(1-2a_n^2)(M-n+i+1)}{\rho a_n^4}}\right), \end{align}
and its high SNR approximation is given by
\begin{align}\label{user n high}
\mathrm{P}(R_n>\bar{R}_n)
&\approx 1- \varpi_3 \frac{(1-2a_n^2)^{n}}{n\rho^{n} a_n^{4n}}.
\end{align}
As can be seen from \eqref{user m high} and \eqref{user n high}, the two users will have totally different experience in NOMA systems. Particularly, a user with a better channel condition is more willing to perform NOMA since $\mathrm{P}(R_n>\bar{R}_n)\rightarrow 1$, which is not true for a user with a poor channel condition. Furthermore, it is preferable to pair two users whose channel conditions are significantly distinct, since \eqref{user m high} and \eqref{user n high} implies that $m$ should be as small as possible and $n$ should be as large as possible.
\begin{figure*}[bt!]
\begin{align}\label{theorem1}
&\mathrm{P}_{n}^o=\varpi_5 \sum^{M-n}_{i=0}{M-n \choose i}(-1)^i \frac{\left[G(b)\right]^{m+i}}{m+i} + \sum^{n-1-m}_{i=0}{n-1-m \choose i} (-1)^i\int^{a\epsilon_1}_b g(y) \left(1-G(y)\right)^{M-n}G(y)^{n-1-m-i} \varpi_1 \\ \nonumber &\times \frac{\left(G(y)^{m+i} - G(b)^{m+i}\right)}{m+i}dy +\sum^{n-1-m}_{i=0}{n-1-m \choose i} (-1)^i\int^{b+a\epsilon_1}_{a\epsilon_1} \left(1-G(y)\right)^{M-n}G(y)^{n-1-m-i}\frac{\left(G(y)^{m+i} - G(b)^{m+i}\right)}{m+i}\\\nonumber &\times \varpi_1 g(y) dy +\sum^{n-1-m}_{i=0}{n-1-m \choose i} (-1)^i\int^\infty_{b+a\epsilon_1} g(y) \left(1-G(y)\right)^{M-n} G(y)^{n-1-m-i} \varpi_1 \frac{\left(G\left(\frac{b}{1-\frac{a\epsilon_1}{|h_n|^2}}\right)^{m+i} - G(b)^{m+i}\right)}{m+i}dy.
\end{align}
\end{figure*}
\section{ Cognitive Radio Inspired NOMA}
NOMA can be also viewed as a special case of cognitive radio systems \cite{4840529} and \cite{5403537}, in which a user with a strong channel condition, viewed as a secondary user, is squeezed into the spectrum occupied by a user with a poor channel condition, viewed as a primary user. Following the concept of cognitive radio networks, a variation of NOMA, termed as CR-NOMA, can be designed as follows. Suppose that the BS needs to serve the $m$-th user, i.e., a user a with poor channel condition, due to either the high priority of this user's messages or user fairness, e.g., this user has not been served for a long time. This user can be viewed as a primary user in a cognitive radio system. The $n$-th user can be admitted into this channel on the condition that the $n$-th user will not cause too much performance degradation to the $m$-th user.
Consider that the targeted SINR at the $m$-th user is $I$, which means that the choices of the power allocation coefficients, $a_m$ and $a_n$, need to satisfy the following constraint:
\begin{align}\label{an dymanic2}
\frac{|h_m|^2a_m^2}{|h_m|^2a_n^2+\frac{1}{\rho}} \geq I.
\end{align}
This means that the maximal transmit power that can be allocated to the $n$-th user is given by
\begin{align}\label{an dymanic1}
a_n^2= \max \left\{0,\frac{|h_m|^2 -\frac{I}{\rho}}{|h_m|^2(1+I)}\right\},
\end{align}
which means that $a_n=0$ if $|h_m|^2 <\frac{I}{\rho}$.
Note that the choice of $a_n$ in \eqref{an dymanic1} is a function of the channel coefficient $h_m$, unlike the constant choice of $a_n$ used by F-NOMA in the previous section.
Since the $m$-th user's QoS can be guaranteed due to \eqref{an dymanic2}, we only need to study the performance experienced by the $n$-th user. Particularly the outage performance of the $n$-th user is defined as follows:
\begin{align}
\mathrm{P}_o^n\triangleq \mathrm{P}\left(\log(1+a_n^2\rho|h_n|^2)<R\right),
\end{align}
and the following theorem provides an exact expression for the above outage probability as well as its approximation.
\begin{theorem}\label{theorm2}
Suppose that the transmit power allocated to the $n$-th user can satisfy the predetermined SINR threshold, $I$, as shown in \eqref{an dymanic1}. The $n$-th user's outage probability achieved by CR-NOMA is given by \eqref{theorem1}, where $g(y)=e^{-y}$, $G(y) = 1-e^{-y}$, $\epsilon_1=\frac{2^R-1}{\rho}$, $b=\frac{I}{\rho}$, $a=1+I$ and $b\leq a\epsilon_1$. The diversity order achieved by CR-NOMA is given by
\[
\underset{\rho \rightarrow \infty}{\lim}- \frac{\log P_o^n}{\log \rho} = m.
\]
\end{theorem}
\begin{proof}See the appendix.
\end{proof}
Theorem \ref{theorm2} demonstrates an interesting phenomenon that, in CR-NOMA, the diversity order experienced by the $n$-th user is determined by how good the $m$-th user's channel quality is. This is because the $n$-th user can be admitted to the channel occupied by the $m$-th user only if the $m$-th user's QoS is met. For example, if the $m$-th user's channel is poor and its targeted SINR is high, it is very likely that the BS allocates all the power to the $m$-th user, and the $n$-th user might not even get served.
Recall from the previous section that F-NOMA can achieve a diversity gain of $n$ for the $n$-th user, and therefore the diversity order achieved by CR-NOMA could be much smaller than that achieved by F-NOMA, particularly if $n>>m$. This performance difference is again due to the imposed power constraint shown in \eqref{an dymanic1}.
It is important to point out that CR-NOMA can strictly guarantee the $m$-th user's QoS, and therefore achieve better fairness compared to F-NOMA. In particular, the use of CR-NOMA can ensure that a diversity order of $m$ is achievable to the $n$-th user, and admitting the $n$-th user into the same channel as the $m$-th user will not cause too much performance degradation to the $m$-th user. Particularly the SINR experienced by the $m$-th user is strictly maintained at the predetermined level $I$.
\subsection*{Sum rate achieved by CR-NOMA}
Without sharing the spectrum with the $n$-th user, i.e, all the bandwidth resource is allocated to the $m$-th user, the following rate is achievable:
\begin{eqnarray}
\tilde{R}_m = \log \left( 1+ \rho |h_m|^2\right).
\end{eqnarray}
It is easy to show that the use of CR-NOMA always achieves a larger sum rate since
\begin{align}
&R_m+R_n-\tilde{R}_m\\\nonumber
=& \log \left( 1+\frac{|h_m|^2a_m^2}{|h_m|^2a_n^2+\frac{1}{\rho}} \right)+\log \left( 1+ \rho a^2_n |h_n|^2\right) \\ \nonumber &- \log \left(1+\rho |h_m|^2\right)
\\\nonumber
=&\log \frac{ 1+ \rho a^2_n |h_n|^2}{ 1+ \rho a^2_n |h_m|^2}\geq 0.
\end{align}
This superior performance gain is not surprising, since the key idea of CR-NOMA is to serve a user with a strong channel condition, without causing too much performance degradation to the user with a poor channel condition.
In addition, it is of interest to study how much the averaged rate gain CR-NOMA can yield, i.e., $\mathcal{E}\left\{R_n \right\}$. This averaged rate gain can be calculated as follows:
\begin{align}
\mathcal{E}\left\{R_n \right\} &= \int^{\infty}_{b} \int^{\infty}_{x}\log\left(1+\frac{x -b}{xa}\rho y\right)\\ \nonumber &\times f_{|h_{m}|^2,|h_{n}|^2}(x,y) dydx.
\end{align}
In general, the evaluation of the above equation is difficult, and in the following we provide a case study when $n-m=1$. Particularly, the joint pdf of the channels for this special case can be simplified and the averaged rate gain can calculated as follows:
\begin{align}\nonumber
\mathcal{E}\left\{R_n \right\} &= \varpi_1\int^{\infty}_{b}f(x) [F(x)]^{m-1} \int^{\infty}_{x}\log\left(1+\frac{x -b}{xa}\rho y\right)\\ &\times f(y) \left(1-F(y)\right)^{M-n}dydx\\ \nonumber
&= \frac{-\varpi_1}{M-n+1}\int^{\infty}_{b}f(x) [F(x)]^{m-1} \\ \nonumber &\times\int^{\infty}_{x}\log\left(1+\frac{x -b}{xa}\rho y\right) d\left(1-F(y)\right)^{M-n+1}dx.
\end{align}
After some algebraic manipulations, the above equation can be rewritten as follows:
\begin{align}\nonumber
\mathcal{E}\left\{R_n \right\} &= \frac{\varpi_1}{M-n+1}\int^{\infty}_{b}f(x) [F(x)]^{m-1} \\ \nonumber &\times\left( \log\left(1+\frac{x -b}{a}\rho \right) \left(1-F(x)\right)^{M-n+1}\right. \\ \nonumber &\left.+\frac{1}{\ln 2}\int^{\infty}_{x}\left(1-F(y)\right)^{M-n+1} \frac{\frac{x -b}{xa}\rho }{ 1+\frac{x -b}{xa}\rho y} dy\right)dx.
\end{align}
Now applying Eq. (3.352.2) in \cite{GRADSHTEYN}, the average rate gain can be expressed as follows:
\begin{align}\label{cr noma rate}
\mathcal{E}\left\{R_n \right\} &= \frac{\varpi_1}{M-n+1}\int^{\infty}_{b}f(x) [F(x)]^{m-1} \\ \nonumber &\times\left( \log\left(1+\frac{x -b}{a}\rho \right) \left(1-F(x)\right)^{M-n+1}- \frac{e^{\frac{x^2a}{\rho(x -b)}}}{\ln 2}\right. \\ \nonumber &\left.\times\text{Ei}\left(-(M-n+1)x-\frac{(M-n+1)xa}{\rho(x -b)}\right)\right)dx,
\end{align}
where $\text{Ei}(\cdot)$ denotes the exponential integral.
\begin{figure}[!htp]
\begin{center} \subfigure[ $m=1$ ]{\includegraphics[width=0.47\textwidth]{fig1m1.eps}}
\subfigure[$m=2$]{\includegraphics[width=0.47\textwidth]{fig1m2.eps}}
\end{center}
\caption{The probability that F-NOMA realizes a lower sum rate than conventional MA. $M=5$. The analytical results are based on Theorem \ref{lemma1}. }\label{fig 1}
\end{figure}
\section{Numerical Studies}
In this section, computer simulations are used to evaluate the performance of two NOMA schemes as well as the accuracy of the developed analytical results.
\subsection{NOMA with fixed power allocation}
In Fig. \ref{fig 1}, the probability that F-NOMA realizes a lower sum rate than conventional MA, i.e., $\mathrm{P}(R_m+R_n<\bar{R}_m+\bar{R}_n)$, is shown as a function of SNR. $a_m^2=\frac{4}{5}$ and $a_n^2=\frac{1}{5}$. As can be seen from both figures, F-NOMA almost always outperforms conventional MA, particularly at high SNR. The simulation results in Fig. \ref{fig 1} also demonstrate the accuracy of the analytical results provided in Theorem \ref{lemma1}. For example, the exact expression of $\mathrm{P}(R_m+R_n<\bar{R}_m+\bar{R}_n)$ shown in Theorem \ref{lemma1} matches perfectly with the simulation results, whereas the developed approximation results become accurate at high SNR.
Another important observation from Fig. \ref{fig 1} is that increasing $n$, i.e., scheduling a user with a better channel condition, will make the probability decrease at a faster rate. This observation is consistent to the high SNR approximation results provided in Theorem \ref{lemma1} which show that the slope of the curve for the probability $\mathrm{P}(R_m+R_n<\bar{R}_m+\bar{R}_n)$ is a function of $n$. In Fig. \ref{fig2}, the probability $\mathrm{P}(R_m+R_n-\bar{R}_m-\bar{R}_n<R)$ is shown with different choices of $R$. Comparing Fig. \ref{fig 1} to Fig. \ref{fig2}, one can observe that $\mathrm{P}(R_m+R_n-\bar{R}_m-\bar{R}_n<R)$ never approaches zero, regardless of how large the SNR is. This observation confirms the analytical results developed in \eqref{sum rate gap} which show that the probability $\mathrm{P}(R_m+R_n-\bar{R}_m-\bar{R}_n<R)$ is no longer a function of SNR, when $\rho\rightarrow 0$. It is interesting to observe that the choice of a smaller $m$ is preferable to reduce $\mathrm{P}(R_m+R_n-\bar{R}_m-\bar{R}_n<R)$, a phenomenon previously reported in \cite{Zhiguo_conoma}.
\begin{figure}[!htbp]\centering
\epsfig{file=fig2error.eps, width=0.47\textwidth, clip=}
\caption{ The probability that the sum rate gap between F-NOMA and conventional MA is larger than $R$. $M=5$ and $n=M$. The analytical results are based on \eqref{sum rate gap}. }\label{fig2}
\end{figure}
In Fig. \ref{fig3}, two different but related probabilities are shown together. One is $\mathrm{P}(R_m>\bar{R}_m)$, i.e., the probability that it is beneficial for the user with a poor channel condition to perform F-NOMA, and the other is $\mathrm{P}(R_n<\bar{R}_n)$, i.e., the probability that the user with a strong channel condition prefers conventional MA. In Section \ref{section noma}.C, analytical results have been developed to show that both $\mathrm{P}(R_m>\bar{R}_m)$ and $\mathrm{P}(R_n<\bar{R}_n)$ are decreasing with increasing SNR, which is confirmed by the simulation results in Fig. \ref{fig3}. The reason that $\mathrm{P}(R_m>\bar{R}_m)$ is reduced at a higher SNR is that the $m$-th user's rate in an F-NOMA system becomes a constant, i.e., $\log \left( 1+\frac{|h_m|^2a_m^2}{|h_m|^2a_n^2+\frac{1}{\rho}} \right)\underset{\rho\rightarrow \infty}{\rightarrow} \log \left( 1+\frac{ a_m^2}{a_n^2} \right)$, which is much smaller than $\bar{R}_m$, at high SNR. On the other hand, it is more likely for $R_n$ to be larger than $\bar{R}_n$ since there is a factor of $\frac{1}{2}$ outside of the logarithm of $\bar{R}_n$.
\begin{figure}[!htbp]\centering
\epsfig{file=figind.eps, width=0.47\textwidth, clip=}
\caption{ The behavior of individual data rates achieved by F-NOMA, $\mathrm{P}(R_n<\bar{R}_n)$ and $\mathrm{P}(R_m>\bar{R}_m)$. $M=5$. The analytical results are based on \eqref{indvidtual 1} and \eqref{individutal 2}. }\label{fig3}
\end{figure}
\subsection{Cognitive radio inspired NOMA}
In Fig. \ref{fig4} the $n$-th user's outage probability achieved by CR-NOMA is shown as a function of SNR. As can be seen from the figure, the exact expression for the outage probability $\mathrm{P}_n^o\triangleq \mathrm{P}(R_n<R)$ developed in Theorem \ref{theorm2} matches the simulation results perfectly. Recall from Theorem~\ref{theorm2} that the diversity order achievable for the $n$-th user is $m$. Or in other words, the slope of the outage probability is determined by the channel quality of the $m$-th user, which is also confirmed by Fig. \ref{fig4}. For example, when increasing $m$ from $1$ to $2$, the outage probability is significantly reduced, and its slope is also increased. To clearly demonstrate the diversity order, we have provided an auxiliary curve in the figure which is proportional to $\frac{1}{\rho^m}$. As can be observed in the figure, this auxiliary curve is parallel to the one for $ \mathrm{P}(R_n<R)$, which confirms that the diversity order achieved by CR-NOMA is $m$.
\begin{figure}[!htbp]\centering
\epsfig{file=figCRnM.eps, width=0.47\textwidth, clip=}
\caption{ The outage probability for the $n$-th user achieved by CR-NOMA, when $n=M$. $M=5$, $R=1$ bit per channel use (BPCU) and $I=5$. The analytical results are Theorem \ref{theorm2}. }\label{fig4}
\end{figure}
\begin{figure}[!htbp]\centering
\epsfig{file=figCR_I.eps, width=0.47\textwidth, clip=}
\caption{ The outage probability for the $n$-th user achieved by CR-NOMA. $m=1$, $M=5$, and $R=1$ BPCU. }\label{fig5}
\end{figure}
Since Theorem \ref{theorm2} states that the diversity order of $ \mathrm{P}(R_n<R)$ is not a function of $n$, an interesting question is whether a different choice of $n$ matters. Fig. \ref{fig5} is provided to answer this question. While the use of a larger $n$ does bring some reduction of $ \mathrm{P}(R_n<R)$, the performance gain of increasing $n$ is negligible, particularly at high SNR. This is because the channel quality of the $m$-th user becomes a bottleneck for admitting the $n$-th user into the same channel.
\begin{figure}[!htp]
\begin{center} \subfigure[ $n=m+1$ ]{\includegraphics[width=0.47\textwidth]{figCR_rate1.eps}}
\subfigure[General Cases]{\label{fig set comparison
b2}\includegraphics[width=0.47\textwidth]{figCR_rate2.eps}}
\end{center}
\caption{The ergodic data rate for the $n$-th user achieved by CR-NOMA. $M=5$ and $I=5$. Analytical results are based on \eqref{cr noma rate}. }\label{fig6}
\end{figure}
In Fig. \ref{fig6} the performance of CR-NOMA is evaluated by using the ergodic data rate as the criterion. Due to the use of \eqref{an dymanic1}, the $m$-th user's QoS can be satisfied, and therefore we only focus on the $n$-th user's data rate, which is the performance gain of CR-NOMA over conventional MA. Fig. \ref{fig6} demonstrates that, by fixing $(n-m)$, it is beneficial to select two users with better channel conditions. While Fig. \ref{fig5} shows that changing $n$ with a fixed $m$ does not affect the outage probability, Fig. \ref{fig6} demonstrates that user pairing has a significant impact on the ergodic rate. Specifically, when fixing the choice of $m$, pairing it with a user with a better channel condition can yield a gain of more than $1$ bit per channel use (BPCU) at $30$dB. Another interesting observation from Fig. \ref{fig6} is that with a fixed $n$, increasing $m$ will improve the performance of CR-NOMA, which is different from F-NOMA. For example, when $n=M$, Fig. \ref{fig2} shows that the user with the worst channel condition, $m=1$, is the best partner, whereas Fig. \ref{fig6} shows that the user with the second best channel condition, i.e., $m=M-1$, is the best choice.
\section{Conclusions}
In this paper the impact of user pairing on the performance of two NOMA systems, NOMA with fixed power allocation (F-NOMA) and cognitive radio inspired NOMA (CR-NOMA), has been studied. For F-NOMA, both analytical and numerical results have been provided to demonstrate that F-NOMA can offer a larger sum rate than orthogonal MA, and the performance gain of F-NOMA over conventional MA can be further enlarged by selecting users whose channel conditions are more distinctive. For CR-NOMA, the channel quality of the user with a poor channel condition is critical, since the transmit power allocated to the other user is constrained following the concept of cognitive radio networks. One promising future direction of this paper is that the analytical results can be used as criteria designing distributed approaches for dynamic user pairing/grouping.
\bibliographystyle{IEEEtran}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,172 |
<?php
/**
* @namespace
*/
namespace Zend\XmlRpc\Server;
/**
* Zend_XmlRpc_Server_Exception
*
* @uses \Zend\XmlRpc\Exception
* @category Zend
* @package Zend_XmlRpc
* @subpackage Server
* @copyright Copyright (c) 2005-2010 Zend Technologies USA Inc. (http://www.zend.com)
* @license http://framework.zend.com/license/new-bsd New BSD License
*/
class Exception extends \Zend\XmlRpc\Exception
{
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,593 |
Uniqa Österreich (Eigenschreibweise: UNIQA Österreich Versicherungen AG) ist ein österreichisches Versicherungsunternehmen und Teil der Uniqa Insurance Group mit Sitz im Uniqa Tower in Wien.
Uniqa Österreich Versicherungen AG
Die 6.000 Mitarbeiter von Uniqa Österreich betreuen 3,6 Millionen Kunden mit rund 10,5 Millionen Versicherungsverträgen. Uniqa Österreich erreichte 2019 einen Marktanteil von 21 Prozent und ist das größte Unternehmen unter den mehr als 50 in Österreich tätigen Versicherern sowie laut Versicherungsverband Österreich die bekannteste heimische Versicherungsmarke. Im Jahr 2016 wurden die Salzburger-Landesversicherung, die Finance Life und die Raiffeisen Versicherung in die Uniqa Österreich als aufnehmende Gesellschaft fusioniert.
Vorstandsvorsitzender der Uniqa Österreich war von 2011 bis Dezember 2017 Hartwig Löger, im Dezember 2017 folgte ihm Kurt Svoboda in dieser Funktion nach.
Leistungsspektrum
Die Uniqa Österreich Versicherungen AG betreibt alle Sparten der Personen- und Sach-Versicherung. Die Gesellschaft vertreibt die Produkte über den konzerneigenen Ausschließlichkeitsvertrieb sowie über Makler und Generalagenturen. Mit Marktanteilen von rund 28 % in der Unfallversicherung, 16 % in der Schadenversicherung bzw. 45 Prozent in der Krankenversicherung war Uniqa Österreich im Jahr 2019 Marktführer im Land und mit 18 % an zweiter Stelle in der Lebensversicherung.
Sponsoring
Uniqa Österreich hat aktuell und hatte in der Vergangenheit einige ehemalige österreichische Spitzensportler als Testimonial unter Vertrag:
Matthias Mayer
Benjamin Raich
Marlies Schild
Marco Schwarz
Stephan Eberharter
Weblinks
Website der Uniqa Österreich Versicherungen AG
Website der Uniqa Insurance Group AG
Einzelnachweise
Versicherungsunternehmen (Österreich)
Gegründet 1890
Finanzdienstleister (Wien) | {
"redpajama_set_name": "RedPajamaWikipedia"
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Tim Boron Announces His Retirement From Hockey
Thursday, July 9 2015 6:21 PM
Wichita, KS (July 9th) – The Wichita Thunder, proud member of the ECHL and powered by Toyota, learned today that goaltender Tim Boron has announced his retirement.
"I would like to thank all the players and coaches I have played with and for. The camaraderie that is formed in hockey is the glue that holds the game together," commented Boron. "You all helped me become a better goalie and teammate, and even though we all part ways at season's end, I consider you all friends forever."
Boron, 32, finishes a nine-year career that started in 2006-07 with the Colorado Eagles and ends this past season in Wichita. A native of Winnipeg, Manitoba, the 6-foot, 177-pound netminder finished tied for 14th in wins (20), seventh in minutes played (2,569) and 18th in saves (1,157). Boron played for the Thunder in 2008-09 and parts of the 2009-10 season before heading to the Mississippi RiverKings. He played the next four seasons in Rapid City, winning at least 20 games during three of those and put up an impressive 74-35-7 record with a goals against of 2.44 and a save percentage of .916 in 129 starts. He was nominated as a finalist for Most Outstanding Goalie two seasons ago in the CHL as his goals against average (2.45) was best among all goaltenders while finishing second in wins (30), fifth in saves (1,254) and save percentage (.915). In the league's annual Best-of-the-Best poll, Boron was named Best Goaltender in Shootouts. He won six times with games finishing in penalty shots, stopping 43-of-47 (.915 SOS%).
"Thank you to all the organizations as well as the great fans, boosters and friends I have met along the way. Everyone in Colorado, Las Vegas, Stockton, Mississippi, Rapid City and Wichita were great hosts to me and my wife. You took care of us players, made us comfortable and made our new homes feel a little more like home."
Boron played a three-year career at St. Cloud State University before turning pro with Colorado. He collected three shutouts during the playoff run, which was a CHL record. Boron still holds that record for most saves in a single game, stopping 68 of 70 shots on May 5th, 2011 against the Colorado Eagles in Game 4 of the Turner Conference Finals. His performance broke a CHL-record that stood for over 15 seasons.
Season tickets are on sale now. Don't delay! Call the Wichita Thunder office and visit with a season ticket rep today to learn more. Stay up-to-date on all the news during the off-season by visiting www.wichitathunder.com.
About the ECHL
Began in 1988-89 with five teams in four states, the ECHL has grown into a coast-to-coast league with 28 teams in 21 states and one Canadian province for its 28th season in 2015-16. There have been 569 players who have started their career in the ECHL have gone on to play in the National Hockey League, including 28 who made their NHL debuts in the 2014-15 season. The ECHL had affiliations with 29 of the 30 NHL teams in 2014-15, marking the 18th consecutive season that the league had affiliations with at least 20 teams in the NHL. Further information on the ECHL is available on its website at ECHL.com.
-Thunder-
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Calvin Zippin (born July 17, 1926) is a cancer epidemiologist and biostatistician, and Professor Emeritus in the Department of Epidemiology and Biostatistics at the University of California School of Medicine in San Francisco (UCSF). He is a Fellow of the American Statistical Association, the American College of Epidemiology and the Royal Statistical Society of Great Britain. His doctoral thesis was the basis for the Zippin Estimator, a procedure for estimating wildlife populations using data from trapping experiments. He was a principal investigator in the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute (NCI) which assesses the magnitude and nature of the cancer problem in the United States. In 1961, he created training programs for cancer registry personnel, which he conducted nationally and internationally. He carried out research on the epidemiology and rules for staging of various cancers. He received a Lifetime Achievement and Leadership Award from the NCI in 2003.
Early life and education
Zippin was born on July 17, 1926, in Albany, New York, United States, the son of Samuel and Jennie (Perkel) Zippin. He received an AB degree magna cum laude in biology and mathematics, from the State University of New York at Albany in 1947. He was a research assistant at the Sterling-Winthrop Research Institute in Rensselaer, New York beginning in 1947.
He was awarded a Doctor of Science degree in Biostatistics by the Johns Hopkins School of Hygiene and Public Health in Baltimore, Maryland in 1953.
His thesis advisor was William G. Cochran
a statistician known for Cochran's theorem, Cochran-Mantel-Haenzel Test and author of standard biostatistical texts: "Experimental Designs" and "Sampling Techniques". Zippin's doctoral thesis, An Evaluation of the Removal Method of Estimating Animal Populations became the basis for the Zippin Estimator, and has been used for estimating populations of a wide variety of animal species. It is considered among the easiest and most accurate methods for estimating animal populations in the wild.
Career
At the Sterling-Winthrop Research Institute, Zippin performed various laboratory and statistical duties under Lloyd C. Miller, Ph.D., later Director of Revision (1950-1970) of the United States Pharmacopoeia. Dr. Miller encouraged Zippin to pursue a career in statistics which led to his graduate work at Johns Hopkins where he also held an appointment as a Research Assistant in Biostatistics from 1950 to 1953.
Following graduate school, Zippin became an instructor in biostatistics (1953-1955) at the School of Public Health, University of California, Berkeley. He moved to the School of Medicine at the University of California, San Francisco where, at the level of assistant professor, he held appointments in the Cancer Research Institute and the Department of Preventive Medicine. With further advancement, in 1967 he became Professor of Epidemiology in the Cancer Research Institute, Department of Epidemiology and Biostatistics, and Department of Pathology. Since 1991 he has been Professor Emeritus.
Zippin was a Visiting associate professor of statistics, Stanford University, Palo Alto, CA (1962); National Institutes of Health (NIH) Special Postdoctoral Fellow, London School of Hygiene and Tropical Medicine (1964-1965); Visiting Research Worker, Middlesex Hospital Medical School, London (1975); Research Advisor, Assaf Harofeh Medical Center, Zerifin, Israel (1976-2010); Faculty Advisor, Regional Cancer Centre, Trivandrum, Kerala State, India (1984-1991).
Research
Zippin's doctoral thesis became the basis for the Zippin Estimator, a mathematical procedure for estimating wildlife population size based on capture and removal of sequentially trapped animal samples. The method was explored by P. A. P. Moran (1951) and its properties elaborated by Zippin in 1956 and 1958.
Zippin has done extensive research on cancer staging, particularly cancer of the breast and colon-rectum with the American Joint Committee on Cancer and the International Union Against Cancer. He has published on the epidemiology of breast, uterine, and nasopharyngeal cancer, late effects of radiation, and survival patterns in acute lymphocytic and chronic lymphocytic leukemia. His 1960 and 1966 JNCI breast cancer staging articles were included in the "Yearbook of Cancer" compendium of the most influential cancer publications for those years, respectively.
Zippin collaborated with Peter Armitage, extending a mathematical model assuming survival time of cancer patients to follow an exponential distribution whose key parameter (expected survival time) is linearly related to a measure of the severity (e.g., white blood count in leukemia) of disease. The extension provided for the common situation where some patients were still alive and their limited (censored) survival information could be used in estimating the value of the desired parameter.
From 1973 to 1995, Zippin collaborated with Dr. Yoav Horn comparing characteristics of Arab cancer patients living on the West Bank, their disease and survival with those of patients in Israel and the United States. This project documented the need for improved treatment facilities and the training of oncologists in that region. Horn, an Israeli oncologist, started two cancer clinics in Nablus and Beit Jala and developed a training program for Arab oncologists for which Dr. Horn received the Sasakawa Health Prize from the World Health Organization in 2000.
Honors and awards
Zippin is a Fellow of the American Statistical Association (1980), American College of Epidemiology (1982), and the Royal Statistical Society of Great Britain (1965). He was President of the Western North American Region of the International Biometric Society (1979-1980) and a member of the Committee of Presidents of Statistical Societies (1979-1981). He is a member of Phi Beta Kappa, Sigma Xi, Delta Omega (honorary public health society), and Signum Laudis (honorary academic society).
In 1994, he was elected an honorary Member of the International Association of Cancer Registries, which is administered by the World Health Organization, and the California Cancer Registrars Association. From 1989 to 1995, he served on the Board of Governors of the National Cancer Database (NCDB), a clinical oncology database sourced from hospital registry data which is jointly sponsored by the American College of Surgeons and the American Cancer Society.
Dr. Zippin was on the editorial boards of Statistics in Medicine and the Journal of Soviet Oncology. He received the Distinguished Alumnus Award from the State University of New York at Albany (1969) and a Lifetime Achievement and Leadership Award from the National Cancer Institute (2003). Dr. Zippin appeared on the cover of the journal "Cancer Research" in recognition of his contributions to the NCI's SEER (Surveillance, Epidemiology, and End Results ) program.
References
American epidemiologists
American statisticians
Living people
1926 births
People from Albany, New York
Johns Hopkins Bloomberg School of Public Health alumni
Fellows of the American Statistical Association
University at Albany, SUNY alumni
UCSF School of Medicine faculty | {
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Design d intérieur, design de jardin et inspiration paysagère Copyright © 2017. | {
"redpajama_set_name": "RedPajamaC4"
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A lesson in effective outreach presented by Cheerios.
Check out this 30 second spot from Cheerios on the outreach work of Salomon Anaya and consider the applications.
I came up with this mobile art gallery to bring art to the people.
I strongly believe there's art in every single person.
Sharing art is the highest calling for me.
Without my health I wouldn't be able to do anything.
To keep doing what you love, keep your heart healthy. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,021 |
{"url":"http:\/\/sites.science.oregonstate.edu\/physics\/coursewikis\/LinAlgBook\/book\/linalg\/deltaexp.html","text":"Chapter 11: Delta Functions\n\n### The Exponential Representation of the Delta Function\n\nAs discussed in \u00a7\u00a0{Representations of the Dirac Delta Function}, the Dirac delta function can be written in the form $$\\delta(x) = \\frac{1}{2\\pi}\\int_{-\\infty}^\\infty e^{ikx}\\, dk .\\\\$$ We outline here the derivation of this representation.\n\nIn order to evaluate the integral, we introduce a regularization factor, $e^{-k\\epsilon}$, as follows: \\begin{eqnarray} \\int_{-\\infty}^{\\infty} e^{ikx}\\, dk &= \\int_{-\\infty}^0 e^{ikx}\\, dk + \\int_0^\\infty e^{ikx}\\, dk \\nonumber\\\\ &= \\int_0^\\infty e^{-ikx}\\, dk + \\int_0^\\infty e^{ikx}\\, dk \\nonumber\\\\ &= \\int_0^\\infty (e^{ikx} + e^{-ikx})\\, dk \\nonumber\\\\ &= \\lim_{\\epsilon\\to0^+}\\int_0^\\infty (e^{ikx} + e^{-ikx}) \\,e^{-k\\epsilon}\\, dk \\nonumber\\\\ &= \\lim_{\\epsilon\\to0^+}\\int_0^\\infty (e^{ik(x+i\\epsilon)} + e^{-ik(x-i\\epsilon)}) \\,dk \\nonumber\\\\ &= \\lim_{\\epsilon\\to0^+} \\left[ \\frac{e^{ik(x+i\\epsilon)}}{i(x+i\\epsilon)} + \\frac{e^{-ik(x-i\\epsilon)}}{-i(x-i\\epsilon)} \\right]_0^\\infty \\nonumber\\\\ &= \\lim_{\\epsilon\\to0^+} \\left( 0 + 0 - \\frac1{i(x+i\\epsilon)} - \\frac1{-i(x-i\\epsilon)} \\right) \\nonumber\\\\ &= \\lim_{\\epsilon\\to0^+} \\left( \\frac{i}{x+i\\epsilon} - \\frac{i}{x-i\\epsilon} \\right) \\nonumber\\\\ &= \\lim_{\\epsilon\\to0^+} \\frac{2\\epsilon}{x^2+\\epsilon^2} = \\cases{0 & $x\\ne0$ \\cr \\infty & $x=0$ \\cr} \\end{eqnarray} where we have used the fact that, for $\\epsilon>0$, $e^{-k\\epsilon}$ goes to $0$ as $k$ goes to $\\infty$. 1)\n\nIt remains to show that the final expression has the correct normalization. But $$\\int_{-\\infty}^\\infty \\frac{2\\epsilon}{x^2+\\epsilon^2} \\,dx = 2 \\arctan\\left(\\frac{x}{\\epsilon}\\right) \\Bigg|_{-\\infty}^\\infty = 2\\pi ,$$ which is independent of $\\epsilon$. Thus, \\begin{eqnarray} \\frac{1}{2\\pi} \\int_{-\\infty}^\\infty f(x) \\,e^{ikx}\\, dk &=& \\lim_{\\epsilon\u21920^+} \\frac{1}{2\\pi} \\int_{-\\infty}^\\infty \\frac{2\\epsilon f(x)}{x^2+\\epsilon^2} \\,dx \\nonumber\\\\ &=& \\lim_{\\epsilon\u21920^+} \\frac{1}{2\\pi} \\int_{-\\infty}^\\infty \\frac{2\\epsilon f(0)}{x^2+\\epsilon^2} \\,dx \\nonumber\\\\ &=& f(0) , \\end{eqnarray} which is the defining property of the delta function.\n\n1) The use of such regularization factors is quite common. Rigorous mathematical justification can be given, but informal arguments along the lines above are usually sufficient\u2014if the informal argument works, the formal derivation should also, for an appropriate, reasonable class of functions.","date":"2020-09-30 06:12:16","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 2, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 1.0000081062316895, \"perplexity\": 1983.8595552925858}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-40\/segments\/1600402118004.92\/warc\/CC-MAIN-20200930044533-20200930074533-00577.warc.gz\"}"} | null | null |
Q: Laravel URL::asset issue I have this code in HTML
<li class="user-footer">
<div class="pull-right">
<a href="{{ URL::route('logout') }}" class="btn btn-default btn-flat">Sign out</a>
</div>
</li>
My question is, why href URL is generating like this
I'm using Laravel 5.5.
A: Looking at your error you are trying to call Named Routes.
You should have route like this to use Named Routes (if you don't already have).
Route::get('user/logout', 'UserController@logout')->name('logout');
And your view should be like this:
<li class="user-footer">
<div class="pull-right">
<a href="{{ route('logout') }}" class="btn btn-default btn-flat">Sign out</a>
</div>
</li>
Laravel Named Routes document: https://laravel.com/docs/5.5/routing#named-routes
| {
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{"url":"https:\/\/www.vrcbuzz.com\/travelling-salesman-problem\/","text":"# Travelling Salesman Problem\n\nTravelling Salesman Problem\n\n## Travelling Salesman Problem\n\nSuppose a salesman wants to visit certain number of cities, say, $n$. Let $c_{ij}$ be the distance from city $i$ to city $j$. Then the problem of salesman is to select such a route that starts from his home city, passes through each city once and only once, and returns to his home city in the shortest possible distance. Such a problem is known as Travelling Salesman Problem.\n\n## Formulation\n\nSuppose $x_{ij}=1$ if the salesman goes directly from city $i$ to city $j$, and $x_{ij}=0$ otherwise. Then the objective function is to\n\n $$\\begin{equation*} \\min z= \\sum_{i=1}^n\\sum_{j=1}^n x_{ij}c_{ij} \\end{equation*}$$\nsubject to\n $$\\begin{equation*} \\sum_{j=1}^n x_{ij} =1,\\; \\text{ for } i=1,2,\\ldots, n \\end{equation*}$$\n\n $$\\begin{equation*} \\sum_{i=1}^n x_{ij} =1,\\; \\text{ for } j=1,2,\\ldots,n \\end{equation*}$$\n\nwhere\n\n \\begin{align*} x_{ij}&= \\begin{cases} 1, & \\text{if salesman goes from } i^{th} \\text{ city to } j^{th} \\text{ city}; \\\\ 0, & \\text{Otherwise}. \\end{cases} \\end{align*}\n\nWith one more restriction that no city is visited twice before the tour of all cities is completed. The salesman cannot go from city $i$ to city $i$ itself. This possibility may be avoided by adopting the convention $c_{ii} = \\infty$ which insures that $x_{ii}$ can never be one.\n\nFrom \\ To $A_1$ $A_2$ $\\cdots$ $A_j$ $\\cdots$ $A_n$\n$A_1$ $\\infty$ $c_{12}$ $\\cdots$ $c_{1j}$ $\\cdots$ $c_{1n}$\n$A_2$ $c_{21}$ $\\infty$ $\\cdots$ $c_{2j}$ $\\cdots$ $c_{2n}$\n$\\vdots$ $\\vdots$ $\\vdots$ $\\vdots$ $\\vdots$ $\\vdots$ $\\vdots$\n$A_i$ $c_{i1}$ $c_{i2}$ $\\cdots$ $c_{ij}$ $\\cdots$ $c_{in}$\n$\\vdots$ $\\vdots$ $\\vdots$ $\\vdots$ $\\vdots$ $\\vdots$ $\\vdots$\n$A_n$ $c_{n1}$ $c_{n2}$ $\\cdots$ $c_{nj}$ $\\cdots$ $\\infty$\n\nApply the usual Hungarian method to find the optimal route. (It should be in cyclic order, i.e., no city should be visited twice).\n\nHope you enjoyed reading this article on Travelling Salesman problem.\n\nYou can read about how to solve the step by step procedure of Hungarian metod to solve assignment problem with restriction.\n\nIf you have any doubt or queries feel free to post them in the comment section.\n\nVRCBuzz co-founder and passionate about making every day the greatest day of life. Raju is nerd at heart with a background in Statistics. Raju looks after overseeing day to day operations as well as focusing on strategic planning and growth of VRCBuzz products and services. Raju has more than 25 years of experience in Teaching fields. He gain energy by helping people to reach their goal and motivate to align to their passion. Raju holds a Ph.D. degree in Statistics. Raju loves to spend his leisure time on reading and implementing AI and machine learning concepts using statistical models.","date":"2021-12-05 14:50:33","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.3540607690811157, \"perplexity\": 427.3729329283666}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-49\/segments\/1637964363189.92\/warc\/CC-MAIN-20211205130619-20211205160619-00411.warc.gz\"}"} | null | null |
{"url":"https:\/\/17calculus.com\/vectors\/cross-product\/?v","text":"You CAN Ace Calculus\n\n basics of vectors dot product linear algebra\n\n17Calculus Subjects Listed Alphabetically\n\nSingle Variable Calculus\n\n Absolute Convergence Alternating Series Arc Length Area Under Curves Chain Rule Concavity Conics Conics in Polar Form Conditional Convergence Continuity & Discontinuities Convolution, Laplace Transforms Cosine\/Sine Integration Critical Points Cylinder-Shell Method - Volume Integrals Definite Integrals Derivatives Differentials Direct Comparison Test Divergence (nth-Term) Test\n Ellipses (Rectangular Conics) Epsilon-Delta Limit Definition Exponential Derivatives Exponential Growth\/Decay Finite Limits First Derivative First Derivative Test Formal Limit Definition Fourier Series Geometric Series Graphing Higher Order Derivatives Hyperbolas (Rectangular Conics) Hyperbolic Derivatives\n Implicit Differentiation Improper Integrals Indeterminate Forms Infinite Limits Infinite Series Infinite Series Table Infinite Series Study Techniques Infinite Series, Choosing a Test Infinite Series Exam Preparation Infinite Series Exam A Inflection Points Initial Value Problems, Laplace Transforms Integral Test Integrals Integration by Partial Fractions Integration By Parts Integration By Substitution Intermediate Value Theorem Interval of Convergence Inverse Function Derivatives Inverse Hyperbolic Derivatives Inverse Trig Derivatives\n Laplace Transforms L'H\u00f4pital's Rule Limit Comparison Test Limits Linear Motion Logarithm Derivatives Logarithmic Differentiation Moments, Center of Mass Mean Value Theorem Normal Lines One-Sided Limits Optimization\n p-Series Parabolas (Rectangular Conics) Parabolas (Polar Conics) Parametric Equations Parametric Curves Parametric Surfaces Pinching Theorem Polar Coordinates Plane Regions, Describing Power Rule Power Series Product Rule\n Quotient Rule Radius of Convergence Ratio Test Related Rates Related Rates Areas Related Rates Distances Related Rates Volumes Remainder & Error Bounds Root Test Secant\/Tangent Integration Second Derivative Second Derivative Test Shifting Theorems Sine\/Cosine Integration Slope and Tangent Lines Square Wave Surface Area\n Tangent\/Secant Integration Taylor\/Maclaurin Series Telescoping Series Trig Derivatives Trig Integration Trig Limits Trig Substitution Unit Step Function Unit Impulse Function Volume Integrals Washer-Disc Method - Volume Integrals Work\n\nMulti-Variable Calculus\n\n Acceleration Vector Arc Length (Vector Functions) Arc Length Function Arc Length Parameter Conservative Vector Fields Cross Product Curl Curvature Cylindrical Coordinates\n Directional Derivatives Divergence (Vector Fields) Divergence Theorem Dot Product Double Integrals - Area & Volume Double Integrals - Polar Coordinates Double Integrals - Rectangular Gradients Green's Theorem\n Lagrange Multipliers Line Integrals Partial Derivatives Partial Integrals Path Integrals Potential Functions Principal Unit Normal Vector\n Spherical Coordinates Stokes' Theorem Surface Integrals Tangent Planes Triple Integrals - Cylindrical Triple Integrals - Rectangular Triple Integrals - Spherical\n Unit Tangent Vector Unit Vectors Vector Fields Vectors Vector Functions Vector Functions Equations\n\nDifferential Equations\n\n Boundary Value Problems Bernoulli Equation Cauchy-Euler Equation Chebyshev's Equation Chemical Concentration Classify Differential Equations Differential Equations Euler's Method Exact Equations Existence and Uniqueness Exponential Growth\/Decay\n First Order, Linear Fluids, Mixing Fourier Series Inhomogeneous ODE's Integrating Factors, Exact Integrating Factors, Linear Laplace Transforms, Solve Initial Value Problems Linear, First Order Linear, Second Order Linear Systems\n Partial Differential Equations Polynomial Coefficients Population Dynamics Projectile Motion Reduction of Order Resonance\n Second Order, Linear Separation of Variables Slope Fields Stability Substitution Undetermined Coefficients Variation of Parameters Vibration Wronskian\n\nSearch Practice Problems\n\nDo you have a practice problem number but do not know on which page it is found? If so, enter the number below and click 'page' to go to the page on which it is found or click 'practice' to be taken to the practice problem.\n\n17calculus > vectors > cross product\n\nIn order to understand the material on this page, you need to know some linear algebra, specifically, how to calculate the determinant of 2x2 and 3x3 matrices. You can find a quick review on the linear algebra page.\n\n Calculating The Cross Product\n\nThe Cross Product is one way to 'multiply' two vectors (the other way is the dot product). Unlike the dot product, the cross product only makes sense when performed on two 3-dim vectors. Taking the cross product of the two vectors $$3\\hat{i}+2\\hat{j}$$ and $$\\hat{i}+\\hat{j}$$ is not possible, unless you mean $$3\\hat{i}+2\\hat{j}+0\\hat{k}$$ and $$\\hat{i}+\\hat{j}+0\\hat{k}$$, in which case, you need to write out the $$\\hat{k}$$ term even if it is zero.\n\nIf we have two vectors, $$\\vec{u}=\\langle u_1, u_2, u_3 \\rangle$$ and $$\\vec{v} = \\langle v_1, v_2, v_3 \\rangle$$, we write the cross product of these two vectors as $$\\vec{u} \\times \\vec{v}$$.\n\nThe result of the cross product of two vectors is another vector. It's meaning is discussed later on this page. For now, let's focus on how we calculate the cross product.\n\nTo calculate the cross product, we use some linear algebra. If you haven't already, now would be good time to review the linear algebra page to make sure your skills calculating a 3x3 determinant are sharp. To calculate the cross product we calculate the following determinant.\n\n$$\\vec{u} \\times \\vec{v} = \\begin{vmatrix} \\hat{i} & \\hat{j} & \\hat{k} \\\\ u_1 & u_2 & u_3 \\\\ v_1 & v_2 & v_3 \\end{vmatrix}$$ $$= (u_2 v_3 - u_3 v_2)\\hat{i} - (u_1 v_3 - u_3 v_1)\\hat{j} + (u_1 v_2 - u_2 v_1)\\hat{k}$$\n\n1. It is best NOT to memorize the last expression. Instead, set up and evaluate the determinant.\n2. Remember to subtract the middle term.\n3. It is important to set up the determinant correctly, i.e.\n- The first row is the set of unit vectors.\n- The second row is the first vector of the cross product.\n- The third row is the second vector of the cross product.\nThe rows cannot be in any other order (more on this in the properties section below).\n\nThe name 'cross product' comes from the notation using '$$\\times$$' between the two vectors. Just like with the dot product, it is important to use the '$$\\times$$' between the vectors to indicate a cross product. Writing $$\\vec{u} \\vec{v}$$ makes no sense and is considered incorrect notation.\n\nNote: Recently we heard that what we call the 'determinant' above is not strictly a determinant but just a mnemonic device to calculate the cross product, since a true determinant consists of only numbers not vectors. We have not verified this at this time but it certainly could be true. When we verify it, we will update this page accordingly.\n\nOkay, so let's watch a video clip discussing the cross product and its geometric interpretation.\n\nPatrickJMT - geometric interpretation of the cross product [2mins-25secs]\n\nvideo by PatrickJMT\n\nGiven $$\\vec{A} = 2\\hat{i} + 3\\hat{j} + 4\\hat{k}$$ and $$\\vec{B} = \\hat{i} + 3\\hat{k}$$, calculate the cross product $$\\vec{A} \\times \\vec{B}$$.\n\nProblem Statement\n\nGiven $$\\vec{A} = 2\\hat{i} + 3\\hat{j} + 4\\hat{k}$$ and $$\\vec{B} = \\hat{i} + 3\\hat{k}$$, calculate the cross product $$\\vec{A} \\times \\vec{B}$$.\n\n$$(2\\hat{i} + 3\\hat{j} + 4\\hat{k} ) \\times ( \\hat{i} + 3\\hat{k} ) = 9\\hat{i} - 2\\hat{j} - 3\\hat{k}$$\n\nProblem Statement\n\nGiven $$\\vec{A} = 2\\hat{i} + 3\\hat{j} + 4\\hat{k}$$ and $$\\vec{B} = \\hat{i} + 3\\hat{k}$$, calculate the cross product $$\\vec{A} \\times \\vec{B}$$.\n\nSolution\n\nSetting up the determinant, we have\n$$\\vec{A} \\times \\vec{B} = \\begin{vmatrix} \\hat{i} & \\hat{j} & \\hat{k} \\\\ 2 & 3 & 4 \\\\ 1 & 0 & 3 \\end{vmatrix} =$$ $$(9-0)\\hat{i} - (6-4)\\hat{j} + (0-3)\\hat{k} =$$ $$9\\hat{i} - 2\\hat{j} - 3\\hat{k}$$\n\n$$(2\\hat{i} + 3\\hat{j} + 4\\hat{k} ) \\times ( \\hat{i} + 3\\hat{k} ) = 9\\hat{i} - 2\\hat{j} - 3\\hat{k}$$\n\nGiven $$\\vec{A} = \\hat{i}-2\\hat{j}+2\\hat{k}$$ and $$\\vec{B} = 3\\hat{i}-\\hat{j}-\\hat{k}$$, calculate the cross product $$\\vec{A}\\times\\vec{B}$$.\n\nProblem Statement\n\nGiven $$\\vec{A} = \\hat{i}-2\\hat{j}+2\\hat{k}$$ and $$\\vec{B} = 3\\hat{i}-\\hat{j}-\\hat{k}$$, calculate the cross product $$\\vec{A}\\times\\vec{B}$$.\n\n$$\\vec{A} \\times \\vec{B} = 4\\hat{i} + 7\\hat{j} + 5\\hat{k}$$\n\nProblem Statement\n\nGiven $$\\vec{A} = \\hat{i}-2\\hat{j}+2\\hat{k}$$ and $$\\vec{B} = 3\\hat{i}-\\hat{j}-\\hat{k}$$, calculate the cross product $$\\vec{A}\\times\\vec{B}$$.\n\nSolution\n\n$$\\vec{A} \\times \\vec{B} = (\\hat{i}-2\\hat{j}+2\\hat{k}) \\times (3\\hat{i}-\\hat{j}-\\hat{k}) =$$ $$\\begin{vmatrix} \\hat{i} & \\hat{j} & \\hat{k} \\\\ 1 & -2 & 2 \\\\ 3 & -1 & -1 \\end{vmatrix} =$$ $$(2 -(-2))\\hat{i} - (-1-6)\\hat{j} + (-1-(-6))\\hat{k} =$$ $$4\\hat{i} + 7\\hat{j} +5\\hat{k}$$\n\n$$\\vec{A} \\times \\vec{B} = 4\\hat{i} + 7\\hat{j} + 5\\hat{k}$$\n\nCalculate the cross product of $$\\hat{i}$$ and $$\\hat{j}$$.\n\nProblem Statement\n\nCalculate the cross product of $$\\hat{i}$$ and $$\\hat{j}$$.\n\n$$\\hat{i}\\times\\hat{j}=\\hat{k}$$\n\nProblem Statement\n\nCalculate the cross product of $$\\hat{i}$$ and $$\\hat{j}$$.\n\nSolution\n\nBefore doing the calculation, stop and think for a minute what the answer might be. Think about the properties of the cross product and the right hand rule. Do you have an idea of what the answer might be?\nOkay, let's do the calculation.\n$$\\hat{i} \\times \\hat{j} =$$ $$\\begin{vmatrix} \\hat{i} & \\hat{j} & \\hat{k} \\\\ 1 & 0 & 0 \\\\ 0 & 1 & 0 \\end{vmatrix} =$$ $$(0-0)\\hat{i} - (0-0)\\hat{j} + (1-0)\\hat{k} = \\hat{k}$$\nLet's think about this answer for a minute. Notice that the standard unit vectors are vectors of length one that coincide with the Cartesian coordinate system. All of the vectors are perpendicular to one another, so it makes sense that the vector perpendicular to $$\\hat{i}$$ and $$\\hat{j}$$ would be in the direction of the z-axis or $$\\hat{k}$$.\nA question to consider: If you take the cross product of two unit vectors, will the result always be a unit vector? Why or why not?\n\n$$\\hat{i}\\times\\hat{j}=\\hat{k}$$\n\nCalculate the cross product of the vectors $$\\vec{a} = \\langle 5,-1,-2 \\rangle$$ and $$\\vec{b} = \\langle -3,2,4 \\rangle$$.\n\nProblem Statement\n\nCalculate the cross product of the vectors $$\\vec{a} = \\langle 5,-1,-2 \\rangle$$ and $$\\vec{b} = \\langle -3,2,4 \\rangle$$.\n\nSolution\n\n41 solution video\n\nvideo by Krista King Math\n\nCalculate the cross product of the vectors $$\\vec{a} = \\hat{i} - \\hat{j} + 3\\hat{k}$$ and $$\\vec{b} = -2\\hat{i} + 3\\hat{j} + \\hat{k}$$.\n\nProblem Statement\n\nCalculate the cross product of the vectors $$\\vec{a} = \\hat{i} - \\hat{j} + 3\\hat{k}$$ and $$\\vec{b} = -2\\hat{i} + 3\\hat{j} + \\hat{k}$$.\n\nSolution\n\n42 solution video\n\nvideo by Krista King Math\n\nCalculate the cross product of the vectors $$\\vec{a} = \\langle 2,-3 \\rangle$$ and $$\\vec{b} = \\langle 4,5 \\rangle$$.\n\nProblem Statement\n\nCalculate the cross product of the vectors $$\\vec{a} = \\langle 2,-3 \\rangle$$ and $$\\vec{b} = \\langle 4,5 \\rangle$$.\n\nSolution\n\n43 solution video\n\nvideo by Krista King Math\n\nCalculate the cross product of the vectors $$\\vec{a} = \\langle 5,1,4 \\rangle$$ and $$\\vec{b} = \\langle -1,0,2 \\rangle$$.\n\nProblem Statement\n\nCalculate the cross product of the vectors $$\\vec{a} = \\langle 5,1,4 \\rangle$$ and $$\\vec{b} = \\langle -1,0,2 \\rangle$$.\n\nSolution\n\n45 solution video\n\nvideo by PatrickJMT\n\n Cross Product Properties\n\nHere are some cross product properties.\nAlgebraic Properties\nLet $$\\vec{u}$$, $$\\vec{v}$$ and $$\\vec{w}$$ be vectors in space and let $$a$$ be a scalar.\n1. $$\\vec{u} \\times \\vec{v} = -(\\vec{v} \\times \\vec{u})$$\n2. $$\\vec{u} \\times (\\vec{v}+\\vec{w}) = (\\vec{u} \\times \\vec{v}) + (\\vec{u} \\times \\vec{w})$$\n3. $$a(\\vec{u} \\times \\vec{v}) = (a\\vec{u}) \\times \\vec{v} = \\vec{u} \\times (a\\vec{v})$$\n4. $$\\vec{u} \\times \\vec{0} = \\vec{0}$$\n5. $$\\vec{u} \\times \\vec{u} = \\vec{0}$$\nNotes:\n- property 1 implies that the cross product is not commutative\n- in property 2, the vector $$\\vec{u}$$ is on the left, so when it is distributed across the addition, it must remain on the left in both cases\n- property 5 seems trivial but it is very powerful; later on this page, this will be discussed in more detail.\n\nHere is a video with proofs of some of these algebraic properties.\n\nLarson Calculus - proofs of some algebraic properties [2mins-3secs]\n\nvideo by Larson Calculus\n\nGeometric Properties\nLet $$\\vec{u}$$ and $$\\vec{v}$$ be nonzero vectors in space and let $$\\theta$$ be the angle between $$\\vec{u}$$ and $$\\vec{v}$$.\n6. $$\\vec{u} \\times \\vec{v}$$ is orthogonal to both $$\\vec{u}$$ and $$\\vec{v}$$.\n7. $$\\| \\vec{u} \\times \\vec{v} \\| = \\|\\vec{u}\\| \\|\\vec{v}\\| \\sin \\theta$$\n8. $$\\vec{u} \\times \\vec{v} = \\vec{0}$$ if and only if $$\\vec{u}$$ is a scalar multiple of $$\\vec{v}$$\n9. $$\\| \\vec{u} \\times \\vec{v} \\|$$ represents the area of the parallelogram formed with $$\\vec{u}$$ and $$\\vec{v}$$ as adjacent sides.\nNotes:\n- for the geometric properties, both vectors must be nonzero; this is not a requirement in the algebraic properties\n- notice in property 7, the cross product involves the sine of angle $$\\theta$$ while the dot product involves the cosine of the angle\n- as mentioned in property 9, the cross product is the area of a parallelogram; here is a great video that discusses this in more detail.\n\nDr Chris Tisdell - Cross Product and Area of Parallelogram [9mins]\n\nvideo by Dr Chris Tisdell\n\nHere is a video with proofs of some of these geometric properties.\n\nLarson Calculus - proofs [3mins-39secs]\n\nvideo by Larson Calculus\n\nThere is a simple rule to use when you need to know the direction of the resulting vector from the cross product. It's called the right hand rule. The idea is to lay out your hand with all fingers straight out. Place the middle of your hand at the point of intersection of the two vectors involved in the cross product with your fingers in the direction of the first vector. Fold your fingers in the direction of the second vector. Your thumb will then be pointing in the direction of the result of the cross product. Here is a quick video showing this idea.\n\nRight Hand Rule for Cross Products [10secs]\n\nAll this information may be a bit overwhelming. So let's take a few minutes and watch this video. He explains the cross product very well and shows some examples.\n\nDr Chris Tisdell - Cross product of vectors [20mins-24secs]\n\nvideo by Dr Chris Tisdell\n\nOkay, let's use some of these properties to solve these problems.\n\nGiven $$\\vec{A} = 2\\hat{i} + 3\\hat{j} + 4\\hat{k}$$ and $$\\vec{B} = \\hat{i} + 3\\hat{k}$$, use the cross product to find the angle between $$\\vec{A}$$ and $$\\vec{B}$$.\n\nProblem Statement\n\nGiven $$\\vec{A} = 2\\hat{i} + 3\\hat{j} + 4\\hat{k}$$ and $$\\vec{B} = \\hat{i} + 3\\hat{k}$$, use the cross product to find the angle between $$\\vec{A}$$ and $$\\vec{B}$$.\n\nThe angle between the vectors $$2\\hat{i} + 3\\hat{j} + 4\\hat{k}$$ and $$\\hat{i} + 3\\hat{k}$$ is approximately 0.606 radians.\n\nProblem Statement\n\nGiven $$\\vec{A} = 2\\hat{i} + 3\\hat{j} + 4\\hat{k}$$ and $$\\vec{B} = \\hat{i} + 3\\hat{k}$$, use the cross product to find the angle between $$\\vec{A}$$ and $$\\vec{B}$$.\n\nSolution\n\nFrom a previous problem, we found the cross product as $$\\vec{A} \\times \\vec{B} = 9\\hat{i} - 2\\hat{j} - 3\\hat{k}$$\nTo find the angle between the two vectors, we use the formula $$\\| \\vec{A} \\times \\vec{B} \\| = \\|\\vec{A}\\| \\|\\vec{B}\\| \\sin (\\theta)$$, where $$\\theta$$ is the angle between the two vectors.\nLet's calculate these magnitudes.\n\n $$\\| \\vec{A} \\times \\vec{B} \\|$$ $$\\| 9\\hat{i} - 2\\hat{j} - 3\\hat{k} \\|$$ $$\\sqrt{9^2 + (-2)^2 + (-3)^2}$$ $$\\sqrt{81+4+9} = \\sqrt{94}$$\n\n$$\\|\\vec{A} \\| = \\sqrt{2^2+3^2+4^2} = \\sqrt{4+9+16} = \\sqrt{29}$$\n$$\\|\\vec{B}\\| = \\sqrt{1^2+0^2+3^2} = \\sqrt{10}$$\n\n $$\\displaystyle{ \\sin(\\theta) = \\frac{\\| \\vec{A} \\times \\vec{B} \\|}{\\|\\vec{A}\\| \\|\\vec{B}\\|} }$$ $$\\displaystyle{ \\sin(\\theta) = \\frac{\\sqrt{94}}{\\sqrt{29}\\sqrt{10}} }$$ $$\\displaystyle{ \\theta = \\arcsin\\left( \\frac{\\sqrt{94}}{\\sqrt{290}} \\right) \\approx 0.606 }$$\n\nThe angle between the vectors $$2\\hat{i} + 3\\hat{j} + 4\\hat{k}$$ and $$\\hat{i} + 3\\hat{k}$$ is approximately 0.606 radians.\n\nFind a unit vector that is perpendicular to $$\\vec{A} = \\hat{i} + 2\\hat{j} + 3\\hat{k}$$ and $$\\vec{B} = 3\\hat{i} + 2\\hat{j} + \\hat{k}$$.\n\nProblem Statement\n\nFind a unit vector that is perpendicular to $$\\vec{A} = \\hat{i} + 2\\hat{j} + 3\\hat{k}$$ and $$\\vec{B} = 3\\hat{i} + 2\\hat{j} + \\hat{k}$$.\n\n$$\\displaystyle{ \\vec{u} = \\frac{\\pm 1}{\\sqrt{6}} (-\\hat{i}+2\\hat{j}-\\hat{k}) }$$\n\nProblem Statement\n\nFind a unit vector that is perpendicular to $$\\vec{A} = \\hat{i} + 2\\hat{j} + 3\\hat{k}$$ and $$\\vec{B} = 3\\hat{i} + 2\\hat{j} + \\hat{k}$$.\n\nSolution\n\nNote: There are two possible answers to this question.\nSince the result of the cross product is perpendicular to both of the vectors used to calculate the cross product, we can calculate the cross product and then find the unit vector of the result.\nSo, let's start by finding the cross product $$\\vec{A}\\times\\vec{B}$$.\n$$\\vec{A}\\times\\vec{B} =$$ $$(\\hat{i}+2\\hat{j}+3\\hat{k}) \\times (3\\hat{i}+2\\hat{j}+\\hat{k}) =$$ $$\\begin{vmatrix} \\hat{i} & \\hat{j} & \\hat{k} \\\\ 1 & 2 & 3 \\\\ 3 & 2 & 1 \\end{vmatrix} =$$ $$(2-6)\\hat{i} - (1-9)\\hat{j} + (2-6)\\hat{k} =$$ $$-4\\hat{i} + 8\\hat{j} - 4\\hat{k}$$\nOkay, now we need to find the unit vector in the same direction as the result of the cross product. Let's call this vector $$\\vec{v} =-4\\hat{i} + 8\\hat{j} - 4\\hat{k}$$.\n\n $$\\displaystyle{ \\vec{u} = \\frac{1}{\\|\\vec{v}\\|}\\vec{v} }$$ $$\\displaystyle{ \\frac{1}{\\sqrt{(-4)^2+8^2+(-4)^2}}(-4\\hat{i} + 8\\hat{j} - 4\\hat{k}) }$$ $$\\displaystyle{ \\frac{1}{\\sqrt{16+64+16}}(-4\\hat{i} + 8\\hat{j} - 4\\hat{k}) }$$ $$\\displaystyle{ \\frac{1}{\\sqrt{96}}(-4\\hat{i} + 8\\hat{j} - 4\\hat{k}) }$$ $$\\displaystyle{ \\frac{1}{4\\sqrt{6}}(-4\\hat{i} + 8\\hat{j} - 4\\hat{k}) }$$ $$\\displaystyle{ \\frac{1}{\\sqrt{6}}(-\\hat{i} + 2\\hat{j} - \\hat{k}) }$$\n\nNote: If you calculated $$\\vec{B}\\times\\vec{A}$$, your unit vector would be $$-\\vec{u}$$, which is the other correct answer.\n\n$$\\displaystyle{ \\vec{u} = \\frac{\\pm 1}{\\sqrt{6}} (-\\hat{i}+2\\hat{j}-\\hat{k}) }$$\n\nShow that the vectors $$\\vec{A} = 2\\hat{i}-3\\hat{j}+4\\hat{k}$$, $$\\vec{B} = 6\\hat{i}+2\\hat{j}+\\hat{k}$$ and $$\\vec{C} = 6\\hat{i}+10\\hat{j}-7\\hat{k}$$ are coplanar.\n\nProblem Statement\n\nShow that the vectors $$\\vec{A} = 2\\hat{i}-3\\hat{j}+4\\hat{k}$$, $$\\vec{B} = 6\\hat{i}+2\\hat{j}+\\hat{k}$$ and $$\\vec{C} = 6\\hat{i}+10\\hat{j}-7\\hat{k}$$ are coplanar.\n\nSince the triple scalar product is zero, the vectors are coplanar.\n\nProblem Statement\n\nShow that the vectors $$\\vec{A} = 2\\hat{i}-3\\hat{j}+4\\hat{k}$$, $$\\vec{B} = 6\\hat{i}+2\\hat{j}+\\hat{k}$$ and $$\\vec{C} = 6\\hat{i}+10\\hat{j}-7\\hat{k}$$ are coplanar.\n\nSolution\n\nWe know that if the 3 vectors are coplanar, then the triple scalar product is zero. Although not explicitly stated here, we can assume the reverse, i.e. if the triple scalar product is zero, then the vectors are coplanar. [Note: The assumption of the reverse being true cannot be always be made. Be careful when making this assumption.]\nSo let's calculate the triple scalar product to see if it is zero.\n$$\\vec{A}\\cdot \\vec{B} \\times \\vec{C} = 2\\hat{i}-3\\hat{j}+4\\hat{k} \\cdot 6\\hat{i}+2\\hat{j}+\\hat{k} \\times 6\\hat{i}+10\\hat{j}-7\\hat{k} =$$ $$\\begin{vmatrix} 2 & -3 & 4 \\\\ 6 & 2 & 1 \\\\ 6 & 10 & -7 \\end{vmatrix} =$$ $$2(-14-10) - (-3)(-42 - 6) + 4(60-12) = 0$$\n\nSince the triple scalar product is zero, the vectors are coplanar.\n\nShow that the vectors $$\\vec{A} = 2\\hat{i} + 3\\hat{j} + 6\\hat{k}$$ and $$\\vec{B} = 6\\hat{i} + 2\\hat{j} - 3\\hat{k}$$ are perpendicular.\n\nProblem Statement\n\nShow that the vectors $$\\vec{A} = 2\\hat{i} + 3\\hat{j} + 6\\hat{k}$$ and $$\\vec{B} = 6\\hat{i} + 2\\hat{j} - 3\\hat{k}$$ are perpendicular.\n\nSince $$\\|\\vec{A}\\times\\vec{B}\\| = \\|\\vec{A}\\|\\|\\vec{B}\\|$$, the angle between the two vectors is $$\\pi\/2$$ and so the vectors are perpendicular.\n\nProblem Statement\n\nShow that the vectors $$\\vec{A} = 2\\hat{i} + 3\\hat{j} + 6\\hat{k}$$ and $$\\vec{B} = 6\\hat{i} + 2\\hat{j} - 3\\hat{k}$$ are perpendicular.\n\nSolution\n\nPerpendicular vectors have a angle of $$\\pi\/2$$ between them. So, we will calculate the angle between the vectors and determine if it is $$\\pi\/2$$. Actually, since we know that $$\\|\\vec{A} \\times \\vec{B}\\| = \\|\\vec{A}\\| \\|\\vec{B}\\| \\sin(\\theta)$$ and when $$\\theta = \\pi\/2$$, $$\\sin(\\theta) = 1$$, we can calculate $$\\|\\vec{A} \\times \\vec{B}\\|$$ and see if it is equal to $$\\|\\vec{A}\\| \\|\\vec{B}\\|$$. If they are equal, then the vectors are perpendicular.\n$$\\vec{A} \\times \\vec{B} = 2\\hat{i}+3\\hat{j}+6\\hat{k} \\times 6\\hat{i} + 2 \\hat{j}-3\\hat{k} =$$ $$\\begin{vmatrix} \\hat{i} & \\hat{j} & \\hat{k} \\\\ 2 & 3 & 6 \\\\ 6 & 2 & -3 \\end{vmatrix} =$$ $$(-9 -12)\\hat{i} - (-6 - 36)\\hat{j} + (4 - 18)\\hat{k} =$$ $$-21\\hat{i} +42\\hat{j} -14\\hat{k}$$\n$$\\| \\vec{A} \\times \\vec{B} \\| =$$ $$\\| -21\\hat{i} +42\\hat{j} -14\\hat{k} \\| =$$ $$\\sqrt{(-21)^2 + 42^2 + (-14)^2} =$$ $$\\sqrt{7^2 (9) + 7^2(36) + 7^2(4)} = 7\\sqrt{49} = 49$$\nSo $$\\| \\vec{A} \\times \\vec{B} \\| = 49$$.\nNow let's calculate $$\\|\\vec{A}\\| \\|\\vec{B}\\|$$.\n\n $$\\|\\vec{A}\\| \\|\\vec{B}\\|$$ $$\\| 2\\hat{i}+3\\hat{j}+6\\hat{k} \\| \\| 6\\hat{i} + 2 \\hat{j}-3\\hat{k} \\|$$ $$\\sqrt{2^2 + 3^2 + 6^2} \\sqrt{6^2 + 2^2 + (-3)^2}$$ $$\\sqrt{4 + 9 + 36} \\sqrt{36 +4 + 9}$$ $$\\sqrt{49}\\sqrt{49} = 7(7) = 49$$\n\nSince $$\\|\\vec{A}\\times\\vec{B}\\| = \\|\\vec{A}\\|\\|\\vec{B}\\|$$, the angle between the two vectors is $$\\pi\/2$$ and so the vectors are perpendicular.\n\nFind a unit vector that is perpendicular to $$\\vec{A} = 2\\hat{i} + 3\\hat{j} + 6\\hat{k}$$ and $$\\vec{B} = 6\\hat{i} + 2\\hat{j} - 3\\hat{k}$$.\n\nProblem Statement\n\nFind a unit vector that is perpendicular to $$\\vec{A} = 2\\hat{i} + 3\\hat{j} + 6\\hat{k}$$ and $$\\vec{B} = 6\\hat{i} + 2\\hat{j} - 3\\hat{k}$$.\n\nThe unit vectors perpendicular to $$2\\hat{i}+3\\hat{j}+6\\hat{k}$$ and $$6\\hat{i}+2\\hat{j}-3\\hat{k}$$ are $$\\displaystyle{\\frac{\\pm 1}{7}[3\\hat{i}-6\\hat{j}+2\\hat{k}]}$$.\n\nProblem Statement\n\nFind a unit vector that is perpendicular to $$\\vec{A} = 2\\hat{i} + 3\\hat{j} + 6\\hat{k}$$ and $$\\vec{B} = 6\\hat{i} + 2\\hat{j} - 3\\hat{k}$$.\n\nSolution\n\nNote: There are two possible answers to this problem.\nSince the result of the cross product of two vectors is a vector perpendicular to the original two vectors, we can use the cross product to get a vector. Then, we just divide by the magnitude of the vector to get a unit vector in the same direction.\n\nFirst, let's take the cross product.\n\n$$\\vec{A} \\times \\vec{B} = (2\\hat{i}+3\\hat{j}+6\\hat{k}) \\times (6\\hat{i} + 2 \\hat{j} -3\\hat{k}) =$$ $$\\begin{vmatrix} \\hat{i} & \\hat{j} & \\hat{k} \\\\ 2 & 3 & 6 \\\\ 6 & 2 & -3 \\end{vmatrix} =$$ $$(-9 - 12)\\hat{i} - (-6 - 36)\\hat{j} + (4 - 18)\\hat{k} =$$ $$-21\\hat{i} + 42\\hat{j} - 14\\hat{k} =$$ $$-7[ 3\\hat{i} - 6\\hat{j} + 2\\hat{k}]$$\nWe factored out the -7 before finding the magnitude to make the calculations easier. However, this is not necessary.\nNow we need to calculate the unit vector in the same direction as this last vector.\n\n $$\\displaystyle{ \\vec{u} = \\frac{(-7[ 3\\hat{i} - 6\\hat{j} + 2\\hat{k}])}{\\| -7[ 3\\hat{i} - 6\\hat{j} + 2\\hat{k}] \\| } }$$ $$\\displaystyle{ \\frac{-7[ 3\\hat{i} - 6\\hat{j} + 2\\hat{k}]}{\\sqrt{(-7)^2[3^2+(-6)^2 +2^2]}} }$$ $$\\displaystyle{ \\frac{-7}{7\\sqrt{9+36+4}}[ 3\\hat{i} - 6\\hat{j} + 2\\hat{k}] }$$ $$\\displaystyle{ \\frac{-1}{\\sqrt{49}}[ 3\\hat{i} - 6\\hat{j} + 2\\hat{k}] }$$ $$\\displaystyle{ \\frac{-1}{7}[ 3\\hat{i} - 6\\hat{j} + 2\\hat{k}] }$$\n\nNotes: When solving this problem, we calculated $$\\vec{A}\\times\\vec{B}$$. If you calculated $$\\vec{B}\\times\\vec{A}$$, your answer would have been $$-\\vec{u}$$, which is also a correct answer.\n\nThe unit vectors perpendicular to $$2\\hat{i}+3\\hat{j}+6\\hat{k}$$ and $$6\\hat{i}+2\\hat{j}-3\\hat{k}$$ are $$\\displaystyle{\\frac{\\pm 1}{7}[3\\hat{i}-6\\hat{j}+2\\hat{k}]}$$.\n\n Cross Product Applications\n\nHere are some applications using the cross product. Some of them also require the use of the dot product.\n\n Triple Scalar Product\n\nThe triple scalar product is a result of combining the dot product with the cross product. First, let's define what it is and then discuss a couple of properties.\n\nDefinition and Notation - If we have three vectors in space, $$\\vec{u} = u_x\\hat{i}+u_y\\hat{j}+u_z\\hat{k}$$, $$\\vec{v} = v_x\\hat{i}+v_y\\hat{j}+v_z\\hat{k}$$ and $$\\vec{w} = w_x\\hat{i}+w_y\\hat{j}+w_z\\hat{k}$$, then the triple scalar product is defined to be $$\\vec{u} \\cdot (\\vec{v} \\times \\vec{w})$$\nThe calculation of this can be done as follows\n$$\\vec{u} \\cdot (\\vec{v} \\times \\vec{w}) = \\begin{vmatrix} u_x & u_y & u_z \\\\ v_x & v_y & v_z \\\\ w_x & w_y & w_z \\end{vmatrix}$$\n\nTriple Scalar Product Proof\n\nTheorem: Triple Scalar Product\n\nIf we have three vectors in space,\n$$\\vec{u} = u_x\\hat{i}+u_y\\hat{j}+u_z\\hat{k}$$, $$\\vec{v} = v_x\\hat{i}+v_y\\hat{j}+v_z\\hat{k}$$ and $$\\vec{w} = w_x\\hat{i}+w_y\\hat{j}+w_z\\hat{k}$$,\nthen the triple scalar product is $$\\vec{u} \\cdot (\\vec{v} \\times \\vec{w}) = \\begin{vmatrix} u_x & u_y & u_z \\\\ v_x & v_y & v_z \\\\ w_x & w_y & w_z \\end{vmatrix}$$\n\nProof - - To prove this, we will calculate $$\\vec{u} \\cdot (\\vec{v} \\times \\vec{w})$$ and then calculate the determinant to show that we get the same result. Let's start with the cross product.\n\n$$\\vec{v} \\times \\vec{w} = \\begin{vmatrix} \\hat{i} & \\hat{j} & \\hat{k} \\\\ v_x & v_y & v_z \\\\ w_x & w_y & w_z \\end{vmatrix} =$$ $$(v_y w_z - v_z w_y)\\hat{i} -$$ $$(v_x w_z - w_x v_z)\\hat{j} +$$ $$(v_x w_y - w_x v_y)\\hat{k}$$\n\nTaking the dot product of $$\\vec{u}$$ and the last equation gives us\n\n$$(u_x\\hat{i}+u_y\\hat{j}+u_z\\hat{k}) \\cdot [ (v_y w_z - v_z w_y)\\hat{i} -$$ $$(v_x w_z - w_x v_z)\\hat{j} +$$ $$(v_x w_y - w_x v_y)\\hat{k} ] =$$ $$u_x(v_y w_z - v_z w_y) -$$ $$u_y(v_x w_z - w_x v_z) +$$ $$u_z(v_x w_y - w_x v_y)$$\n\nWe could certainly multiply the components of vector $$\\vec{u}$$ through each factor, but for reasons you will see later, we will leave the equation as it is. To sum up, we have calculated\n\n$$\\vec{u} \\cdot (\\vec{v} \\times \\vec{w}) =$$ $$u_x(v_y w_z - v_z w_y) -$$ $$u_y(v_x w_z - w_x v_z) +$$ $$u_z(v_x w_y - w_x v_y) ~~~~~ (1)$$\n\nOkay, now let's calculate the determinant\n$$\\begin{vmatrix} u_x & u_y & u_z \\\\ v_x & v_y & v_z \\\\ w_x & w_y & w_z \\end{vmatrix}$$\n\nWe will go across the top row (although going down the first column will give us the same result, going across the top row makes the algebra come out the way want it to).\n\n$$\\begin{vmatrix} u_x & u_y & u_z \\\\ v_x & v_y & v_z \\\\ w_x & w_y & w_z \\end{vmatrix} =$$ $$u_x(v_y w_z - v_z w_y) -$$ $$u_y(v_x w_z - w_x v_z) +$$ $$u_z(v_x w_y - w_x v_y)$$\n\nNotice this last equation is the same as equation (1) above. This is easier to see since we did not multiply out all factors in Equation (1). So, we have shown\n\n$$\\vec{u} \\cdot (\\vec{v} \\times \\vec{w}) = \\begin{vmatrix} u_x & u_y & u_z \\\\ v_x & v_y & v_z \\\\ w_x & w_y & w_z \\end{vmatrix}$$ \u00a0\u00a0\u00a0\u00a0\u00a0 [qed]\n\nThe triple scalar product is so named because the result is a scalar. [For comparison, see the triple vector product section below.]\n\nProperties - The triple scalar product can also be evaluated in one of the following forms.\n$$\\vec{a} \\cdot (\\vec{b} \\times \\vec{c}) = \\vec{b} \\cdot (\\vec{c} \\times \\vec{a}) = \\vec{c} \\cdot (\\vec{a} \\times \\vec{b})$$\nThe parentheses may be omitted since evaluating the dot product first yields a scalar and it doesn't make sense to take the cross product of a scalar with a vector.\nThis property also holds $$[\\vec{a} \\cdot (\\vec{b} \\times \\vec{c})]\\vec{a} = (\\vec{a} \\times \\vec{b}) \\times (\\vec{a} \\times \\vec{c})$$\nWhen the triple scalar product is zero, the 3 vectors are coplanar.\n\nApplications - Geometrically, the triple scalar product $$\\vec{a} \\cdot (\\vec{b} \\times \\vec{c} )$$ is the (signed) volume of the parallelepiped defined by the three vectors given (see figure on the right). The word 'signed' means that the result can be positive or negative depending on the orientation of the vectors.\nYou can probably now see that when the 3 vectors are coplanar, the parallelepiped is flat and has no volume, so the triple scalar product is zero.\n\nOther Names For the Triple Scalar Product -\n- scalar triple product\n- mixed product\n- box product\n\nHere are several videos that explains this in more detail. The first two are especially good and the third contains a proof.\n\nDr Chris Tisdell - Scalar triple product [9mins-30secs]\n\nvideo by Dr Chris Tisdell\n\nDr Chris Tisdell - Scalar triple product and volume [11mins-49secs]\n\nvideo by Dr Chris Tisdell\n\nLarson Calculus - Proof - Geometric Property of the Triple Scalar Product [1mins-40secs]\n\nvideo by Larson Calculus\n\nGiven $$\\vec{A}=\\hat{i}-2\\hat{j}+2\\hat{k}$$, $$\\vec{B}=3\\hat{i}-\\hat{j}-\\hat{k}$$ and $$\\vec{C}=-\\hat{i}-\\hat{k}$$, calculate the triple scalar product $$\\vec{A}\\cdot\\vec{B}\\times\\vec{C}$$.\n\nProblem Statement\n\nGiven $$\\vec{A}=\\hat{i}-2\\hat{j}+2\\hat{k}$$, $$\\vec{B}=3\\hat{i}-\\hat{j}-\\hat{k}$$ and $$\\vec{C}=-\\hat{i}-\\hat{k}$$, calculate the triple scalar product $$\\vec{A}\\cdot\\vec{B}\\times\\vec{C}$$.\n\n$$\\vec{A}\\cdot\\vec{B}\\times\\vec{C}=-9$$\n\nProblem Statement\n\nGiven $$\\vec{A}=\\hat{i}-2\\hat{j}+2\\hat{k}$$, $$\\vec{B}=3\\hat{i}-\\hat{j}-\\hat{k}$$ and $$\\vec{C}=-\\hat{i}-\\hat{k}$$, calculate the triple scalar product $$\\vec{A}\\cdot\\vec{B}\\times\\vec{C}$$.\n\nSolution\n\nFirst, we need to find the cross product.\n\n$$\\vec{B}\\times\\vec{C}$$ = $$(3\\hat{i}-\\hat{j}-\\hat{k}) \\times (-\\hat{i}-\\hat{k}) =$$ $$\\begin{vmatrix} \\hat{i} & \\hat{j} & \\hat{k} \\\\ 3 & -1 & -1 \\\\ -1 & 0 & -1 \\end{vmatrix}$$ $$= (1-0)\\hat{i} - (-3-1)\\hat{j} + (0-1)\\hat{k}$$ $$= \\hat{i} +4\\hat{j} -\\hat{k}$$\n\nNow we do the dot product.\n$$(\\hat{i}-2\\hat{j}+2\\hat{k}) \\cdot (\\hat{i} +4\\hat{j} -\\hat{k}) =$$ $$(1)(1) + (-2)(4) + (2)(-1) =$$ $$1-8-2 = -9$$\n\n$$\\vec{A}\\cdot\\vec{B}\\times\\vec{C}=-9$$\n\n Triple Vector Product\n\nThe triple vector product (or vector triple product, as it is sometimes called) is so named because the result is a vector. [For comparison, see the triple scalar product panel above.]\n\nWhen you have three vectors, $$\\vec{u}$$, $$\\vec{v}$$ and $$\\vec{w}$$, the triple vector product is defined as $$\\vec{u} \\times \\vec{v} \\times \\vec{w}$$.\n\nGiven $$\\vec{A}=\\hat{i}-2\\hat{j}+2\\hat{k}$$, $$\\vec{B} = 3\\hat{i}-\\hat{j}-\\hat{k}$$ and $$\\vec{C}=-\\hat{i}-\\hat{k}$$, calculate the triple vector product $$\\vec{A}\\times\\vec{B}\\times\\vec{C}$$.\n\nProblem Statement\n\nGiven $$\\vec{A}=\\hat{i}-2\\hat{j}+2\\hat{k}$$, $$\\vec{B} = 3\\hat{i}-\\hat{j}-\\hat{k}$$ and $$\\vec{C}=-\\hat{i}-\\hat{k}$$, calculate the triple vector product $$\\vec{A}\\times\\vec{B}\\times\\vec{C}$$.\n\n$$\\vec{A}\\times\\vec{B}\\times\\vec{C}=-7\\hat{i}-\\hat{j}+7\\hat{k}$$\n\nProblem Statement\n\nGiven $$\\vec{A}=\\hat{i}-2\\hat{j}+2\\hat{k}$$, $$\\vec{B} = 3\\hat{i}-\\hat{j}-\\hat{k}$$ and $$\\vec{C}=-\\hat{i}-\\hat{k}$$, calculate the triple vector product $$\\vec{A}\\times\\vec{B}\\times\\vec{C}$$.\n\nSolution\n\nLet's work left to right.\n$$\\vec{A} \\times \\vec{B} = (\\hat{i}-2\\hat{j}+2\\hat{k}) \\times (3\\hat{i}-\\hat{j}-\\hat{k}) =$$ $$\\begin{vmatrix} \\hat{i} & \\hat{j} & \\hat{k} \\\\ 1 & -2 & 2 \\\\ 3 & -1 & -1 \\end{vmatrix} =$$ $$(2-(-2))\\hat{i} - (-1-6)\\hat{j} + (-1-(-6))\\hat{k} =$$ $$4\\hat{i} + 7\\hat{j} +5\\hat{k} = \\vec{v}$$\nNow we need to calculate $$\\vec{v} \\times \\vec{C}$$.\n$$(4\\hat{i} + 7\\hat{j} +5\\hat{k}) \\times (-\\hat{i}-\\hat{k}) =$$ $$\\begin{vmatrix} \\hat{i} & \\hat{j} & \\hat{k} \\\\ 4 & 7 & 5 \\\\ -1 & 0 & -1 \\end{vmatrix} =$$ $$(-7-0)\\hat{i} - (-4-(-5))\\hat{j} +(0-(-7))\\hat{k} =$$ $$-7\\hat{i} -\\hat{j} +7\\hat{k}$$\n\n$$\\vec{A}\\times\\vec{B}\\times\\vec{C}=-7\\hat{i}-\\hat{j}+7\\hat{k}$$","date":"2018-01-23 13:33:39","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9179362058639526, \"perplexity\": 315.79764555494364}, \"config\": {\"markdown_headings\": false, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-05\/segments\/1516084891976.74\/warc\/CC-MAIN-20180123131643-20180123151643-00735.warc.gz\"}"} | null | null |
Q: How to make users gain root privileges from another account? How can I make something like that:
There are two users: user with normal privileges, and administrator with admin privileges.
I want to make it like that:
user@localhost:~$ sudo vim
[sudo] password for administrator: <admin's password here>
And I am on the administrator account now.
A: Simply add the user to the sudo group:
sudo adduser <username> sudo
More detailed explanation: https://help.ubuntu.com/community/RootSudo#Allowing_other_users_to_run_sudo
If you really need to run vim as a user named "administrator" (not root!) you should use
sudo -u adminstrator vim
But even in that case the normal user has to be member of the sudo group.
A: sudo vim would mean to execute the vim command as super-user. If you are looking for the command to start a shell, use
sudo -i
or
sudo su
These will have you type the password of your user, and the user needs to be in the sudoers file.
If you don't want the user to be added to that file, you could just use the command
su
which will have you type in the root (administrator) account.
And finally, if there is an account called administrator, you could do
su administrator
to gain access to that.
A: If you meant that when logged in as user you want to execute a command as administrator then you need to do:
user@localhost:~$ sudo -u administrator vim
However, the user's password will be asked not the one from adminitrator. To do so you need to run as administrator (hmm) the following command to configure sudo:
visudo
Then scroll down in the opened file and look for other Defaults definition. In this section, preferrably at the end of it, add a new line with:
Defaults targetpw
And save the file and exit. Note that this will change the default behaviour for all sudo users, so if your user administrator needs to use sudo to have root privilege, you would better know the root password!
| {
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Our checklist will help you decide whether or not it's time to move into a smaller abode.
With 1.3 acres of land and a two-storey home in Horseshoe Valley, Ont., you might say that Sylvia and Warren Andrews had it all. But Sylvia, a former teacher, and Warren, a retired engineer, saw things differently: They had way too much.
Move when it makes sense for you. You might want to put off downsizing, for instance, until you're older and less active, or until you know more about where the kids and grandkids want to settle. Or you may not want to downsize at all.
The Andrews bought the home in 1995, when they were 50 and 64, respectively. The property seemed perfect for middle age. "The house in Horseshoe Valley was a great place to live, but we realized we needed somewhere to live for where we're at now, and where we'll be in the future," she says.
About a year ago, the couple, now 73 and 88, downsized again to Orillia, Ont., where they live in a newly renovated bungalow more suited to their needs.
While Andrews is happy – "I've been wondering why we didn't do this sooner," she says – downsizing involves a lot more than just buying a smaller home. People need to think about the lifestyle they want, if the place will still suit them in the future, if they'll save money by moving, and more.
What should you be thinking about before making the big move? Our checklist of questions can help.
1. Is moving the right move?
Often, there's pressure to downsize from friends and family because of market conditions or to suit their own plans. "We see people getting pushed into circumstances by well-meaning other parties, because they think it's a good time for their acquaintances or relatives to make the move," says Barry Gordon, president of Gordon's Downsizing and Estate Services, an Ontario company that helps clients with all the intricacies of downsizing.
Instead, move when it makes sense for you. You might want to put off downsizing, for instance, until you're older and less active, or until you know more about where the kids and grandkids want to settle. Or you may not want to downsize at all. "You need a moving plan that fits your needs, and to do whatever is best to make your life more comfortable," says Gordon.
2. Can you age into your house?
Many people, like the Andrews, move into homes that won't necessarily work for them as they age. That's fine for those who retire early and don't mind a second move a few decades later, though they'll pay land transfer taxes, realtor's fees and moving costs again.
Carri Hand, assistant professor in the School of Occupational Therapy at Western University, says downsizers should choose accommodations they can age into.
For instance, look for houses or condos without barriers like stairs, narrow doorways and long driveways. Properties with acres of land will also require physically intensive maintenance. "Almost everybody who's aging is wondering what's down the road," she says, so think ahead when it comes to a new home.
Consider hiring an occupational therapist – they'll be able to tell if doorway and hallway width can accommodate mobility devices like wheelchairs or walkers.
3. Is the neighbourhood right for you?
Choosing the right locale is key for downsizers. Some want to be close to nightlife, others to health-care facilities – often it's both. "Make sure there are all the supports in your new neighbourhood to allow you to continue to do what matters to you," says Hand.
Ease of travel is important, too, which could be a problem if you want to live in a small town with no transit. Ideally, move near bus routes and amenities like grocery stores, community centres, libraries and hospitals.
4. Will you save money?
Many people downsize because they need the money they've saved up in their homes. But, before making the decision to sell, do the math: Buying a condo in a hot urban area, like downtown Toronto or Vancouver, can cost a pretty penny. In fact, depending on where you live now, it can be more expensive to buy a smaller place.
In that case, you may want to consider renting, says Gordon. However, money isn't always the deciding factor on choosing whether to rent or buy, he says. Some people rent because it's all that's available in the area they want to live in – and geography, says Gordon, is the number one factor in determining where people downsize to – while others may want access to the funds made off their house. "Renting means a person is unlocking the equity in their current home, which could be invested to grow or to offset rental costs going forward," he says.
If finances are a motivation to move, make sure you do the math to see what makes the most sense, says Gordon. | {
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Q: Odoo installed on Docker I have Odoo's enterprise addons and i 'm trying to start a container using this addons and my own custom addons. Can someone help me how to add enterprise addons. for now, i've add path of my custom addons and it work but i don't know how to do with enterprise addons.
Thanks for reply
A: First of all you've to search for the config file of your installed odoo. In your docker the running OS is linux then your config file may be in /etc
Then add your enterprise addons path in your config file like following.
addons_path = /opt/odoo13/odoo/enterprise/addons
In docker if your running OS is windows then your config file may be in C:\Program File (x86)\Odoo12.0\server\odoo.conf
If you want to add two path one for custom addons and second is for enterprise addons then try this in your config file.
addons_path = /opt/odoo13/odoo/enterprise/addons, /opt/odoo13/odoo/custom_addons
A: You have to first update the addons_path in the config file as explained by Adam Strauss, then, depending on the usage of docker-compose or docker you will type different commands but the point is to mount the two addons' volumes, the first for the enterprise's version addons and the second for the custom addons.
For docker-compose, the docker-compose.yml should mount both addons directories as stated in the config file. Make sure to make the config file match the container filesystem and not the host file system. Find below an example of what it will look like.
version: '2'
services:
web:
image: odoo:12.0
depends_on:
- db
ports:
- "8069:8069"
volumes:
- ./config:/etc/odoo
- ./odoo/enterprise/addons:/opt/odoo13/addons
- ./odoo/custom_addons:/opt/odoo13/custom_addons
db:
image: postgres:10
environment:
- POSTGRES_DB=postgres
- POSTGRES_PASSWORD=odoo
- POSTGRES_USER=odoo
All details are well explained here.
| {
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"get_label_info: Get an attribute from a target's label.\n"
" Given the label of a target, returns some attribute of that target.\n"
" The target need not have been previously defined in the same file,\n"
" since none of the attributes depend on the actual target definition,\n"
" only the label itself.\n"
" See also \"gn help get_target_outputs\".\n"
" The short name of the target. This will match the value of the\n"
" \"target_name\" variable inside that target's declaration. For the\n"
" label \"//foo/bar:baz\" this will return \"baz\".\n"
" The directory containing the target's definition, with no slash at\n"
" the end. For the label \"//foo/bar:baz\" this will return\n"
" The generated file directory for the target. This will match the\n"
" value of the \"target_gen_dir\" variable when inside that target's\n"
" The root of the generated file tree for the target. This will\n"
" match the value of the \"root_gen_dir\" variable when inside that\n"
" The output directory for the target. This will match the\n"
" value of the \"target_out_dir\" variable when inside that target's\n"
" The root of the output file tree for the target. This will\n"
" The fully qualified version of this label, not including the\n"
" toolchain. For the input \":bar\" it might return\n"
" The fully qualified version of this label, including the\n"
" The label of the toolchain. This will match the value of the\n"
" \"current_toolchain\" variable when inside that target's\n"
" # Returns string \"foo\".\n"
// Resolve the requested label.
// Extract the "what" parameter. | {
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Kaspersky Antivirus is famous worldwide for its effective and robust antivirus and other anti-malware applications. The user interface of this Antivirus is lightweight and has all the important options required by the user to safeguard the workstations. However this antivirus is an effective antivirus but there are many users who have reported that sometimes they have to face issue some technical issue so in the case that if you are also having issue with your antivirus then you can make contact to Kaspersky experts by dialing Kaspersky Phone Number 0-800-098-8929 which is toll free for the users of U.K. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,944 |
Premier League News Now
Home Latest News "Adams was Arsenal Captain at 20, why not Guendouzi?" – Ian Wright...
"Adams was Arsenal Captain at 20, why not Guendouzi?" – Ian Wright says Emery
Gopal Tikmani
Arsenal legend Ian Wright considers it "crazy" that not Matteo Guendouzi, but Granit Xhaka has taken on captaincy duties, with Unai Emery marked, "not strong enough" to make a big decision. The Gunners boss continues to favor working with a leadership group, but wants one person wearing the captain's armband more regularly.
A voting process was held with the help of a blind ballot, where the Swiss, Granit Xhaka was chosen to lead the side. Emery has faced a lot of criticism for reluctance to take the call himself, with many suggesting that there were more suitable options available in the likes of Pierre-Emerick Aubameyang and David Luiz.
And now, Gunners legend Ian Wright has claims that 20-year old, French midfielder Matteo Guendouzi should've also been considered as a holder of the armband. In an interview to Premier League Productions after seeing Guendouzi's noteworthy performance in the 1-1 draw against Manchester United, he said: "If you are going to take any positives out of it, the form and the emergence of Matteo Guendouzi is fantastic. He's somebody that is driving the team forward."
"When he came in the first season to play that many games, I thought it was too much, I thought it was too many. But now you're seeing someone that looks totally in control in what he's doing. He's getting himself into great spaces, against Tottenham, he was fantastic. Got the assist for Aubameyang."
"And for me, I know they've chosen the captain but Xhaka should not be the captain in front of this guy or Aubameyang, for me. He's leading by example for a 20-year old. We know Tony Adams was a captain at 20, maybe Unai's not strong enough to give somebody like Matteo Guendouzi [the captaincy]."
"When you look at him here and what he is doing, that is taking the game by the scruff of the neck and driving Arsenal forward, and he's not been made captain or vice-captain."
"It's crazy, for me"
After arriving in North London in the Summer of 2018, many doubted the quality and talent of Matteo Guendouzi, but he has made his presence felt in English football, and looks to be a prominent figure in Unai Emery's future plans for the team, and also a major contender for the armband in the coming seasons.
Arsenal News Now | Get Latest Arsenal Football News
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modern house interior designs in kerala houses by ii style design ideas pictures. | {
"redpajama_set_name": "RedPajamaC4"
} | 483 |
{"url":"http:\/\/www.reddit.com\/r\/cheatatmathhomework\/comments\/1473xv\/integratation_by_substitution\/?sort=top","text":"[\u2013] 1 point2 points ago\n\nsorry, this has been archived and can no longer be voted on\n\nHint: what happens when you differentiate ex + e-x?\n\n[\u2013] 1 point2 points ago\n\nsorry, this has been archived and can no longer be voted on\n\nWhen I differentiate it? What happens is ethis is wrong\n\nReal answer: differentiating the above yields ex -e-x\n\n[\u2013] 1 point2 points ago\n\nsorry, this has been archived and can no longer be voted on\n\nethis is wrong\n\nHilarious\n\n[\u2013] 1 point2 points ago\n\nsorry, this has been archived and can no longer be voted on\n\nA stronger hint than aanimo was willing to give: Substitute u=ex + e-x\n\n[\u2013] 0 points1 point ago\n\nsorry, this has been archived and can no longer be voted on\n\nYou can do a really tricky thing to make this look much simpler if you remember your hyperbolic functions.\n\nRecall that cosh(x) = (1\/2)(ex + e-x) and sinh(x) = (1\/2)(ex - e-x)\n\nTake the original problem:\n\n\u222b (ex - e-x) \/ (ex + e-x) dx and multiply by 1 in the form of (1\/2) \/ (1\/2)\n\n\u222b (1\/2)(ex - e-x) \/ (1\/2)(ex + e-x) dx\n\n\u222b sinh(x) \/ cosh(x) dx\n\nNow a u-sub is a bit more obvious.\n\n[\u2013] -1 points0 points ago\n\nsorry, this has been archived and can no longer be voted on\n\nLet u = ex. Solving for e-x, you can plug replace ex and e-x with stuff involving u. Also du = ex dx = u dx, so you can solve for dx and replace it with stuff involving u and du.\n\nThen you have an integral involving u where the integrand is a rational function (a function with a polynomial in the numerator and a polynomial in the denominator) involving u. It might be tricky but it is hopefully do-able.","date":"2014-03-11 10:54:04","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8534607887268066, \"perplexity\": 3039.6628074077926}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-10\/segments\/1394011174089\/warc\/CC-MAIN-20140305091934-00054-ip-10-183-142-35.ec2.internal.warc.gz\"}"} | null | null |
title: PapljStructureViewModel.PapljTreeElement.getChildrenBase - aesi-intellij
---
[aesi-intellij](../../../index.html) / [org.metaborg.paplj.structureoutline](../../index.html) / [PapljStructureViewModel](../index.html) / [PapljTreeElement](index.html) / [getChildrenBase](.)
# getChildrenBase
`fun getChildrenBase(): `[`MutableCollection`](https://kotlinlang.org/api/latest/jvm/stdlib/kotlin.collections/-mutable-collection/index.html)`<StructureViewTreeElement>` | {
"redpajama_set_name": "RedPajamaGithub"
} | 8,562 |
José de Sousa Nunes foi um engenheiro e ferroviário português.
Biografia
Iniciou a sua carreira em 1919, como engenheiro praticante na Companhia dos Caminhos de Ferro Portugueses. Em 1927 foi promovido a chefe de serviço das Instalações Eléctricas na Divisão de Via e Obras, e em 1930 a engenheiro chefe de serviço da Conservação de Via e Obras. Pouco tempo depois, tornou-se chefe da Sala de Estudos, em 1942 passou a engenheiro subchefe, e em 1947 a engenheiro chefe da Divisão. Reformou-se no dia 1 de Dezembro de 1955, após 36 anos de serviço da Companhia.
Colaborou igualmente na organização do Pavilhão da Companhia na Exposição do Mundo Português, em 1940, tendo recebido um louvor por parte do Conselho de Administração. Em 1943 chefiou as obras de construção da Colónia de Férias da Praia das Maçãs, e em 1947 orientou a reparação dos estragos provocados por um descarrilamento na Estação Ferroviária de Vila Franca de Xira. Em 1948 liderou os trabalhos de restabelecimento da circulação ferroviária na Ponte de Santana, e no ano seguinte organizou um comboio especial, entre Queluz e Luso, onde viajou o General Franco.
Engenheiros de Portugal
Ferroviários de Portugal | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,505 |
Toby Price (* 18. August 1987 in Hillston) ist ein australischer Motorradrennfahrer.
Price begann 2004 im Alter von 16 Jahren seine Profikarriere und ist mehrfacher australischer sowie internationaler Titelgewinner in verschiedenen Motocross- und Enduro-Wettbewerben sowie zweifacher Rallye Dakar Gewinner in der Motorradklasse. Er nimmt seit 2015 für das Red-Bull-KTM-Factory-Racing-Team an der Rallye Dakar teil und gewann diese als erster Australier 2016 und 2019. Price verlor zur Rallye Dakar 2020 beim Versuch Paulo Gonçalves nach einem Sturz zu helfen eine Stunde und 20 Minuten und wurde schlussendlich Drittplatzierter in der Motorradwertung.
Weblinks
Toby Price auf dakar.com
Rallye Raid
Motorrad-Rennfahrer (Australien)
Australier
Geboren 1987
Mann | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,837 |
Stenocarus is a genus of beetles belonging to the family Curculionidae. The species of this genus are found in Europe.
Species
Stenocarus canaliculatus Gyll, 1837
Stenocarus cardui (Herbst, 1784)
Stenocarus ruficornis Stephens, 1831
References
Curculionidae
Curculionidae genera | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 624 |
<?php
namespace Echosign\Creators;
use Echosign\Agreements;
use Echosign\Exceptions\JsonApiResponseException;
use Echosign\RequestBuilders\Agreement\DocumentCreationInfo;
use Echosign\RequestBuilders\Agreement\FileInfo;
use Echosign\RequestBuilders\Agreement\InteractiveOptions;
use Echosign\RequestBuilders\AgreementCreationInfo;
class Agreement extends CreatorBase
{
/**
* @var Agreements
*/
protected $agreement;
/**
* @var string
*/
protected $signatureType = 'ESIGN';
/**
* @var string
*/
protected $signatureFlow = 'SENDER_SIGNS_LAST';
/**
* Create an agreement from a libraryDocumentId for specified signerEmail with message. You can use
* $this->getResponse() to get created agreement. If successful it returns the agreementId.
* @param $signerEmail
* @param $message
* @param $libraryDocumentId
* @param $agreementName
* @return bool|string
* @internal param $signatureType
* @internal param $signatureFlow
*/
public function createFromLibraryDocumentId( $signerEmail, $message, $libraryDocumentId, $agreementName )
{
$this->agreement = new Agreements( $this->getToken(), $this->getTransport() );
$fileInfo = new FileInfo();
$fileInfo->libraryDocumentId = $libraryDocumentId;
$docCreationInfo = new DocumentCreationInfo(
$fileInfo,
$agreementName,
$this->getSignatureType(),
$this->getSignatureFlow()
);
$docCreationInfo->setMessage( $message )
->addRecipient( 'SIGNER', $signerEmail );
$agreementCreationInfo = new AgreementCreationInfo( $docCreationInfo, new InteractiveOptions() );
try {
$this->response = $this->agreement->create( $agreementCreationInfo );
} catch ( JsonApiResponseException $e ) {
$this->errorMessages[ $e->getCode() ] = sprintf( '%s - %s', $e->getApiCode(), $e->getMessage() );
return false;
} catch ( \Exception $e ) {
$this->errorMessages[ $e->getCode() ] = $e->getMessage();
return false;
}
return $this->response->getAgreementId();
}
/**
* Create an agreement from a libraryDocumentName for specified signerEmail with message. You can use
* $this->getResponse() to get created agreement. If successful it returns the agreementId.
* @param $signerEmail
* @param $message
* @param $libraryDocumentName
* @param $agreementName
* @return bool|string
* @internal param $signatureType
* @internal param $signatureFlow
*/
public function createFromLibraryDocumentName( $signerEmail, $message, $libraryDocumentName, $agreementName )
{
$this->agreement = new Agreements( $this->getToken(), $this->getTransport() );
$fileInfo = new FileInfo();
$fileInfo->libraryDocumentName = $libraryDocumentName;
$docCreationInfo = new DocumentCreationInfo(
$fileInfo,
$agreementName,
$this->getSignatureType(),
$this->getSignatureFlow()
)
;
$docCreationInfo->setMessage( $message )
->addRecipient( 'SIGNER', $signerEmail );
$agreementCreationInfo = new AgreementCreationInfo( $docCreationInfo, new InteractiveOptions() );
try {
$this->response = $this->agreement->create( $agreementCreationInfo );
} catch ( JsonApiResponseException $e ) {
$this->errorMessages[ $e->getCode() ] = sprintf( '%s - %s', $e->getApiCode(), $e->getMessage() );
return false;
} catch ( \Exception $e ) {
$this->errorMessages[ $e->getCode() ] = $e->getMessage();
return false;
}
return $this->response->getAgreementId();
}
/**
* Create an agreement from a file hosted on a remote server, for specified signerEmail with message. You can use
* $this->getResponse() to get created agreement. If successful it returns the agreementId.
* @param $signerEmail
* @param $message
* @param $fileName
* @param $url
* @param $agreementName
* @return bool|string
* @internal param $signatureType
* @internal param $signatureFlow
*/
public function createFromUrl( $signerEmail, $message, $fileName, $url, $agreementName )
{
$this->agreement = new Agreements( $this->getToken(), $this->getTransport() );
$fileInfo = new FileInfo();
$fileInfo->setDocumentURL( $fileName, $url );
$docCreationInfo = new DocumentCreationInfo(
$fileInfo,
$agreementName,
$this->getSignatureType(),
$this->getSignatureFlow()
);
$docCreationInfo->setMessage( $message )
->addRecipient( 'SIGNER', $signerEmail );
$agreementCreationInfo = new AgreementCreationInfo( $docCreationInfo, new InteractiveOptions() );
try {
$this->response = $this->agreement->create( $agreementCreationInfo );
} catch ( JsonApiResponseException $e ) {
$this->errorMessages[ $e->getCode() ] = sprintf( '%s - %s', $e->getApiCode(), $e->getMessage() );
return false;
} catch ( \Exception $e ) {
$this->errorMessages[ $e->getCode() ] = $e->getMessage();
return false;
}
return $this->response->getAgreementId();
}
/**
* Create an agreement from a transientDocumentId, for specified signerEmail with message. You can use
* $this->getResponse() to get created agreement. If successful it returns the agreementId.
* @param $signerEmail
* @param $message
* @param $transientDocumentId
* @param $agreementName
* @return bool|string
* @internal param $signatureType
* @internal param $signatureFlow
*/
public function createFromTransientDocumentId( $signerEmail, $message, $transientDocumentId, $agreementName )
{
$this->agreement = new Agreements( $this->getToken(), $this->getTransport() );
$fileInfo = new FileInfo();
$fileInfo->transientDocumentId = $transientDocumentId;
$docCreationInfo = new DocumentCreationInfo(
$fileInfo,
$agreementName,
$this->getSignatureType(),
$this->getSignatureFlow()
);
$docCreationInfo->setMessage( $message )
->addRecipient( 'SIGNER', $signerEmail );
$agreementCreationInfo = new AgreementCreationInfo( $docCreationInfo, new InteractiveOptions() );
try {
$this->response = $this->agreement->create( $agreementCreationInfo );
} catch ( JsonApiResponseException $e ) {
$this->errorMessages[ $e->getCode() ] = sprintf( '%s - %s', $e->getApiCode(), $e->getMessage() );
return false;
} catch ( \Exception $e ) {
$this->errorMessages[ $e->getCode() ] = $e->getMessage();
return false;
}
return $this->response->getAgreementId();
}
/**
* Create an agreement from a local file, for specified signerEmail with message. It first creates a transient
* document, then creates the agreement. You can use $this->getResponse() to get created agreement. If successful
* it returns the agreementId.
* @param $signerEmail
* @param $message
* @param $filename
* @param $agreementName
* @return bool|string
* @internal param $signatureType
* @internal param $signatureFlow
*/
public function createTransientAgreement( $signerEmail, $message, $filename, $agreementName )
{
$transientDocument = new TransientDocument( $this->getToken(), $this->getTransport() );
$transientDocumentId = $transientDocument->create( $filename );
if ($transientDocumentId === false) {
$this->response = $transientDocument->getResponse();
$this->errorMessages = $transientDocument->getErrorMessages();
return false;
}
return $this->createFromTransientDocumentId( $signerEmail, $message, $transientDocumentId, $agreementName );
}
/**
* Create an agreement from a local file, for specified signerEmail with message. It first creates a library
* document, then creates the agreement. You can use $this->getResponse() to get created agreement. If successful
* it returns the agreementId.
* @param $signerEmail
* @param $message
* @param $filename
* @param $agreementName
* @return bool|string
*/
public function createLibraryDocumentAgreement( $signerEmail, $message, $filename, $agreementName )
{
$libraryDocument = new LibraryDocument( $this->getToken(), $this->getTransport() );
$libraryDocumentId = $libraryDocument->createFromLocalFile( $filename, basename( $filename ), 'DOCUMENT' );
if ($libraryDocumentId === false) {
$this->response = $libraryDocument->getResponse();
$this->errorMessages = $libraryDocument->getErrorMessages();
return false;
}
return $this->createFromLibraryDocumentId( $signerEmail, $message, $libraryDocumentId, $agreementName );
}
/**
* @return Agreements
*/
public function getAgreement()
{
return $this->agreement;
}
/**
* @return string
*/
public function getSignatureType()
{
return $this->signatureType;
}
/**
* @param string $signatureType
* @return $this
*/
public function setSignatureType( $signatureType )
{
$this->signatureType = $signatureType;
return $this;
}
/**
* @return string
*/
public function getSignatureFlow()
{
return $this->signatureFlow;
}
/**
* @param string $signatureFlow
* @return $this
*/
public function setSignatureFlow( $signatureFlow )
{
$this->signatureFlow = $signatureFlow;
return $this;
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 9,384 |
Ю́лий Ла́цис (; 25 декабря 1892, Ледурга, Лифляндская губерния, Российская империя — 15 декабря 1941, Астрахань, СССР) — латышский , , общественный и государственный деятель Латвийской ССР. Член Союза писателей Латвии.
Биография
Из крестьян. После окончания школы, в 1914 году поступил в Рижский политехнический институт. Был женат на Анне (Асе) Лацис (до замужества — Лиепа). После окончания Первой мировой войны вместе с женой отправился на учёбу в Психоневрологический институт имени Бехтерева в Петрограде.
В 1921—1923 годах продолжил обучение в Латвийском университете, затем отправился во Францию, где в 1925—1926 годах изучал журналистику в Парижской Высшей школе социальных наук. Ю. Лацис был одним из первых журналистов в Латвии, получивших профессиональное образование.
Работал в латышских газетах («Jaunākās Ziņas») и журналах («Atpūta»). Публиковал свои статьи, стихи и рассказы. Пользовался псевдонимами Ju-Ju и Sinus.
Член Коммунистической партии Латвии. После ввода советских войск в Латвию в 1940 году был избран депутатом Народного Сейма.
Был назначен министром народного благосостояния (21 июня — 21 июля 1940) в правительстве А. Кирхенштейна, позже — народным комиссаром по образованию. Член делегации, направленной в Москву с просьбой принять Латвию в состав СССР.
8 января 1941 года по обвинению в антисоветской агитации был арестован. Умер 15 декабря того же года в Астраханской тюрьме.
Избранные произведения
«Mūža meža maldi» (роман о жизни латышей в джунглях штата Сан-Паулу, Бразилия).
Примечания
Ссылки
Jūlijs Lācis
Jūlijs Lācis — represēts tautas komisārs
Родившиеся в Кримулдском крае
Латышские писатели
Народные комиссары и министры Латвийской ССР
Министры благосостояния Латвии
Министры образования Латвии
Репрессированные в СССР
Умершие в местах лишения свободы
Члены Коммунистической партии Латвии
Депутаты «Народного Сейма» Латвии
Кабинет Августа Кирхенштейна
Кабинет Вилиса Лациса
Члены Союза писателей Латвии | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,552 |
Home Environment Page 2
Russia Ready for Dialogue with EU on Carbon Tax
Russia Tops Index of Climate Disparity
Russia Most Affected by New European Carbon Tax Plan
According to a collaborative research by two European climate think tanks, the world's first carbon border tax planned by the European Union is expected to impact Russia the most while leaving Chinese commerce relatively unaffected, Reuters reports. In July, the EU proposed a Carbon Border Adjustment Mechanism (CBAM), or CO2...
Wildfires Cause State of Emergency around Nuclear Sites in Russia
Interfax reported Tuesday that Russian officials have declared an interregional state of emergency as difficult-to-control forest fires threaten the country's top-secret nuclear weapons development site. Since early August, wildfires have burned in Nizhny Novgorod and the adjacent republic of Mordovia, both around 500 kilometers east of Moscow, The Moscow Times...
Crimea to Be Saturated with Water from the Azov
Large reserves of fresh water have been found under the bottom of the Sea of Azov, Russian media report. Experts now determine the quality of this water, the presence of solid particles in it, and "chemistry in general," said the head of Crimea, Sergei Aksenov, in an interview with the...
Moscow is 14th Most Innovative City in Europe
Moscow has improved its position in the fDi Intelligence analytics company's international Tech Cities of the future, updating its position on four lines and ranking 14th among 76 European cities, according to the information available on Tuesday on the mayor's and municipal administrations official website, TASS reports. The ranking assesses...
In a Historic First, Smoke from a Siberian Wildfire Reaches the North Pole
According to satellite data, smoke from wildfires burning across Russia's biggest and coldest area reached the North Pole for the first time in recorded history last week, Moscow Times writes. According to the European Union's Copernicus satellite monitoring program, forest fires in the Siberian republic of Sakha (Yakutia), driven by...
Arctic and Antarctic Research Institute Sends out New Expedition
In a post on its Telegram channel, Arctic and Antarctic Research Institute (AARI, St. Petersburg) announced that the Arctic-2021 global expedition had left Murmansk aboard its Akademik Tryoshnikov diesel-electric research vessel. The expedition will carry out complex studies of Arctic nature in a changing climate, TASS reports. Aboard the Akademik...
European Commission Technically Renews Antidumping Duties against Russian Steel
According to a source, the European Commission (EC) has technically prolonged antidumping penalties against Russian and Chinese steel that were set to expire on August 5, according to TASS on Wednesday. "Antidumping duties on Russia and China will stay in force until the review procedure for these measures is finished....
Turkey Praises Russia for Selfless Aid in Battling Wildfires
The President of Turkey Recep Tayyip Erdogan spoke by phone with Russian President Vladimir Putin on Saturday, according to Turkey's Communications Directorate, Daily Sabah reported. Per a statement, Erdogan praised Putin for allocating five firefighting planes and three additional helicopters to help Turkey battle wildfires throughout the nation. According to the...
Rosrybolovstvo Sues Nornickel for $801mn in Oil Spill Damages
Russia's national fishing department announced on Thursday that it has filed a claim against Norilsk Nickel, the world's largest nickel and palladium supplier, for $801 million in damages related to an Arctic fuel leakage last year. After 20,000 tons of petrochemicals that leaked out of a power plant in the industrial...
EU Carbon Tax May Cost Russian Exporters 1.1 Billion Euros per Year
According to the RBC news website, the European Union's planned carbon border tax may cost Russian exporters with a significant carbon footprint at least 1.1 billion euros per year, the largest penalty of any country. The border fee, suggested as part of the EU's grand goals to combat climate change...
Record-Breaking 6mn Russian Tourists Visit Turkey in 2018
Rossiya Airlines to Sue Passenger Who Opened Airplane Door on Moscow-Antalya...
EC: Russia-Ukraine Gas Talks to Begin Next Week | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,406 |
Football: Looking to earn spot in Indian team through ISL performances, says fit-again Amarjit Singh
The India U-17 World Cup captain, who was undergoing rehabilitation, started training with his club Jamshedpur FC.
Amarjit Singh Kiyam druing Indian football team's practice session | Indian Football/Twitter
Young midfielder Amarjit Singh is aiming to get back into the national team setup via the Indian Super League after recovering from an injury to his forearm.
The India U-17 World Cup captain, who was undergoing rehabilitation, started training with his club Jamshedpur FC, and was even on the bench in their last ISL match. "My sole resolution at the moment is to get back into my club team, and then the national team. I was on the bench in our last ISL match but I am still awaiting a chance," Amarjit said.
The 19-year-old added, "And it's not just about the chance, it's about me proving to my coaches that I am good enough and better than others. If they get the confidence that I can make an impact on the field, it's only then I will get my chance."
When asked if has been in touch with national team coach Igor Stimac, Amarjit responded in the positive. "Coach keeps a constant tab on what I am doing. He regularly takes updates. In addition, professor [Luka Radman] has been advising me on the workouts, constantly checking on my status."
Amarjit, who started training around last December, considers former India goalkeeper Subrata Pal as his mentor. "Having him around itself brings in positive vibes. He has been constantly motivating me, reminding me of the path ahead, and the hard work that I need to put in."
Asked about the time when he was out of action with an injury, he said, "In such a phase, I needed to stay mentally strong. Otherwise, during those moments when self-doubts creep in, you would struggle.
He added, "I am extremely grateful to the mental support and guidance from the medical staff, both at the national team setup, and at my club. My parents and well-wishers have been with me all throughout. I owe a bit to Paul da as well [Subrata Paul]. He has been special to me."
Amarjit Singh
Keeping dignity of our club is a priority: East Bengal official says they'd never sell their club | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,520 |
Clonezilla Live 20190707-disco - 16GB USB Flash Drive (32-bit)
$14.95 & FREE Shipping on orders over $20
Contents: 1 USB Flash Drive
Media Type: Live
Categories: System Utilities
Desktop Environment: No Desktop
OSDisc.com Rank: #21
Date Added to OSDisc.com: July 12, 2019
Project Website: https://www.clonezilla.org/
Item ID: YP3KN3MDCV
Persistence: No
Drive Model: Kingston DataTraveler SE9 (USB 2.0)
Transfer Speed: 15MB/s read; 5MB/s write
Drive Features: Unique and Sophisticated Metallic Design
Dimensions: 1.54" x 0.48" x 0.18" (39.0mm x 12.4mm x 4.6mm)
Warranty: 5-year Manufacturer Warranty
Clonezilla Live 2.6.2-15 - Live CD (32-bit)
You're probably familiar with the popular proprietary commercial package Norton Ghost, and its OpenSource counterpart, Partition Image. The problem with these software packages is that it takes a lot of time to massively clone systems to many computers. You've probably also heard of Symantec's solution to this problem, Symantec Ghost Corporate Edition with multicasting. Well, now there is an OpenSource clone system (OCS) solution called Clonezilla with unicasting and multicasting!
Clonezilla, based on DRBL, Partition Image, ntfsclone, and udpcast, allows you to do bare metal backup and recovery. Clonezilla live is suitable for single machine backup and restore. Clonezilla saves and restores only used blocks in the harddisk. This increases the clone efficiency.
Clonezilla Live features
Many File systems are supported: (1) ext2, ext3, ext4, reiserfs, reiser4, xfs, jfs, btrfs, f2fs and nilfs2 of GNU/Linux, (2) FAT12, FAT16, FAT32, NTFS of MS Windows, (3) HFS+ of Mac OS, (4) UFS of FreeBSD, NetBSD, and OpenBSD, (5) minix of Minix, and (6) VMFS3 and VMFS5 of VMWare ESX. Therefore you can clone GNU/Linux, MS windows, Intel-based Mac OS, FreeBSD, NetBSD, OpenBSD, Minix, VMWare ESX and Chrome OS/Chromium OS, no matter it's 32-bit (x86) or 64-bit (x86-64) OS. For these file systems, only used blocks in partition are saved and restored. For unsupported file system, sector-to-sector copy is done by dd in Clonezilla.
LVM2 under GNU/Linux is supported (LVM version 1 is not).
Boot loader, including grub (version 1 and version 2) and syslinux, could be reinstalled.
Both MBR and GPT partition formats of hard drive are supported.
Unattended mode is supported. Almost all steps can be done via commands and options. You can also use a lot of boot parameters to customize your own imaging and cloning.
One image restoring to multiple local devices is supported.
Image could be encrypted. This is done with ecryptfs, a POSIX-compliant enterprise cryptographic stacked filesystem.
The image file can be on local disk, ssh server, samba server, NFS server or WebDAV server.
AES-256 encryption could be used to secures data access, storage and transfer.
Based on Partclone (default), Partimage (optional), ntfsclone (optional), or dd to image or clone a partition. However, Clonezilla, containing some other programs, can save and restore not only partitions, but also a whole disk.
By using another free software drbl-winroll, which is also developed by us, the hostname, group, and SID of cloned MS windows machine can be automatically changed.
Clonezilla Alternate
The alternate version is based on Ubuntu Linux instead of Debian. It includes support for hardware that requires non-free firmware, and supports uEFI secure boot (64-bit version only). | {
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} | 5,304 |
WATCH: Trump Mocks Reuters' Jeff Mason for Wearing a Mask in Oval Office Packed With Maskless WH Officials
By Joe DePaoloOct 23rd, 2020, 1:34 pm
Just weeks after a coronavirus outbreak at the White House, President Donald Trump mocked a member of the press corps for adhering to safety guidelines flouted by numerous members of his administration.
During a Friday afternoon Oval Office pool spray announcing a U.S.-brokered normalization deal between Israel and Sudan, Trump chided Reuters' Jeff Mason for taking safety precautions. Mason was trying to direct a question to Israeli Prime Minister Benjamin Netanyahu, who was participating via conference call. Trump relayed the query – citing Mason wearing a mask as the reason Netanyahu could not hear the question.
"This is Jeff Mason," Trump told Netanyahu. "He's got a mask on that's the largest mask I think I've ever seen. So I don't know if you can hear him."
The line drew laughter from Trump officials and others in the room — many of whom were not wearing masks. According to the White House pool report, there were 40-50 people in the Oval Office altogether.
In call with Israel's Netanyahu, @realDonaldTrump says: do you think Sleepy Joe could have made this deal, Bibi? pic.twitter.com/pmCLou4h0Y
— Jeff Mason (@jeffmason1) October 23, 2020
Trump, on multiple occasions, has called out Mason for wearing a mask. The president's mockery comes less than one month after the White House event widely deemed by experts to be a coronavirus superspreader — with the president and numerous others who attended testing positive in subsequent days. It also comes just as the U.S. reported more than 71,000 Covid-19 cases on Thursday, according to data from Johns Hopkins — a number approaching a single day high for the nation.
CoronavirusDonald Trumpjeff masonMasksReuters
Joe DePaolo - Senior Editor
Joe DePaolo is a Senior Editor at Mediaite. Email him here: joed@mediaite.com Follow him on Twitter: @joe_depaolo
More Stories by Joe DePaolo
NH Libertarian Party Celebrates MLK Day By Tweeting, 'America Isn't In Debt to Black People… It's the Other Way Around'
By Michael LucianoJan 17th, 2022, 10:30 pm | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,210 |
Q: How to specify a specific StepDefinitions file for a Cucumber (.feature) file I'm doing some tests with cucumber, currently I have two .feature files, one for login and one for registration) and a StepDefinitions file for each .feature file.
Each StepDefinitions file has a @Before method, so I can do some settings before starting the tests.
The problem is that when I run all the login tests both the @Before specified for the login test and the @Before that I specified in the test for registration.
Cucumber file (test for registration):
Feature: Sign up
As a user
I want to create a new account
So that I can use the application
Background:
Given I am on the sign up page
Scenario Outline: User can create a new account
When I fill name with "<first_name>"
And I fill lastname with "<last_name>"
And I fill email with "<email>"
And I fill password with "<password>"
And I fill password confirmation with "<password_confirmation>"
When I click on Sign up
Then I must be authenticated
Examples:
| first_name | last_name | email | password | password_confirmation |
| Rita | A. Cheatham | RitaACyheatham@armyspy.com | 123456789 | 123456789 |
StepDefinitions for Cucumber file:
public class SignUpStepDefinitions {
private SignUp signUp;
@Before
public void before() {
signUp = new SignUp();
signUp.beforeEach();
}
# Code continuation...
}
A: Option 1
This is a bad practice to have different implementations for the same step. To have things properly arranged you can use conditional hooks. So that you tag your feature in one feature file as say @mytag1 and feature in another feature file with @mytag2.
Now you can distinguish Before hook for both the cases like:
@Before("@mytag1")
public void before1() {
// Some logic
}
@Before("@mytag2")
public void before2() {
// Some different logic
}
P.S. - Avoid using @Before wherever possible because it hides test logic from a person who just analyses the gherkin script
Option 2
Do not use @Before at all but make use power of Background so that you have different set up for both your cases. Use different step sytax where the actual actions are different
Option 3
The last and less desirable option is to to what you are particulary asking. When Cucumber glues everything together (having no explisit setup) it uses package structure to distinguish what is glued to what.
Say you have feature files like this:
Feature: my feature1
Scenario: test
When doing a step
and
Feature: my feature2
Scenario: test
When doing a step
Now. You can have different implementation for When doing a step if you have the class/package structure like this:
rootpkg
somepkg1
TestRunnerClass1
somepkg2
StepDef1
somepkg3
TestRunnerClass2
somepkg4
StepDef2
And also you have the following resource structure:
rootpkg/somepkg1/somepkg2/myfeature1.feature
rootpkg/somepkg3/somepkg4/myfeature2.feature
So once you are running mvn test it picks both test runners and since each in isolated package "branch" it would use different step definition implmentation.
| {
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} | 2,592 |
Your April 9 Arts pages article about a fictional artist whom people at a book party referred to as if he had really existed may seem less amusing when you consider how often people accept as historic truth a preposterous event of fiction.
My recent film, ''The Landing,'' described as fact the tragic conclusion of a fictitious moon mission, Apollo 18. At every screening across the country my co-director and I were confronted by people who said they recalled the dreadful event -- a few even claimed to have met one of the astronauts.
Our pleasure at having duped audiences with the realism of our film faded when we paused long enough to consider what such an impulse to associate oneself with a fictitious event really meant.
In a media society where slavish devotion to ''breaking news'' about freeway chases and celebrity incarcerations is considered the same as knowing what's going on, we should not have been surprised that many people don't have the slightest clue as to what is real and what is not.
Your article and my own experience remind us that history is ultimately not a catalogue of what is true but rather of what we decide is true. | {
"redpajama_set_name": "RedPajamaC4"
} | 5,910 |
130 - The Secrets of Branding on a Budget with Kasia Johnson
podcast | Dec 04, 2017
Kasia Johnson of Merge Forward, helps some of today's biggest brands with their branding and marketing. We've had several conversations about branding, and what it really means for businesses. Yes, it's so much more than a logo, however, it also doesn't need to be the extensive crazy expensive thing that we all think of when we think of companies like Apple. Even if you're a solo shop, there are small things you can do now that make a huge difference in how your business is perceived by the world.
What's your best description of what branding your business even is? It's visual storytelling and visually telling what your company is. It's such an important aspect too because it's the first thing that clients see and how they identify with your company. People don't realize that our brains process something sixty thousand times faster anything that's visual. So a lot of buying decisions are made on what you see first.
Is branding just a logo...
129 - Why You Should Consider an Event To Grow Your Business
Last year I ventured into my first live event, knowing absolutely nothing about doing one. I can't tell you it went off without a hitch, however, it was one of the best decisions I ever made for my business. I had no idea what would be on the other side for myself and my business by doing one.
In this podcast, I share:
Why I did one
The ins and outs of putting one together
Some basics you should know as to how to make this work for your business
For more info on my event visit:http://www.entrepreneursummitdallas.com
128 - Three Tips To Use Social Proof To Grow Your Business with Afton Negrea
Afton Negra is one of the sharpest people I know when it comes to systems and building a business. She has some of today's biggest online personalities as some of her clients, and she's a rockstar at tips and tricks and tools to simplify your business life. She's technically a social media strategist but does so much more beyond just that title. Her mission is to help the smaller companies learn the tips and tricks to get the bigger reach and leverage that they may need to grow.
In this podcast, we're covering three areas where you can improve your social proof of your business.
The first one is content, can we dig deep into understanding how your content aligns with the social proof of your business and how to use it grow? First, social proof is the positive influence when others find out when someone is doing something. This is crucial in social media. A great example of this is a nightclub, and why they make people wait outside....
127 - Writing and Publishing Your First Book with Morgan Gist MacDonald
I can speak from experience when I say writing a book can be a huge game changer in your business. It immediately positions you as an expert and shines a completely different light upon you. It can seem like a daunting task, and that's why I wanted Morgan of Paper Raven Books to talk about how to break down the process and use this to leverage your business.
What's the advice you give that first person trying to figure out what to write? Morgan likes to start by talking about their business. A book should be a strategic part of your business. They discuss who they serve now, and who they want to serve in the future, and focus on topics for those people.
It's also a great tool for pivoting in your business. Morgan was a broad general editor, and she wanted to focus on book editing. So she wrote a book on how to write a book, and now her clients are from the book industry. Make sure you're writing for that person who you want to...
125 - Getting Out of Your Own Way with Coach Jennie
Have you ever found yourself really excited about something, only to eventually talk yourself out of doing it with questions like 'who the hell are you?' 'Why would you think about doing something like this?' Or a statement of 'you're crazy to believe this will work.'
The good news is that you're not crazy. We all have that inner voice talking us out of greatness and doing amazing things. There's just a difference between people who succeed and those who don't. Those who succeed have learned to turn off the voice.
Coach Jennie, has named this inner voice 'Hilda', and she's been using her with her coaching clients for years. She has now published a book that talks about the four types of Hilda-isms that we seem to tell ourselves the most. She came by to talk more in-depth about Hilda!
Everyone has a naysayer in your head ? That will say "Who do you think you are ?", " What if they laugh at you?" Who is Hilda and does everybody have...
122 - Finding A Need in Real Estate and Filling It with Joshua Dorkin
Joshua Dorkin was a teacher who decided to be a real estate investor. After discovering the market was full of people more about making money than actually helping, he decided to do something about it.
Using a little bit of web design experience from college, he launched BiggerPockets.com. Over the years, the site slowly grew until it became a full-time income for Joshua. He shares how he got it rolling, some of the struggles he has faced, and what has made this such a successful site over 10 years later.
How did you start to monetize this business idea going against the grain of the industry? Joshua was working another job, so he was able to keep the business going in the beginning. He then started to put ads up with Google AdSense and started to slowly make money.
Talk about the side hustle part of it, when did you decide to make the leap? Joshua started substitute teaching and on his first job, the teacher he was working for quit....
119 - Continuing To Beat the Odds With Dr. Susan O'Malley
Dr. Susan O'Malley's story is an incredible journey of beating the odds time and time again. After dropping out of college, she worked as a secretary for 11 years. When her life took a drastic change, she decided to go back to school. It was then when she changed her major from being a nutritionist to being a doctor.
After she was rejected from every medical school in the country, perseverance kicked in. It took her that long to figure out what her dream was, and she wasn't going to be shut out of it. She was accepted just a few weeks before school started.
Times had changed, as she found herself pregnant and no husband. However, she decided to follow through and go to school.
How did you do it all being by yourself, with a baby, and in med school? Dr. O'Malley got through it one day at a time, and sometimes it was one hour at a time. Had she looked at graduation the first day of medical school, it would have been too overwhelming....
118 - Tip Tuesday - Self Publishing and Tips to a Successful Book Launch
Master the Start is out and holding strong as an Amazon Best Seller!!! It's been a journey and a process so beyond the steps it took to write and get it out to the world.
I share my struggles with getting it complete, and all of the things I learned about what needed to happen once you have completed the book.
I also get into things I want to do better next time, and things I wish I would have known!
116 - Tip Tuesday - Taking Facebook Groups to a New Level With Gary Leland
Facebook Groups have become a popular way to build your business. How it's typically done is where you have one group, and then you make comments, ask questions, connect people, etc. Gary Leland has taken Facebook Groups to an entirely new level and is using it as a way to build and connect the entire Fast Pitch Softball Community in the US. He gives us some tips and tricks for how he manages it all, and how he is using it also to build his business.
Let's first talk about your group of 20,000, how are you utilizing that? The main one started when groups started; Gary thought he would start a group. It's a basic group, and he advertises his business in there. His rules are that you can't sell anything in there, so he is the only allowed to sell. Now, as he approaches close to 20,000, there are a lot of people to sell to. He tries not to sell to them all the time. He does put stuff in there every week or every other week. The only...
115 - What You Legally Need to Know About Facebook Groups with Tamsen Horton
Facebook groups are the latest and greatest way to build a community for your business. However, as great as they are, you also have to be sure to protect yourself from what legally could happen to you.
Yes, it's not a lot of fun to think about. However, by putting precautions in place now, you could save yourself a lot of headaches down the line.
What are the general things we should know about Facebook Groups? No matter what type of group you have, there should be general term rules. Basically terms of use and terms and conditions. The big thing is that when they come into the group (especially if it's not part of a paid program), you make this a pinned post, especially when you're first starting. Make sure that you make it clear that being in the group isn't a free for all.
What kind of rules are you making? Be specific, so like a promo day, don't just say the day it is. Also say what kind of promo it is. You want to let people know if...
think like an entrepreneur
tlae
Think Like An Entrepreneur Thursday - The Business Process Challenge
[Think Like An Entrepreneur Thursday] How To Build Confidence As An Entrepreneur
think like an entrepreneur vlog
[Think Like An Entrepreneur Thursday] How To Find a Mentor
tlae vlog | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,840 |
Cambs Times > News > Business
Seminar is aimed to help businesses tackle issue of costly fire false alarms
Published: 3:10 PM November 3, 2011 Updated: 9:27 PM October 31, 2020
FIRE crews in Cambridgeshire answered 2,618 false alarms in 12 months at a cost of �334,512 says a report out today.
The figures were revealed by safety group The Fire Industry Association which is to team up with Cambridgeshire fire service to tackle the problem.
The association says it will talk to firms about ways they can reduce these false alarms and in turn reduce the cost to the fire service.
They will be co hosting with Cambs fire a seminar on Reducing False Alarms in Your Business on January 12 at the Holiday Inn Cambridge with the aim of providing practical advice and guidance on what business owners can do to reduce the risk of false alarms.
"False alarms are a serious matter for Cambridgeshire businesses," said an association spokesman.
"If Cambridgeshire FRS can't cut their costs in this problematic area, they may be forced into investigating the potential of a risk based non attendance policy to fire alarm calls as is in operation in other UK fire and rescue services."
Assistant Director for Cambridgeshire Fire and Rescue, Rick Hylton said: "Cambridgeshire FRS welcomes the support of the FIA to help us in driving down the number of false alarms we attend.
"Reducing these calls will not only reduce costs but will also ensure that our fire engines are available to respond to the most serious calls as quickly as possible."
The half-day seminar will look at false alarms, what they are, the main causes of them and focus on what businesses can do to reduce them.
The event costs �10 to attend and is bookable via the FIA's website – www.fia.uk.com. | {
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{"url":"http:\/\/openstudy.com\/updates\/4dd58038d95c8b0b900a5bc4","text":"## anonymous 5 years ago \u221a(169y^6 ) simplify\n\n1. anonymous\n\n$\\sqrt{169y ^{6}}$\n\n2. anonymous\n\nf(x)=3-5\u221c(3t+42)\n\n3. anonymous\n\n13y^3\n\n4. anonymous\n\nf(x)=3-5\u221c(3t+42) what do you have to do with this?\n\n5. anonymous\n\n@ Andras determin the domain of the function","date":"2016-10-27 09:03:35","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.33429136872291565, \"perplexity\": 12563.699823583891}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-44\/segments\/1476988721174.97\/warc\/CC-MAIN-20161020183841-00221-ip-10-171-6-4.ec2.internal.warc.gz\"}"} | null | null |
Stanley Ben Prusiner (born May 28, 1942) is an American neurologist and biochemist. Currently the director of the Institute for Neurodegenerative Diseases at University of California, San Francisco (UCSF). Prusiner discovered prions, a class of infectious self-reproducing pathogens primarily or solely composed of protein. He received the Albert Lasker Award for Basic Medical Research in 1994 and the Nobel Prize in Physiology or Medicine in 1997 for his prion research.
Prusiner was born in Des Moines, Iowa and spent his childhood in Des Moines and Cincinnati, Ohio, where he attended Walnut Hills High School. Prusiner received a Bachelor of Science degree in chemistry from the University of Pennsylvania and later received his M.D. from the University of Pennsylvania School of Medicine. Prusiner then completed an internship in medicine at the University of California, San Francisco. Later Prusiner moved to the National Institutes of Health, where he studied glutaminases in E. coli in the laboratory of Earl Stadtman.
After three years at NIH, Prusiner returned to UCSF to complete a residency in neurology. Upon completion of the residency in 1974, Prusiner joined the faculty of the UCSF neurology department. Since that time, Prusiner has held various faculty and visiting faculty positions at both UCSF and UC Berkeley.
Prusiner won the Nobel Prize in Physiology or Medicine in 1997 for his work proposing an explanation for the cause of bovine spongiform encephalopathy ("mad cow disease") and its human equivalent, Creutzfeldt-Jakob disease. In this work, he coined the term prion, which comes from "proteinaceous infectious particle that lacks nucleic acid" to refer to a previously undescribed form of infection due to protein misfolding.
Prusiner was elected to the National Academy of Science in 1992 and to its governing council in 2007. He is also an elected member of the American Academy of Arts and Sciences (1993), the Royal Society (1996), the American Philosophical Society (1998), the Serbian Academy of Sciences and Arts (2003), and the Institute of Medicine.
^ a b c "Stanley B. Prusiner - Autobiography". NobelPrize.org. http://nobelprize.org/nobel_prizes/medicine/laureates/1997/prusiner-autobio.html. Retrieved 2007-01-02.
^ "What really causes mad cow disease?". Wired. January 31, 2007. http://blog.wired.com/wiredscience/2007/01/what_really_cau.html. Retrieved 2007-01-02.
Prusiner S. B. (1982). "Novel proteinaceous infectious particles cause scrapie". Science 216: 136–144. doi:10.1126/science.6801762. PMID 6801762.
Prusiner S. B. (1991). "Molecular biology of prion diseases". Science 252: 1515–1522. doi:10.1126/science.1675487. PMID 1675487. | {
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{"url":"https:\/\/www.nature.com\/articles\/s41524-018-0089-4","text":"Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.\n\n# Phase-field model of pitting corrosion kinetics in metallic materials\n\n## Abstract\n\nPitting corrosion is one of the most destructive forms of corrosion that can lead to catastrophic failure of structures. This study presents a thermodynamically consistent phase field model for the quantitative prediction of the pitting corrosion kinetics in metallic materials. An order parameter is introduced to represent the local physical state of the metal within a metal-electrolyte system. The free energy of the system is described in terms of its metal ion concentration and the order parameter. Both the ion transport in the electrolyte and the electrochemical reactions at the electrolyte\/metal interface are explicitly taken into consideration. The temporal evolution of ion concentration profile and the order parameter field is driven by the reduction in the total free energy of the system and is obtained by numerically solving the governing equations. A calibration study is performed to couple the kinetic interface parameter with the corrosion current density to obtain a direct relationship between overpotential and the kinetic interface parameter. The phase field model is validated against the experimental results, and several examples are presented for applications of the phase-field model to understand the corrosion behavior of closely located pits, stressed material, ceramic particles-reinforced steel, and their crystallographic orientation dependence.\n\n## Introduction\n\nCorrosion is the gradual destruction of materials (usually metallic materials) via chemical and\/or electrochemical reaction with their environment. It costs about 3.1% of the gross domestic product (GDP) in the United States, which is much more than the cost of all natural disasters combined. Localized corrosion, such as pitting corrosion, is one of the most destructive forms of corrosion; it leads to the catastrophic failure of structures and raises both human safety and financial concerns.1,2,3 Pitting corrosion of stainless steel usually occurs in two different stages: (1) pit initiation from passive film breakage4,5,6 and (2) pit growth.2,3,7,8,9,10,11,12 In this study, we focused on the development of a phase-field modeling capability to study pit growth by considering both anodic and cathodic reactions.\n\nIn the past few decades, great efforts have been made to develop numerical models for pitting corrosion. The moving interface and the electrical double layer at the metal\/electrolyte interface are the two challenging problems faced by most of these numerical models. These numerical models can be divided according to the method in which a moving interface is incorporated in their models. Several steady state9,10,13,14,15,16,17,18 and transient state19,20,21,22,23,24,25,26,27,28 models have been developed over the years that did not allow for changes in the shape and dimensions of the pits\/crevices as corrosion proceeds.\n\nRecent advances in numerical techniques, such as the finite element method, the finite volume method, the arbitrary Lagrangian\u2013Eulerian method, the mesh-free method, and the level set method have encouraged researchers to model the evolving morphology of the pits with a moving interface. Most of these modeling efforts have used a sharp interface to represent the corroding surface, which requires the matching mesh at each time step,11,29 thus increasing the errors associated with the violation of mass conservation laws and increasing the computation cost. The finite volume method models overcome this problem by creating a matching mesh as a function of the concentration of ions, but they are still unable to model complex microstructures.12,30,31 A mesh-free method, the peridynamic model, has been implemented to model pitting corrosion, but it only considered electrochemical reactions without considering the ionic transport in the electrolyte.7\n\nOver the past three decades, the phase field (PF) method has emerged as a powerful simulation tool for modeling of microstructure evolution. PF models study the phase transformation by defining the system\u2019s free energy, and the system\u2019s microstructure evolution is predicted by free energy minimization. The PF approach has been extensively applied to many materials processes, such as solidification, dendrite growth, solute diffusion and segregation, phase transformation, electrochemical deposition, dislocation dynamics, crack propagation, void formation and migration, gas bubble evolution, and electrochemical processes.32\n\nPF models assume a diffusive interface at the phase boundaries rather than a sharp one, which makes the mathematical functions continuous at the interface. A few recent attempts have been made to use the PF method to model pitting corrosion and stress corrosion cracking without the consideration of cathodic reactions, ionic transport and in particular the dependence of overpotential on metal ion concentration in the electrolyte.33,34 In reality, the transport of ionic species in the electrolyte often plays a very important role in diffusion controlled corrosion processes, and the effects of these ionic species must be incorporated to model the process adequately. In this study, a PF method is used to model pitting corrosion by considering both anodic and cathodic reactions, transport of ionic species and the dependence of overpotential on metal ion concentration in the electrolyte.\n\nThis paper is organized as follows. Firstly, we describe the system and the electrochemical reactions considered in this work followed by the construction of PF model. The total free energy of this PF model consists of three parts: bulk free energy, gradient energy and electrostatic energy. We used the KKS model35 to construct the bulk free energy and the interfacial energy. Secondly, we developed the governing equations which comprise of mass diffusion, electromigration, and chemical reaction terms, whereas the interface conditions are incorporated by introducing an order parameter that defines the system\u2019s physical state at each material point. Thirdly, a study is included to couple the kinetic interface parameter and the system\u2019s total overpotential. Fourthly, the PF model is validated against the experimental results and previous numerical models. Lastly, several case studies are presented to demonstrate the strength of this proposed PF model.\n\n## Results and discussion\n\n### The system and electrochemical reactions considered\n\nThe system studied consists of stainless steel 304 (SS304) in dilute salt water (Fig. 1). It is assumed that new passive film will not form in this system. We will consider the effects of passive film formation in a future study. In this model, the following electrochemical reactions and kinetics are considered.\n\nFor the oxidation of main metal alloy elements in SS304,\n\n$$Fe\\,\\rightarrow\\,Fe^{+ 2} + 2e^-$$\n$$Ni\\,\\rightarrow\\,Ni^{ + 2} + 2e^ -$$\n$$Cr\\,\\rightarrow\\,Cr^{ + 3} + 3e^ -$$\n\nIn the following, Me is used to represent the effective metal in SS304 with an average charge number of z1. The material properties of SS304 such as molar concentration in solid phase (csolid\u2009=\u2009143\u2009mol\/L),12 saturation concentration in the electrolyte (csat\u2009=\u20095.1\u2009mol\/L),12 effective diffusion coefficient (D1\u2009=\u20098.5\u2009\u00d7\u200910\u221210\u2009m2\/s),12 and the average charge number (z1\u2009=\u20092.19) based on Fe, Ni, Cr, and their mole fractions within the alloy (taken from Ref. 12). The above reactions can then be simplified to\n\n$$M_e\\,\\rightarrow\\,M_e^{z_1} + z_1e^ -$$\n(1)\n\nThe anodic dissolution of the metal is assumed to follow Butler\u2013Volmer equation,\n\n$$i_a = i_0\\left[ {\\exp \\left( {\\frac{{\\alpha _az_1F\\varphi _{s,o}}}{{R_gT}}} \\right) - \\exp \\left( { - \\frac{{\\alpha _cz_1F\\varphi _{s,o}}}{{R_gT}}} \\right)} \\right]$$\n(2)\n\nwhere F is the Faraday constant, Rg is the gas constant, T is the temperature, \u03c6s,o is the polarization overpotential, io is the exchange current density, \u03b1a is the anodic charge transfer coefficient, \u03b1c is the cathodic charge coefficient (\u03b1c\u2009=\u20091\u2009\u2212\u2009\u03b1a). The values of the above mentioned parameters are reported in Table 1s (supplementary material).\n\nFor the hydrogen discharge reaction in Eq. (3), the corresponding rate is given in Eq. (4)\n\n$$H^ + + e^ - \\to \\frac{1}{2}H_2$$\n(3)\n$$J_5 = J_{50}\\left[ {H^ + } \\right]exp\\left( {\\frac{{\\alpha _5F}}{{R_gT}}\\varphi _{s,o}} \\right)$$\n(4)\n\nFor reduction of water (Eq. (5)), the corresponding rate is given in Eq. (6)\n\n$$H_2O + e^ - \\to H + OH^ -$$\n(5)\n$$J_6 = J_{60}exp\\left( {\\frac{{\\alpha _6F}}{{R_gT}}\\varphi _{s,o}} \\right)$$\n(6)\n\nExperimental values of i0, J50, J60, \u03b1a, \u03b15, and \u03b16 are given in Table 1s.\n\nIn this work, the following two reactions in the electrolyte are considered\n\n$$M_e^{z_1} + H_2O\\rightleftharpoons\\,M_eOH^{z_1 - 1} + H^ +$$\n(7)\n$$H_2O\\rightleftharpoons\\,OH^ - + H^ +$$\n(8)\n\nThe equilibrium constants of reactions in Eqs. (7) and (8) are defined as K1 and K2, respectively.\n\n$$K_1 = \\frac{{k_{1f}}}{{k_{1b}}},\\,K_2 = \\frac{{k_{2f}}}{{k_{2b}}}$$\n\nwhere k1f, k1b, k2f, and k2b are the forward and backward reaction rates. Therefore, a total of six ion species are considered in this model,\n\n$$M_e^{z_1} = c_1;M_eOH^{z_2} = c_2;Cl^{z_3} = c_3;Na^{z_4} = c_4;H^{z_5} = c_5;OH^{z_6} = c_6$$\n\nwhere zi (i\u2009=\u20091, 2, \u2026\u20266) are the charge numbers of the respective species (their values are given in Table 2s), and ci (i\u2009=\u20091, 2, \u2026\u20266) are the normalized concentrations of the respective species. The normalized concentration ci is determined by Ci\u2009=\u2009Ci\/Csolid for i\u2009=\u20091,2,\u2026,6, where Ci represents the molar concentration of ionic species. The constants K1 and K2 can also be expressed as a function of Ci.\n\n$$K_1 = C_2C_5\/C_1,\\,K_2 = C_5C_6$$\n\n### The phase field model for corrosion\n\nThe surface of the metal is normally covered with the passive film; however, a partial breakdown in the film can occur, which may initiate pits like the one illustrated in Fig. 1. The model consists of two phases: the solid phase Me (i.e., the metal part) and the liquid phase (i.e., the electrolyte part). The driving force for metal corrosion and microstructure evolution is from the minimization of the system\u2019s total free energy, which usually consists of bulk free energy Eb, interface energy Ei, and long-range interaction energies such as elastic strain energy Es and electrostatic energy Ee.36,37 The system\u2019s total energy can be expressed as\n\n$$E = E_b + E_i + E_s + E_e$$\n(9)\n\nThe inclusion of elastic and\/or plastic deformation in the model is completely feasible because it has been done in other systems.38,39,40 It can be even necessary to include the strain energy term if a volumetric non-compatible passive film develops during corrosion. Because the formation of a passive film will not be considered in the first stage of this work, for simplicity, the elastic strain energy is not considered here. In a later section, the effect of applied or residual stress on pitting will be studied using the concept of overpotential rather than strain energy. Now we have,\n\n$$E = E_b + E_i + E_e$$\n(10)\n$$E = {\\int} {\\left[ {f_b\\left( {c_1,\\eta } \\right) + \\frac{{\\alpha _u}}{2}\\left( {\\nabla \\eta } \\right)^2 + z_1FC_1\\varphi } \\right]} dV$$\n(11)\n\nwhere fb(c1, \u03b7), derived in the next section, is the local bulk free energy density, which is a function of the normalized concentration of the ionic species c1 and order parameter \u03b7; the second term in Eq. (11) represents the gradient energy density that contributes to the interfacial energy, in which \u03b1u is the gradient energy coefficient, which is related to physical parameters in a later section; and the third term in Eq. (11) represents the electrostatic energy density where C1 is the molar concentration of metal ion and \u03c6 is the electrostatic potential.\n\n### Bulk free energy density\n\nTo determine the bulk free energy density fb(c1, \u03b7), we use the model proposed by Kim et al. for binary alloys.35 We chose KKS model because the model has less limitations on the interface thickness as compared to some other models such as model presented by the model by Wheeler et al.41 The detailed derivations of all functions in the KKS model were skipped here and readers are referred to the original paper.35 In KKS model, the model parameters can be analytically determined by material properties and experimental conditions for the concerned system. In KKS model, at each point, the material is regarded as a mixture of two coexisting phases, and a local equilibrium between the two phases is always assumed:\n\n$$c_1 = h\\left( \\eta \\right)c_s + \\left[ {1 - h\\left( \\eta \\right)} \\right]c_l$$\n(12)\n$$\\partial f_s\\left( {c_s} \\right)\/\\partial c_s = \\partial f_l\\left( {c_l} \\right)\/\\partial c_l$$\n(13)\n\nwhere cs and cl represent the normalized concentrations of the solid and liquid phases, respectively; h(\u03b7) is a monotonously varying function from h(0)\u2009=\u20090 to h(1)\u2009=\u20091. In this study, it is assumed that h(\u03b7)\u2009=\u2009\u03b72(\u22122\u03b7\u2009+\u20093). In Eq. (13), the free energy densities of the solid and liquid phases are expressed as fs(cs) and fl(cl), respectively. Because the concentration is considered to be a mixture of solid and liquid phases at each point, by following the same argument, the bulk free energy density of the solid and liquid phases are expressed in a similar manner,\n\n$$f_b(c_1,\\eta ) = h\\left( \\eta \\right)f_s(c_s) + \\left[ {1 - h\\left( \\eta \\right)} \\right]f_l(c_l) + wg(\\eta )$$\n(14)\n\nThis is a double well potential in the energy space. The height of the double well potential is w, and g(\u03b7)\u2009=\u2009\u03b72(1\u2009\u2212\u2009\u03b7)2. This expression has two minima at \u03b7\u2009=\u20090 and \u03b7\u2009=\u20091, which represent the electrolyte phase and the solid phase, respectively.\n\nFor this system, fs(cs) and fl(cl) can reasonably be considered as parabolic functions.42\n\n$$f_s\\left( {c_s} \\right) = A(c_s - c_{eq,s})^2$$\n(15)\n$$f_l\\left( {c_l} \\right) = A\\left( {c_l - c_{eq,l}} \\right)^2$$\n(16)\n\nwhere ceq,s\u2009=\u20091 and ceq,l\u2009=\u2009Csat\/Csolid are the normalized equilibrium concentrations of the solid and liquid phases, respectively. The temperature-dependent free energy density proportionality constant A is considered to be equal for both the liquid and solid phases. Its value is calculated in such a manner that the driving force for the metal corrosion in the approximated resulting system is quite close to that of the original thermodynamic system.42\n\nThe evolution of phase order parameter \u03b7 and metal ion concentration c1 in time and space are assumed to obey the Ginzburg\u2013Landau (also known as Allen\u2013Cahn)43 and Cahn\u2013Hilliard44 equations, respectively.\n\n$$\\frac{{\\partial \\eta }}{{\\partial t}} = - L\\frac{{\\delta E}}{{\\delta \\eta }} = L\\left[ {\\nabla \\alpha _u\\nabla \\eta + h\\prime \\left( \\eta \\right)\\left\\{ {f_l\\left( {c_l} \\right) - f_s\\left( {c_s} \\right) - \\left( {c_l - c_s} \\right)\\frac{{\\partial f_l\\left( {c_l} \\right)}}{{\\partial c_l}}} \\right\\} - wg\\prime \\left( \\eta \\right)} \\right]$$\n(17)\n$$\\begin{array}{*{20}{l}} {\\frac{{\\partial {\\mathrm{c}}_1}}{{\\partial {\\mathrm{t}}}}} \\hfill & = \\hfill & {\\nabla M\\nabla \\frac{{\\delta E}}{{\\delta c_1}} + R_1} \\hfill \\cr {} \\hfill & = \\hfill & {\\nabla \\left[ {D_1\\left( \\eta \\right)\\nabla c_1} \\right] + \\nabla \\left[ {D_1\\left( \\eta \\right)h\\prime \\left( \\eta \\right)\\left( {c_l - c_s} \\right)\\nabla \\eta } \\right]} \\hfill \\cr {} \\hfill & {} \\hfill & {+ \\nabla \\left[ {\\frac{{z_1Fc_1D_1\\left( \\eta \\right)}}{{R_gT}}\\nabla \\varphi } \\right]y_1\\left( \\eta \\right) + R_1} \\hfill \\end{array}$$\n(18)\n\nwhere L is the kinetic parameter that represents the solid\u2013liquid interface mobility, and M is the mobility of metal ions and expressed as $$M = D_1(\\eta )\/(\\partial ^2f_b\/\\partial c_1^2)$$. In Eq. (18), R1 is the source and\/or sink term for metal ions due to reaction (Eq. (7)), and it takes the form of (\u2212k1fc1\u2009+\u2009k1bc2c5)y1(u). The function y1) defined below is to ensure that reaction (Eq. (7)) occurs only in the electrolyte phase.\n\n$${\\mathrm{y}}_1\\left( \\eta \\right) = \\left\\{ {\\begin{array}{*{20}{l}} {1;} \\hfill & {\\eta \\le 0} \\hfill \\cr {} \\hfill & {0 < \\eta < 0.1} \\hfill \\cr {0;} \\hfill & {\\eta \\ge 0.1} \\hfill \\end{array}} \\right.\\left( {{\\mathrm{linearly}}\\,{\\mathrm{change}}\\,{\\mathrm{from}}1\\,{\\mathrm{to}}\\,0} \\right)$$\n(19)\n\n### Conservation of charge\n\nIn this study, we follow Dassault\u2019s work rather than following Guyer\u2019s model45,46 which simplifies the model by removing the need to discretize the double layer at the metal\u2013electrolyte interface. It allows our PF model to simulate the corrosion process from meso- to macro-length scales, as compared to Guyer\u2019s model, which was limited to nanoscale. It is also possible to incorporate the effect of the laminar\/turbulent flow of the electrolyte on the metal\u2013electrolyte interface in case of moving electrolyte.47 Here, the conservation of charge can be expressed as\n\n$$\\frac{{\\partial \\rho _e}}{{\\partial t}} = \\nabla \\left\\{ {\\sigma _e\\left[ {1 - y_1\\left( \\eta \\right)} \\right]\\nabla \\varphi } \\right\\} + y_1\\left( \\eta \\right)FC_{solid}{\\sum} {z_i} \\frac{{\\partial c_i}}{{\\partial t}}$$\n(20)\n\nwhere \u03c1e is the charge density and \u03c3e is the electrical conductivity of the metal in the solid phase. The function [1\u2009\u2212\u2009y1(\u03b7)] interpolates the electrical conductivity, \u03c3e in the solid phase to zero in the electrolyte phase, where y1(\u03b7) is defined in Eq. (19). The time needed for charge accumulation across the interface due to the diffusion of ionic species is much longer than that required to achieve steady-state charge accumulation across the interface, so the conservation of charge in the above system can be considered at a steady state. The relation given in Eq. (20) is reduced to\n\n$$0 = \\nabla \\left\\{ {\\sigma _e\\left[ {1 - y_1\\left( \\eta \\right)} \\right]\\nabla \\varphi } \\right\\} + y_1(\\eta )FC_{solid}{\\sum} {z_i} \\frac{{\\partial c_i}}{{\\partial t}}$$\n(21)\n\nThe height of the double well potential w and the gradient energy coefficient \u03b1u can be related to the interface energy \u03f1 and the interface thickness l33\n\n$${\\it{\\varrho }} = 4\\sqrt {w\\alpha _u}$$\n(22)\n$$l = \\sqrt 2 \\alpha \\prime \\sqrt {\\frac{{\\alpha _u}}{w}}$$\n(23)\n\nwhere \u03b1\u2032 is a constant value determined by the order parameter u. If the interface region is defined as 0.05\u2009<\u2009\u03b7\u2009<\u20090.95; the value of \u03b1\u2032 is 2.94.35\n\n### Transport equations for other ionic species in the electrolyte\n\nThe governing equations of the other five ionic species are the Nernst\u2013Planck equations with chemical reaction terms. They are expressed as\n\n$$\\frac{{\\partial {\\mathrm{c}}_2\\left( {{\\boldsymbol{x}},t} \\right)}}{{\\partial {\\mathrm{t}}}} = \\nabla \\left[ {D_2\\left( \\eta \\right)\\nabla c_2} \\right] + \\nabla \\left[ {\\frac{{z_2Fc_2D_2\\left( \\eta \\right)}}{{R_gT}}\\nabla \\varphi } \\right]y_1\\left( \\eta \\right) + R_2$$\n(24)\n$$\\frac{{\\partial {\\mathrm{c}}_3\\left( {{\\boldsymbol{x}},t} \\right)}}{{\\partial {\\mathrm{t}}}} = \\nabla \\left[ {D_3\\left( \\eta \\right)\\nabla c_3} \\right] + \\nabla \\left[ {\\frac{{z_3Fc_3D_3\\left( \\eta \\right)}}{{R_gT}}\\nabla \\varphi } \\right]y_1\\left( \\eta \\right)$$\n(25)\n$$\\frac{{\\partial {\\mathrm{c}}_4\\left( {{\\boldsymbol{x}},t} \\right)}}{{\\partial {\\mathrm{t}}}} = \\nabla \\left[ {D_4\\left( \\eta \\right)\\nabla c_4} \\right] + \\nabla \\left[ {\\frac{{z_4Fc_4D_4\\left( \\eta \\right)}}{{R_gT}}\\nabla \\varphi } \\right]y_1\\left( \\eta \\right)$$\n(26)\n$$\\frac{{\\partial {\\mathrm{c}}_5\\left( {{\\boldsymbol{x}},t} \\right)}}{{\\partial {\\mathrm{t}}}} = \\nabla \\left[ {D_5\\left( \\eta \\right)\\nabla c_5} \\right] + \\nabla \\left[ {\\frac{{z_5Fc_5D_5\\left( \\eta \\right)}}{{R_gT}}\\nabla \\varphi } \\right]y_1\\left( \\eta \\right) + R_5$$\n(27)\n$$\\frac{{\\partial {\\mathrm{c}}_6\\left( {{\\boldsymbol{x}},t} \\right)}}{{\\partial {\\mathrm{t}}}} = \\nabla \\left[ {D_6\\left( \\eta \\right)\\nabla c_6} \\right] + \\nabla \\left[ {\\frac{{z_6Fc_6D_6\\left( \\eta \\right)}}{{R_gT}}\\nabla \\varphi } \\right]y_1\\left( \\eta \\right) + R_6$$\n(28)\n\nwhere R2 is the source\/sink term originated from the electrochemical reaction in Eq. (7) which takes the form as [k1fc1\u2009\u2212\u2009k1bc2c5]y1(\u03b7). The rates of forward and backward reaction are expressed by k1f and k1b respectively. It is assumed that no electrochemical reaction occurs inside the metal part. This is ensured by y1(\u03b7) defined in Eq. (19). R5 and R6 are the source\/sink terms originated from electrochemical reactions in Eqs. (7) and (8) and take the form as $$\\left[ {k_{1f}c_1 - k_{1b}c_2c_5 + k_{2f} - k_{2b}c_5c_6} \\right]y_1\\left( \\eta \\right) - \\left( {\\frac{{J_5}}{{z_5FC_{solid}}}} \\right)y_2\\left( \\eta \\right)$$ and $$\\left[ {k_{2f} - k_{2b}c_5c_6} \\right]y_1\\left( \\eta \\right) - \\left( {\\frac{{J_6}}{{z_6FC_{solid}}}} \\right)y_2\\left( \\eta \\right)$$ respectively. The rates of forward and backward reactions for the hydrolysis of water are represented by k2f and k2b, respectively. It should be noted that R5 and R6 have an additional term near the metal\u2013electrolyte interface due to the cathodic reactions considered in Eqs. (3) and (5) where J5 and J6 are defined in Eqs. (4) and (6) respectively. These reaction terms are multiplied by a step function y2(\u03b7) to ensure that these reactions only happen in a small region near the metal surface.\n\n$${\\mathrm{y}}_2\\left( \\eta \\right) = \\left\\{ {\\begin{array}{*{20}{l}} {1;} \\hfill & {0.01 \\le \\eta < 0.05} \\hfill \\cr {0;} \\hfill & {\\eta \\ge 0.05} \\hfill \\cr {0;} \\hfill & {\\eta < 0.01} \\hfill \\end{array}} \\right.$$\n(29)\n\nIt should also be noted that, in Eqs. (25) and (26) there are no source\/sink terms because it was assumed that c3 (Cl) and c4 (Na+) does not take part in any reactions. This is not true if a salt film can be formed. The effect of salt film formation will be studied in a future study.\n\nThe electrostatic potential, \u03c6, is governed by Eq. (21) coupled with the governing Eqs. (18) and (2428). The diffusivity Di is a function of the order parameter \u03b7. As it is known, the diffusivity of ionic species differs in the metal and electrolyte phase. The diffusivities of all the ions were defined using a step function of the order parameter \u03b7. For metal ion c1, a step function as expressed in Eq. (30) is used in which the diffusivity value in metal is assumed to be \u03b3 times less than that in electrolyte. A step function as expressed in Eq. (31) is used for all other ionic species (c2, c3, c4, c5, and c6).\n\n$${\\mathrm{D}}_1\\left( \\eta \\right) = \\left\\{ {\\begin{array}{*{20}{l}} {D_1;} \\hfill & {\\eta < 0.90} \\hfill \\cr {} \\hfill & {0.90 \\le \\eta \\le 0.95} \\hfill \\cr {D_1\/\\gamma ;} \\hfill & {\\eta > 0.95} \\hfill \\end{array}} \\right.\\,\\left( {{\\mathrm{linearly}}\\,{\\mathrm{change}}\\,{\\mathrm{from}}\\,D_1{\\mathrm{to}}\\,D_1\/\\gamma } \\right)$$\n(30)\n$${\\mathrm{D}}_{\\mathrm{i}}\\left( {\\mathrm{\\eta}} \\right) = \\left\\{ {\\begin{array}{*{20}{l}} {{\\mathrm{D}}_{\\mathrm{i}};} \\hfill & {\\eta < 0.90} \\hfill \\cr {} \\hfill & {0.90 \\le \\eta \\le 0.95} \\hfill \\cr {0;} \\hfill & {\\eta > 0.95} \\hfill \\end{array}} \\right.\\,\\left( {{\\mathrm{linearly}}\\,{\\mathrm{change}}\\,{\\mathrm{from}}\\,D_i\\,{\\mathrm{to}}\\,0} \\right)$$\n(31)\n\nfor i\u2009=\u20092,3,\u2026.,6.\n\n### Overpotential\n\nThe overpotential is expressed as\n\n$$\\varphi _{s,o} = \\varphi _m - \\varphi _{m,se} - \\varphi _c - \\varphi _l$$\n(32)\n\nwhere \u03c6m is the potential in the metal phase also known as applied potential; \u03c6m,se is the standard electrode potential in the metal; and \u03c6c is the concentration overpotential expressed in (33).\n\n$$\\varphi _c = \\frac{{R_gT}}{{Fz_1}}\\ln\\frac{{c_{1b}}}{{c_{eq,l}}}$$\n(33)\n\nThe concentration of $$M_e^{z_1}$$ near the interface is,\n\n$$c_{1b} = \\left\\{ {\\begin{array}{*{20}{l}} {c_1;} \\hfill & {\\left( {\\eta = 0.05} \\right)} \\hfill \\cr {0;} \\hfill & {\\left( {\\eta < 0.05} \\right)} \\hfill \\cr {0;} \\hfill & {\\left( {\\eta > 0.05} \\right)} \\hfill \\end{array}} \\right.$$\n(34)\n\nThe electrostatic potential near the interface is,\n\n$$\\varphi _l = \\left\\{ {\\begin{array}{*{20}{l}} {\\varphi ;} \\hfill & {\\left( {\\eta = 0.05} \\right)} \\hfill \\cr {0;} \\hfill & {\\left( {\\eta < 0.05} \\right)} \\hfill \\cr {0;} \\hfill & {\\left( {\\eta > 0.05} \\right)} \\hfill \\end{array}} \\right.$$\n(35)\n\n### Kinetic interface parameter and overpotential relation\n\nIn this model, the metal corrosion is described by the order parameter \u03b7. The corrosion rate is controlled by the kinetic interface parameter L. The shift in the corrosion mode from activation-controlled to diffusion-controlled can be modeled by continuous variation of the kinetic interface parameter L. The relationship between the kinetic interface parameter L and the corrosion rate is linear in the activation-controlled mode.33 From the Butler\u2013Volmer equation, as expressed in (2), the kinetic interface parameter has an effect on overpotential similar to that of the current density, as expressed below in (36). A similar technique is also implemented in a peridynamic model, in which the interface diffusivity is directly related to the current density for Tafel relation.7\n\n$$L = L_o\\left[ {\\exp \\left( {\\frac{{\\alpha _az_1F\\varphi _{s,o}}}{{R_gT}}} \\right) - \\exp \\left( { - \\frac{{\\alpha _cz_1F\\varphi _{s,o}}}{{R_gT}}} \\right)} \\right]$$\n(36)\n\nFollowing the method developed in Refs 7 and33 and using the experimental values for SS304 (reported in Table 1s), i0\u2009=\u20091.0\u2009\u00d7\u200910\u22126A\/cm2 and \u03b1a\u2009=\u20090.26, we calculated L0\u2009=\u20091.94\u2009\u00d7\u200910\u221213\u2009m3\/(Js).\n\n## 1D PF model\n\nWe implemented the PF model to simulate the corrosion evolution in 1D. The simulations are executed at T\u2009=\u2009293.15\u2009K (20\u2009\u00b0C) with metal potential of 844\u2009mV SHE (standard hydrogen electrode) (i.e., 600\u2009mV SCE [saturated calomel electrode]) in a 1\u2009M NaCl solution. The temperature dependence of the diffusion coefficient is governed by the Einstein relation.12 The PF simulation results for the corrosion length are then compared with the 1D pencil electrode of experimental findings.3 The simulations are performed for 400\u2009s, and the results of the corroded length are plotted against the square root of time $$\\left( {\\sqrt t } \\right)$$. The simulation results agree well with the experimental results, as illustrated in Fig. 2. The 1D PF model and the 1D pencil electrode experimental results show similar slopes.\n\nA qualitative study on the concentration distribution of ionic species inside the electrolyte is performed as done in many classical numerical models for crevice and pitting corrosion.9,10,48 It is difficult to quantitatively measure the molar concentration distribution of ionic species in the electrolyte experimentally. Because such experimental data is lacking, we have discussed these concentration variations theoretically. Figure 1s (supplementary material) shows the concentration in mol\/L on a logarithmic scale. The higher value of metal ions near the interface results in a slight increase in the [H+] ion concentration (i.e., a decrease in the pH value) due to strong coupling between C1, C2, and C5. The value of [H+] increases as the overpotential increases because it results in a higher production rate of metal ions and hydrolysis of metal ions. Although, this study was performed on a lower overpotential, but a small increase in C5 can still be seen in Fig. 1s (supplementary material). This increase in positive charge is neutralized by the migration of chloride ions towards the interface, as shown in Fig. 1s (supplementary material).\n\nTo investigate the effects of metal potential, several simulations were performed to show the behavior of corrosion under different metal potentials. Figure 2s (supplementary material) shows that the corrosion rate obtained for these metal potentials are of the same order of the magnitude as the experimental results.49 The experimental results plotted in Fig. 2s (supplementary material) give the maximum corrosion rates that can be achieved at the corresponding metal potential. A calibration study was also performed to achieve a corrosion rate for PF 1D model simulation close to experimental ones by varying exchange current density (i0). It was found that if the value of i0 is chosen equal to twice the reported value (i0\u2009=\u20091\u2009\u00d7\u200910\u22126 A\/cm2) in Table 1s (supplementary material), then the corrosion rate agree well with the experimental values.49 For the sake of consistency, all the presented modeling results are simulated by using the same of value of i0 as reported in Table 1s (supplementary material). The overpotential for the corresponding corrosion rates are shown in Fig. 3s (supplementary material).\n\n### PF simulations for 2D model\n\nThe 2D simulations are performed with a metal potential of 600\u2009mV SCE (844\u2009mV SHE). The boundary conditions and initial values are the same as described in Fig. 7s (supplementary material). To compare the 2D PF model results with the experimental ones, a 300\u2009\u03bcm by 240\u2009\u03bcm rectangular geometry is considered in which the metal and electrolyte parts are equally divided, as shown in Fig. 4s (supplementary material). A 60\u2009\u03bcm wide and 20\u2009\u03bcm deep semi-elliptical pit is assumed. The remaining surface, as shown in Fig. 4s, is considered to have a passive oxide film. Figure 4s (supplementary material) shows the concentration distribution inside the electrolyte at various time intervals. In Fig. 3, the 2D PF model results are compared with the 2D foil experiment results reported in the literature.3 The evolution of pitting depth over the time shows a trend similar to that found in the experimental results3 but with deeper pitting depths than the experimantal data. As mentioned earlier, the regrowth of passive film may be an important factor. We will include the formation of passive film in a future study. The contours of the electrostatic potential distribution for the simulations with the above conditions are shown in Fig. 5s (supplementary material).\n\n### Case studies\n\n#### Case study 1: Interaction of closely located pits\n\nIn reality, multiple pits can nucleate due to changes in chemistry on the metal surface, whereas most numerical models consider only the nucleation or growth of a single pit. A few efforts have been made to understand both experimentally and numerically the interaction of multiple pits.50,51 Because we have not considered pit initiation in our PF model, we apply our PF model to two narrow initial openings of 5\u2009\u03bcm each at distances of (a) 12\u2009\u03bcm and (b) 5\u2009\u03bcm at an applied metal potential of 200\u2009mV SHE. The boundary conditions and initial values are the same as those given in Fig. 7s (supplementary material). Figure 4 shows the changes in the morphology of pits with and without interaction in (b) and (a), respectively. It can be seen that without their interaction, these pits corrode at a rate similar to that at which they grow individually. After the pits interact, the chemical compositions of the ionic species change in the vicinities of the pits in the electrolyte. The interaction between the two pits can have either a positive or negative effect on pit growth.52 In this study the interaction of the two closely located pits had a positive effect which can be seen in Fig. 4 (b) at t\u2009=\u20096\u2009s. The corroded material in both cases was estimated which suggested that the corrosion rate was increased in case (b). Two pits finally coalesce to form a wider pit, similar to the pits formed in real-life metallic structures (i.e., multiple pits nucleate on the corroding surface and interact with each other), which are wider.\n\n#### Case study 2: Pitting corrosion in a stressed material\n\nLike other alloys, stainless steel can have stressed zones (tensile and compressive). It is believed that overpotential is not uniform in the case of stressed zones, which results in different corrosion rates in different material locations and directions. The experimental findings53 show that most pits grow in locations near the scratched lines on the surface that result from mechanical polishing. These scratched lines could result in strain hardening, as revealed by electrochemical analysis.53 The experimental findings also illustrate that overpotential is not uniform in the presence of residual stresses. Gutman explained the same phenomenon with his theoretical model in which the compressive stress zone has less overpotential than the unstressed zone and the tensile stress zone.54 The overpotential is directly related to the corrosion current density. The relationship between the overpotential of the compressive stress zone (\u03c6comp,s), the unstressed zone (\u03c6s,o), and the tensile stress zone (\u03c6tens,s) is \u03c6comp,s < \u03c6s,o < \u03c6tens,s. It should be noted that corrosion rate in plastically deformed zones is greater than that of elastically deformed zones, due to the presence of high density dislocations in plastically deformed zones. In this study, we applied the overpotential dependence on applied\/residual stress proposed by Gutman.54 According to Gutman\u2019s model,54 residual stress of 600MPa corresponds to a change in overpotential of about 20mV in our system. Here, we model a material with both tensile and compressive stress zones, which have an overpotential difference of \u03c6comp,s\u2009=\u2009\u03c6s,o\u2009\u2212\u200920\u2009mV and \u03c6tens,s\u2009=\u2009\u03c6s,o\u2009+\u200920\u2009mV, whereas \u03c6s,o is calculated from (32). A small opening of 6 \u03bcm is considered at the material\u2019s surface. The boundary conditions and initial values are the same as those given in Fig. 7s (supplementary material). Figure 5 shows that areas under tensile stress corrode at a faster rate than areas in the compressive stress zone. The pit morphology is closer to that of pits formed during a natural corrosion process because, in most natural scenarios, the corrosion process begins when the passive film is damaged by strain hardening of the surface. In fact, in most of these cases, multiple pits coalesce and grow faster along width than depth. This process is already illustrated in the previous case in which two closely located pits interact.\n\n#### Case Study 3: Crystallographic plane-dependent pitting corrosion\n\nSeveral studies suggested that crystallographic orientations greatly affect the propagation rates and morphology of the corroding pits.55,56,57 This dependence is usually attributed to factors such as close packing of crystal planes, reaction rate variation along different plane orientations and density of crystalline defects on micro scale. Here, we demonstrate that this PF model can be a good tool to study this phenomenon in detail. The crystal orientations affect the rate of corrosion because planes with lower atomic densities usually corrode at faster rates than planes with higher atomic densities.57 It has been reported that the corrosion rate tends to increase in the order of {111}\u2009<\u2009{110}\u2009\u2264\u2009{100}. The corrosion rate in the crystallographic plane {111} is one third of {100}.57 The scenario in which planes {110} and {100} corrode at the same rate is considered because no exact value is available for their ratio. We implemented our PF model to study the effects of the crystallographic plane orientation on pit growth. The domain geometry considered is 30\u2009\u03bcm\u2009\u00d7\u200927\u2009\u03bcm, as shown in Fig. 6. The PF simulations are performed at a lower metal potential of \u2212400\u2009mV SHE because it is believed that the crystallographic orientation dependence is limited to lower overpotentials when the corrosion process is activation controlled.33,58 A small opening of 6\u2009\u03bcm is considered at the surface of the material. The initial values and boundary conditions are the same as described in Fig. 7s (supplementary material). Crystallographic planes {111}, {110}, and {100} are represented by blue, brown, and magenta, respectively, in Fig. 6, which shows that the pit shape is no longer uniform because {111} corrodes at one third the rate of the other two planes. This pit morphology illustrates the strength of our PF model under complex microstructures, with which most sharp interface models fail to cope.\n\n#### Case Study 4: Pitting corrosion in ceramic particle\u2013reinforced steel\n\nCeramic particles such as TiB2 and\/or TiC are often embedded into steel to improve its stiffness, strength,59 and wear resistance.60 Although the addition of these ceramic particles improves some of the material\u2019s mechanical properties, it has very little effect on corrosion resistance.61 In fact, these reinforcements may enhance stress corrosion cracking (SCC) because they can change the stress distribution near the pits. In case of SCC, a higher stress concentration can be resulted at the tip of a growing pit when the pit reaches a ceramic particle. Metal corrodes faster at the high tensile stress region in the vicinity of a ceramic particle. As we are not studying SCC in this study, the effect of stress concentration will not be considered here. Because the ceramic particles are far less reactive than steel, we assume that they are non-corrodible in salt solution. To ensure that the ceramic particles do not corrode in the salt solution, we considered L to be equal to zero for the ceramic particles. A small opening of 6 \u03bcm is assumed at the surface of the material. The boundary conditions and initial values are the same as those described in Fig. 7s (supplementary material). Figure 7 shows that the pit morphology changes with the presence of ceramic materials. This example elaborates the ability of this PF model to handle complex structures.\n\nIn this study, we have developed a PF model for metal corrosion with ion transport in the electrolyte and this model is used to study pitting corrosion of SS304 in salt water. It is shown that once the kinetic interface parameter is calibrated with the material\u2019s exchange current density, the model has the potential to predict corrosion behavior over the whole range of reaction and diffusion-controlled processes. The simulation results showed that the PF model predictions agree well with the experimental results and that the model has the ability to handle complex microstructures, such as the interaction of closely located pits, the effects of stress on pitting, the effects of ceramic particles, and crystallographic plane orientation on corrosion.\n\n## Method\n\nFinite element method, Galerkin method,62 is used for space discretization while Backwards differentiation formula (BDF) method63 is used for the time integration of the governing partial differential Eqs (17, 18, 21, 2428). Triangular Lagrangian mesh elements were chosen to discretize the space. It was ensured that we have at least 12 mesh elements inside the diffuse interface to accurately approximate \u03b7 (order parameter) and the piecewise functions based on \u03b7.\n\n### Data availability\n\nThe data and codes supporting the findings of this study are available from the corresponding author on reasonable request.\n\n## References\n\n1. 1.\n\nSharland, S. M. A review of the theoretical modelling of crevice and pitting corrosion. Corros. Sci. 27, 289\u2013323 (1987).\n\n2. 2.\n\nErnst, P. & Newman, R. C. Pit growth studies in stainless steel foils. I. Introduction and pit growth kinetics. Corros. Sci. 44, 927\u2013941 (2002).\n\n3. 3.\n\nErnst, P. & Newman, R. C. Pit growth studies in stainless steel foils. II. Eff. Temp. Chloride Conc. Sulphate Addit. Corros. Sci. 44, 943\u2013954 (2002).\n\n4. 4.\n\nWilliams, D. E., Westcott, C. & Fleischmann, M. Studies of the initiation of pitting corrosion on stainless steels. J. Electroanal. Chem. 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Numerical method for time-dependent localized corrosion analysis with moving boundaries by combining the finite volume method and voxel method. Corros. Sci. 63, 210\u2013224 (2012).\n\n32. 32.\n\nLi, Y., Hu, S., Sun, X. & Stan, M. A review: applications of the phase field method in predicting microstructure and property evolution of irradiated nuclear materials. npj Comput. Mater. 3, 16 (2017).\n\n33. 33.\n\nMai, W., Soghrati, S. & Buchheit, R. G. A phase field model for simulating the pitting corrosion. Corros. Sci. 110, 157\u2013166 (2016).\n\n34. 34.\n\nMai, W. & Soghrati, S. A phase field model for simulating the stress corrosion cracking initiated from pits. Corros. Sci. 125, 87\u201398 (2017).\n\n35. 35.\n\nKim, S. G., Kim, W. T. & Suzuki, T. Phase-field model for binary alloys. Phys. Rev. E 60, 7186\u20137197 (1999).\n\n36. 36.\n\nChen, L. Q. Phase-field models for microstructure evolution. Annu. Rev. Mater. Res. 32, 113\u2013140 (2002).\n\n37. 37.\n\nMoelans, N., Blanpain, B. & Wollants, P. An introduction to phase-field modeling of microstructure evolution. Calphad 32, 268\u2013294 (2008).\n\n38. 38.\n\nGuo, X. H., Shi, S.-Q. & Ma, X. Q. Elastoplastic phase field model for microstructure evolution. Appl. Phys. Lett. 87, 221910 (2005).\n\n39. 39.\n\nGuo, X. H., Shi, S. Q., Zhang, Q. M. & Ma, X. Q. An elastoplastic phase-field model for the evolution of hydride precipitation in zirconium. Part I: smooth specimen. J. Nucl. Mater. 378, 110\u2013119 (2008).\n\n40. 40.\n\nGuo, X. H., Shi, S. Q., Zhang, Q. M. & Ma, X. Q. An elastoplastic phase-field model for the evolution of hydride precipitation in zirconium. Part II: specimen with flaws. J. Nucl. Mater. 378, 120\u2013125 (2008).\n\n41. 41.\n\nWheeler, A. A., Boettinger, W. J. & McFadden, G. B. Phase-field model for isothermal phase transitions in binary alloys. Phys. Rev. A 45, 7424\u20137439 (1992).\n\n42. 42.\n\nHu, S. Y., Murray, J., Weiland, H., Liu, Z. K. & Chen, L. Q. Thermodynamic description and growth kinetics of stoichiometric precipitates in the phase-field approach. Calphad 31, 303\u2013312 (2007).\n\n43. 43.\n\nGinzburg, V. L. On the theory of superconductivity. Il Nuovo Cim. (1955\u20131965) 2, 1234\u20131250 (1955).\n\n44. 44.\n\nCahn, J. W. & Hilliard, J. E. Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28, 258\u2013267 (1958).\n\n45. 45.\n\nPongsaksawad, W., Powell, A. C. & Dussault, D. Phase-field modeling of transport-limited electrolysis in solid and liquid states. J. Electrochem. Soc. 154, F122\u2013F133 (2007).\n\n46. 46.\n\nGuyer, J. E., Boettinger, W. J., Warren, J. A. & McFadden, G. B. Phase field modeling of electrochemistry. II. Kinet. Phys. Rev. E 69, 021604 (2004).\n\n47. 47.\n\nLeblanc, P., Cabaleiro, J., Paillat, T. & Touchard, G. Impact of the laminar flow on the electrical double layer development. J. Electrost. 88, 76\u201380 (2017).\n\n48. 48.\n\nTurnbull, A. & Ferriss, D. Mathematical modelling of the electrochemistry in corrosion fatigue cracks in structural steel cathodically protected in sea water. Corros. Sci. 26, 601\u2013628 (1986).\n\n49. 49.\n\nRevie, R. W. & Uhlig, H. H. Uhlig's Corrosion Handbook, 3rd edn (Wiley, Hoboken, New Jersey, 2011).\n\n50. 50.\n\nBudiansky, N. D., Organ, L., Hudson, J. L. & Scully, J. R. Detection of interactions among localized pitting sites on stainless steel using spatial statistics. J. Electrochem. Soc. 152, B152\u2013B160 (2005).\n\n51. 51.\n\nLaycock, N., White, S. & Krouse, D. Numerical simulation of pittingcorrosion: interactions between pits in potentiostatic conditions. ECS Trans. 1, 37\u201345 (2006).\n\n52. 52.\n\nLaycock, N. J., Krouse, D. P., Hendy, S. C. & Williams, D. E. Computer simulation of pitting corrosion of stainless steels. Electrochem. Soc. Interface 23, 65\u201371 (2014).\n\n53. 53.\n\nMartin, F. A., Bataillon, C. & Cousty, J. In situ AFM detection of pit onset location on a 304L stainless steel. Corros. Sci. 50, 84\u201392 (2008).\n\n54. 54.\n\nGutman, E. M. Mechanochemistry of Solid Surfaces. (World Scientific Publishing Company, Singapore, 1994).\n\n55. 55.\n\nShahryari, A., Szpunar, J. A. & Omanovic, S. The influence of crystallographic orientation distribution on 316LVM stainless steel pitting behavior. Corros. Sci. 51, 677\u2013682 (2009).\n\n56. 56.\n\nKumar, B. R., Singh, R., Mahato, B., De, P. K., Bandyopadhyay, N. R. & Bhattacharya, D. K. Effect of texture on corrosion behavior of AISI 304L stainless steel. Mater. Charact. 54, 141\u2013147 (2005).\n\n57. 57.\n\nLindell, D. & Pettersson, R. Crystallographic effects in corrosion of austenitic stainless steel 316L. Mater. Corros. 66, 727\u2013732 (2015).\n\n58. 58.\n\nFrankel, G. S. Pitting corrosion of metals: a review of the critical factors. J. Electrochem. Soc. 145, 2186\u20132198 (1998).\n\n59. 59.\n\nAkhtar, F. Ceramic reinforced high modulus steel composites: processing, microstructure and properties. Can. Metall. Q. 53, 253\u2013263 (2014).\n\n60. 60.\n\nAkhtar, F. Microstructure evolution and wear properties of in situ synthesized TiB2 and TiC reinforced steel matrix composites. J. Alloy. Compd. 459, 491\u2013497 (2008).\n\n61. 61.\n\nPagounis, E. & Lindroos, V. K. Processing and properties of particulate reinforced steel matrix composites. Mater. Sci. Eng. A 246, 221\u2013234 (1998).\n\n62. 62.\n\nFairweather, G. Finite Element Galerkin Methods for Differential Equations, Lecture Notes in Pure and Applied Mathematics, vol. 34, Marcel Dekker, New York, (1978).\n\n63. 63.\n\nAscher, U. M. & Petzold, L. R. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. Vol. 61 (Society For Industrial Applied Mathematics, U.S., Philadelphia, 1998).\n\n## Acknowledgements\n\nThis work was supported by Research Grants Council of Hong Kong (PolyU 152140\/14E).\n\n## Author information\n\nAuthors\n\n### Contributions\n\nS.Q.S. conceived the idea, designed and supervised the project. T.Q.A. developed the model, performed simulations and wrote the manuscript. Z.X. and S.Q.S. also contributed in developing the model. S.Q.S., S.Y.H., Y.L. and J.L. provided critical comments and contributed to revisions of the manuscript.\n\n### Corresponding author\n\nCorrespondence to San-Qiang Shi.\n\n## Ethics declarations\n\n### Competing interests\n\nThe authors declare no competing interests.\n\nPublisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.\n\nChange history: In the original published HTML version of this Article, some of the characters in the equations were not appearing correctly. This has now been corrected in the HTML version.\n\n## Rights and permissions\n\nReprints and Permissions\n\nAnsari, T.Q., Xiao, Z., Hu, S. et al. Phase-field model of pitting corrosion kinetics in metallic materials. npj Comput Mater 4, 38 (2018). https:\/\/doi.org\/10.1038\/s41524-018-0089-4\n\n\u2022 Revised:\n\n\u2022 Accepted:\n\n\u2022 Published:\n\n\u2022 ### Quantitative assessment of environmental phenomena on maximum pit size predictions in marine environments\n\n\u2022 R.M. Katona\n\u2022 , A.W. Knight\n\u2022 , E.J. Schindelholz\n\u2022 , C.R. Bryan\n\u2022 , R.F. Schaller\n\u2022 \u00a0&\u00a0R.G. Kelly\n\nElectrochimica Acta (2021)\n\n\u2022 ### Selective laser melting of Ti-TiN composites: Formation mechanism and corrosion behaviour in H2SO4\/HCl mixed solution\n\n\u2022 Yu Zhao\n\u2022 , Changyi Wu\n\u2022 , Shengfeng Zhou\n\u2022 , Junjie Yang\n\u2022 , Wei Li\n\u2022 \u00a0&\u00a0Lai-Chang Zhang\n\nJournal of Alloys and Compounds (2021)\n\n\u2022 ### Numerical Phase-Field Model Validation for Dissolution of Minerals\n\n\u2022 Sha Yang\n\u2022 , Neven Ukrainczyk\n\u2022 , Antonio Caggiano\n\u2022 \u00a0&\u00a0Eddie Koenders\n\nApplied Sciences (2021)\n\n\u2022 ### A coupled mechano-chemical peridynamic model for pit-to-crack transition in stress-corrosion cracking\n\n\u2022 Ziguang Chen\n\u2022 , Jiangming Zhao\n\u2022 \u00a0&\u00a0Florin Bobaru\n\nJournal of the Mechanics and Physics of Solids (2021)\n\n\u2022 ### Multi-Phase-Field Model of Intergranular Corrosion Kinetics in Sensitized Metallic Materials\n\n\u2022 Talha Qasim Ansari\n\u2022 , Jing-Li Luo\n\u2022 \u00a0&\u00a0San-Qiang Shi\n\nJournal of The Electrochemical Society (2020)","date":"2021-04-14 03:55:26","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 2, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.58534175157547, \"perplexity\": 2186.8638086743026}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-17\/segments\/1618038076819.36\/warc\/CC-MAIN-20210414034544-20210414064544-00480.warc.gz\"}"} | null | null |
There is an ever-raging "War on Drugs" in our nation and communities. Per a 2010 National Survey released by the Substance Abuse and Mental Health Services Administration, "23.5 million Americans are addicted to alcohol and drugs. That 's approximately one in every 10 Americans over the age of 12. But only 11 percent of those with an addiction receive treatment" (Defining the Addiction Treatment Gap 2-6). The issue of how to solve the addiction problem and the "War on Drugs" is a long-standing and highly debated issue. Drug addiction has become criminalized rather than a disease. This should be changed. Society should be assisting those who are addicted by helping organize and fund rehabilitation programs to help them become sober. I believe that our drug culture needs to change the way our society fights this "War on Drugs." Our society has the resources available and is responsible for helping those addicted to drugs to help build a safer and healthier society.
...ghting" drug addiction the wrong way. Studies show shocking statistics on the financial burden of drug addiction on both the addict and our society. Our current law allows the overdose victim to walk away from an overdose and does not require any intervention or rehab to occur. Drug addiction has become criminalized rather than a disease. We realize there is an issue but nothing is being done to help those addicted to drugs. This needs to be changed. Society should be assisting those who are addicted not punishing them because they are members of our society who are struggling to get their life back. I believe that our drug culture needs to change in some way to help fight this "War on Drugs" the right way. Our society has the resources available and our society should be held responsible for helping those addicted to drugs to help build a safer and healthier society. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,942 |
Q: Laravel controller validation Request does not exist I'm using Laravel 8 validation, and what i'm trying to do is to validate a form with some input name, unique to table Sizes column "name" where it also depends on another column speciesId that the value from $request->speciesId.
The function in Controller is looks like this
public function storeSize(Request $request)
{
$validated = $request->validate(
[
'name' => [
'required', Rule::unique('sizes')->where(function ($query) {
return $query->where('speciesId', $request->speciesId);
})
],
'speciesId' => 'required'
]
);
}
already add use Illuminate\Http\Request; and use Illuminate\Validation\Rule; but still got "ErrorException Undefined variable: request".
when i'm try to var_dump($request) or echo $request->speciesID, the variable and value is present.
my question is, why the validation function doesn't recognize the Request variable?
A: The error occurs because inside your function call $request is not available. You need to make it available by adding use $request to function ($query):
$validated = $request->validate([
'name' => [
'required', Rule::unique('sizes')->where(function ($query) use ($request) {
return $query->where('speciesId', $request->speciesId);
})
],
'speciesId' => 'required'
]);
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 96 |
ORLANDO, November 23 – Taking advantage of Karen's annual physician meeting location, the Aney clan descended on Orlando. Theme park highlights include the Magic Kingdom, Sea World, and Animal Kingdom. However, Nicholas was quoted as saying "Mickey Mouse is a nice enough guy in theory, but if you think I'm getting within 50 feet of that giant mouse, you are crazy!"
Actually, it is quite fun for Tom and girls. Katie enjoys being the oldest and one of the best skaters. Gritty Jessie scored 3 goals and thus proclaimed that she scored a 'Pat-trick' in her first game. Nick (a.k.a. "Rookie" as his Grandpa still refers to him) didn't quite make the cut. Although he skates and has a nice slap shot…at age 2½, Tom thought he needed one more year in the developmental league before making the jump to 'Termites'.
'Jessie Bear' as we affectionately call Jess, loves bugs and animals and art projects and just hanging out with no one 'bugging' her (no pun intended!). A 'non-Jessie' day is referred to as a day we are running all day. Another of her 2002 highlights was our annual trip to Sanibel, FL, where she would spend the days catching and playing with lizards. Sounds like eternal bliss doesn't it?!?!.
As for work, I'm far from retirement. I started a niche software consulting company called Benefit Technology Resources (http://www.benefittech.com). You can hit the site if you are really interested…but I'll say that it has been very exciting so far. My clients consist of the world's largest actuarial firms who seem eager to work with a 'half-breed' (½ actuary + ½ programmer).I've hired my brother Terry to do the 'heavy lifting' in terms of programming and we are having fun.I also work 25% in Mayo Foundation Benefits, providing some technical help with pension and actuarial issues.
Aside from going by too fast, 2002 was a great year for us. The kids help us to see, appreciate and experience life in a different and wonderful way each day. The events of the world remind us to cherish the blessings we have.We wish you, our family and friends, happy holidays and we look forward to seeing you in 2003. | {
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Home People & Inspiration Daily Life
Chalk Campus Crush: Get To Know College Of St. Benilde's Johnvic de Guzman
Chalk Magazine
By Rochelle Joy Gonzales
JOHNVIC DE GUZMAN, 22
De La Salle – College of St. Benilde
@johnvicdeguzman
Year and Course 5th Year, Human Resource Management
Birthday September 22, 1993
Hobbies Playing volleyball, singing
Favorite campus hangout CSB Sports Office and the gym
Ultimate dream Own a company, tour my family around the world, and make them proud!
For his soaring spikes, he has been named his varsity team's best opposite spiker. With his scoring ability, he has also earned a spot on both the National Team (for which he competed in the SEA Games) and semi-pro team PLDT Home Ultera (by telecommunications brand PLDT, which he is a brand ambassador of, along with Alyssa Valdez, Mika Reyes, and other collegiate sports hotshots). He was instrumental in bringing CSB to a finals appearance in Season 90 of the NCAA and a Final Four spot in Season 91. He is Johnvic de Guzman—and he impresses with more than the obvious. Chiseled bones, muscular frame, sexy dark skin, and an imposing 6'2" stature be damned! The 23-year-old is truly a force on the court.
What many do not know, however, is that Johnvic was actually a badminton player before he found success in volleyball. He eventually gave up his old sport in favor of the new, citing more opportunities in the field as his primary motivation. His mother and sister, both former volleyball players, also became his inspiration to get into the sport. Behind his strong Alfred Enoch-like features is a mama's boy—Johnvic grew up without a father figure, with only his mom mostly by his side.
More than being a passionate athlete, Johnvic sees to it that he also remains a responsible student. He manages his time properly, with a rigid schedule of training in the morning and attending classes in the afternoon and evening. Call him Mr. Laser-Focused because no amount of glaring fame or gushing fans can take his eyes off the prize. In fact, he declares, "At first, I hated heavy training, but, since it's part of being an athlete, I eventually loved the pain and enjoyed it. Volleyball is my passion."
On looking good
"Everything about you is reflected in your actions."
On loving hard
"Love is blind."
On living young
"Live life to the fullest!"
ALSO READ: In Focus: Here's a Rundown Of Sports You Thought You Were Too Old For—And Where to Join
Image by Rxandy Capinpin. Styling Red Dimaandal. Grooming Xy Eugenio for Inglot Cosmetics. Hair Jaypee Valera of Triple Luck Brow & Nail Salon. Special thanks to Ogie Rodriguez.
TAGS: campus crush Chalk Magazine College of St. Benilde CSB. CSB Blazers johnvic de guzman
Daily Diaries: If You're an Overachiever, Here are 5 Things You Need to Hear Now
Daily Diaries: 3 Discouragements Every Aspiring Writer Will Hear
In Focus: 5 Homegrown Music Videos that Pierced Our "Marupok" Hearts this 2019
In Focus: 3 Reasons Why You Should Take a Social Media Break During the Holidays | {
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Q: Sending an SMS Message with Rails and Twilio I'm new to ruby and ruby on rails and having trouble setting up Twilio to send text messages.
So far I have the following code in my rails app: When I go to send the SMS message I get the following error:
Missing template twilio/send_text_message, application/send_text_message with {:locale=>[:en], :formats=>[:html], :handlers=>[:erb, :builder, :raw, :ruby, :jbuilder, :slim, :coffee, :haml]}.
my initializer
#config/initializers/twilio.rb (removed keys)
require 'twilio-ruby'
account_sid = "XXXXXXXXX"
auth_token = "XXXXXXX"
$twilio_phone_number = "+XXXXXXXXXX"
$twilio_client = Twilio::REST::Client.new account_sid, auth_token
then added in the route
#routes.rb
post 'twilio/send_text_message' => 'twilio#send_text_message'
then i have my twilio controller
#twilioController
class TwilioController < ApplicationController
def index
end
def send_text_message
end
end
and in my view I've set up a form for a user to enter a message that gets sent to my phone (because i'm in trial mode and it's verified)
#ShareWithWorld.html.slim
= form_for :twilio, url: '/twilio/send_text', method: :post do |f|
=f.text_field "Hey"
=f.submit "Send Text"
A: The reason you're getting that error is the fact you have no view to be rendered, e.g. app/views/twilio/send_text_message.html.slim.
If the code comes to the end of the action without an interrupt, it will try and render the associated view.
class TwilioController < ApplicationController
def send_text_message
$twilio_client.account.messages.create(
:from => '+14159341234',
:to => '+16105557069',
:body => ..params from form..
)
redirect_to root_path, notice: 'Your SMS has been sent' # This is the interrupt that will make it so it doesn't try to render the view
end
end
| {
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{"url":"https:\/\/datascience.stackexchange.com\/questions\/32622\/how-to-make-a-decision-tree-with-both-continuous-and-categorical-variables-in-th","text":"# How to make a decision tree with both continuous and categorical variables in the dataset?\n\nLet's say I have 3 categorical and 2 continuous attributes in a dataset. How do I build a decision tree using these 5 variables?\n\nEdit:\nFor categorical variables, it is easy to say that we will split them just by {yes\/no} and calculate the total gini gain, but my doubt tends to be primarily with the continuous attributes. Let's say I have values for a continuous attribute like {1,2,3,4,5}. What will be my split point choices? Will they be checked at every data point like {<1,>=1......& so on till} or will the splitting point will be something like the mean of column?\n\nDecision trees can handle both categorical and numerical variables at the same time as features, there is not any problem in doing that.\n\n### Theory\n\nEvery split in a decision tree is based on a feature. If the feature is categorical, the split is done with the elements belonging to a particular class. If the feature is contiuous, the split is done with the elements higher than a threshold. At every split, the decision tree will take the best variable at that moment. This will be done according to an impurity measure with the splitted branches. And the fact that the variable used to do split is categorical or continuous is irrelevant (in fact, decision trees categorize contiuous variables by creating binary regions with the threshold).\n\n### Implementation\n\nAlthough, at a theoretical level, is very natural for a decision tree to handle categorical variables, most of the implementations don't do it and only accept continuous variables:\n\n\u2022 This answer reflects on decision trees on scikit-learn not handling categorical variables. However, one of the scikit-learn developers argues that\n\nAt the moment it cannot. However RF tends to be very robust to categorical features abusively encoded as integer features in practice.\n\n\u2022 rpart in R can handle categories passed as factors, as explained in here\n\u2022 Lightgbm and catboost can handle categories. Catboost does an \"on the fly\" target encoding, while lightgbm needs you to encode the categorical variable using ordinal encoding.\n\nHere's an example of how lightgbm handles categories:\n\nimport pandas as pd\nfrom lightgbm import LGBMRegressor\nfrom category_encoders import OrdinalEncoder\n\nX = OrdinalEncoder(cols=[3]).fit_transform(X)\n\ndt = LGBMRegressor()\ndt.fit(X, y, categorical_feature=[3])\n\n\n\u2022 It really depends on algorithm. For example decision trees used in popular Python packages (scikit-learn and XGBoost) can't handle categorical data out of the box (scikit-learn for example uses CART algorithm) Jun 4, 2018 at 18:39\n\u2022 Yes, that was pretty much helpful @DavidMasip. I actually had confusion regarding particulary continuous variables and it got cleared now :) Jun 15, 2018 at 19:42\n\nI am not sure if most answers consider the fact that splitting categorical variables is quite complex. Consider a predictor\/feature that has \"q\" possible values, then there are ~ $$2^q$$ possible splits and for each split we can compute a gini index or any other form of metric. It is conceptually easier to say that \"every split is performed greedily based on metric (MSE for continuous and e.g. gini index for categorical)\" but it is important to addess the fact that number of possible splits for a given feature are exponential in the number of categories. It is correct observation that CART handles it without exponential complexity, but the algorithm it uses to do so is highly non-trivial, and one should acknowledge the difficulty of the task.\n\n\u2022 For a binary tree, the number of all possible splits of a categorical feature of cardinality $q$ is $2^{q-1}-1$ to be exact: For each categorical value, it could be to the either left or right of the split, hence $2^q$; $2^{q-1}$ because of the symmetry between left and right; the last \"-1\" because an empty set to either side of the split is not allowed.\n\u2013\u00a0Lei\nOct 2, 2021 at 0:20\n\nIt depends. Some algorithms, for example ID3 are able to handle categorical variables. Other, like CART algorithm are not.\n\nThere are two basic approaches to encode categorical data as continuous.\n\n\u2022 One-hot encoding\n\u2022 Mean encoding\n\nOne-hot encoding is pretty straightforward and is implemented in most software packages. The drawback is that it runs into problems if you have many categories (because the number of encoding dimensions is equal to number of categories).\n\nMean encoding (also sometimes called target encoding) consists of encoding categories with means of target (for example in regression if you have classes 0 and 1 then class 0 is encoded by mean of response for examples with 0 and so on). There are some answers on this site on that which provide more detail. I also encourage you to see this video if you want to get more about how it works and how you can implement it (there are several ways that to do mean encoding and each has its pros and cons).\n\nIn Python you can do mean encoding yourself (some approaches are shown in the video from the series I linked) or you can try Category Encoders from scikit-learn contrib.\n\n\u2022 I actually want to draw it using numerical calculations and not using scikit learn. I have edited the question. Jun 4, 2018 at 18:54\n\u2022 I don't see how this changes the answer. You can just manually do one-hot or mean encoding. The gini coefficient doesn't depend on datatype, it only depends on grouping and target. Jun 4, 2018 at 18:56\n\nWhen using Decision Trees, what the decision tree does is that for categorical attributes it uses the gini index, information gain etc. But for continuous variable, it uses a probability distribution like the Gaussian Distribution or Multinomial Distribution to discriminate. The second methodology is to convert it to categorical attributes and make rules like this: if a<100 and if a<100.","date":"2022-08-13 07:17:37","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 1, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5039112567901611, \"perplexity\": 926.0472729818481}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-33\/segments\/1659882571909.51\/warc\/CC-MAIN-20220813051311-20220813081311-00237.warc.gz\"}"} | null | null |
El marquesado de Villena es un título nobiliario español concedido por Juan II, el 12 de noviembre de 1445 a Juan Pacheco, maestre de la Orden de Santiago, adelantado mayor de Murcia y posteriormente primer duque de Escalona.
El marquesado, como entidad territorial, es herencia del antiguo señorío de Villena, que revirtió en la corona. Ya fue marquesado anteriormente en la persona de Alfonso de Aragón el Viejo, aunque volvió a revertir en la corona hasta su concesión por el rey Juan II de Castilla en 1445 a Juan Pacheco. El hijo de este, Diego López Pacheco y Portocarrero perdió la mayor parte de las tierras del marquesado, entre ellas la capital, Villena, al sublevarse esta ciudad en favor de los Reyes Católicos en 1476. A esta rebelión, conocida popularmente como la de "las cinco campanadas", le sucederían las del resto de ciudades importantes del marquesado. Los Pacheco seguirían usando el título, pese a no poseer ya el marquesado, convirtiéndose en una distinción que ha perdurado por tradición.
En la actualidad, ostenta el título de marqués de Villena Francisco de Borja Soto y Moreno-Santamaría, duque de Frías y descendiente de la Casa de Escalona.
Marqueses de Villena
Árbol genealógico
Historia de los Marqueses de Villena
Juan Pacheco (1419-4 de octubre de 1474), I marqués de Villena, I duque de Escalona. Uno de los hombres más poderosos en la corte de Castilla bajo los reinados de Enrique IV e Isabel la Católica. Hermano de Pedro Girón, maestre de la Orden de Calatrava y origen de los Osuna. Recibe del rey Enrique IV el marquesado de Villena en 1445 y el ducado de Escalona en 1472. Su tercer hijo es Alonso Téllez-Girón, I señor de la Puebla de Montalbán, de cuya descendencia vendrá el XIII duque de Escalona, Diego Fernández de Velasco.
Casó en primeras nupcias el 27 de septiembre de 1435 con Juana de Luna, matrimonio anulado en 1442. Contrajo un segundo matrimonio en 1442 con María Portocarrero y Enríquez, VII señora de Moguer. Casó en terceras nupcias en 1472 con María Fernández de Velasco y Mendoza. Le sucedió en 1468, por cesión, su hijo primogénito del segundo matrimonio:
Diego López Pacheco (1456-26 de noviembre de 1529), II marqués de Villena, II duque de Escalona. Es el último marqués de facto, pues pierde las principales ciudades del marquesado, incluida la capital, Villena, por sublevación. A pesar de ello se seguiría autodenominando como marqués.
Casó en primeras nupcias en 1469 con Juana de Luna (m. 1480), III condesa de San Esteban de Gormaz. Casó en segundas nupcias en 1484 con Juana Enríquez y Velasco, hija de Alfonso Enríquez, conde de Melgar. De este matrimonio nacería su sucesor en este título, ya sin marquesado:
Diego López Pacheco y Enríquez (1503-7 de febrero de 1556), III marqués de Villena, III duque de Escalona,, VI conde de San Esteban de Gormaz, señor de Belmonte, mayordomo mayor del rey Enrique IV, capitán general de Andalucía y de la frontera de Granada y caballero de la Orden del Toisón de Oro.
Casó con Luisa de Cabrera y Bobadilla, III marquesa de la Moya. Sucedió su hijo:
Francisco López Pacheco y Cabrera (1532-1574), IV marqués de Villena, IV duque de Escalona, IV marqués de Moya y VII conde de San Esteban de Gormaz.
Contrajo matrimonio con Juana Álvarez de Toledo, hija de Fernando Álvarez de Toledo, IV conde de Oropesa, a quien le sucedió su primogénito:
Juan Gaspar Fernández Pacheco y Álvarez de Toledo (1563-5 de mayo de 1616), V marqués de Villena, V duque de Escalona, V marqués de Moya y VIII conde de San Esteban de Gormaz.
Casó con Serafina de Braganza, hija de Juan de Portugal Pereira y Castro, VI duque de Braganza, y de Catalina de Portgugal, infanta de Portugal. Dos de sus hijos suceden a su padre en sus títulos. El primero fue:
Felipe Baltasar Fernández Pacheco (1596-30 de diciembre de 1632), VI marqués de Villena, VI duque de Escalona, VI marqués de Moya y IX conde de San Esteban de Gormaz.
Casó con Catalina de Zúñiga y Sandoval, hija de Diego de Zúñiga II duque de Peñaranda de cuyo matrimonio no hay descendencia. Le sucede su hermano:
Diego López Pacheco (1599-1653), VII marqués de Villena, VII duque de Escalona, IX marqués de Moya (sucede a su hijo del primer matrimonio), X conde de San Esteban de Gormaz, gobernador y virrey de Nueva España, virrey de Navarra, capitán general de Castilla-La Mancha y caballero de la Orden del Toisón de Oro.
Casó en primeras nupcias con su prima hermana, Luisa Bernarda de Cabrera y Bobadilla, VII marquesa de Moya, y en segundas nupcias con Juana de Zúñiga y Mendoza, hija de Francisco Diego López de Zúñiga-Sotomayor y Mendoza, VII duque de Béjar. De su primer matrimonio nació un hijo, José Isidro López Pacheco y Cabrera Bobadilla, que falleció en 1643 sin descendencia, y que fue el VIII marqués de Moya y el XI conde de San Esteban de Gormaz. En el marquesado de Villena, sucedió su hijo del segundo matrimonio:
Juan Manuel Fernández López Pacheco (1648-1725), VIII marqués de Villena, VIII duque de Escalona, X marqués de Moya, XII conde de San Esteban de Gormaz y caballero del Toisón de Oro.
Casó en 1674 con María Josefa de Benavides Manrique y Silva, VI marquesa de la Eliseda. Le sucede su hijo:
Mercurio López Pacheco (1679-7 de julio de 1738) IX marqués de Villena, IX duque de Escalona, XII marqués de Aguilar de Campoo, VII marqués de la Eliseda y XIII conde de San Esteban de Gormaz.
Casó en primeras nupcias con su sobrina, Petronila Antonia de Silva y Mendoza, hija de José María de Silva I marqués de Melgar, con la que no tiene descendencia. Contrajo un segundo matrimonio con María Catalina Teresa de Moscoso Osorio y Benavides, hija de Luis de Moscoso Osorio, VI marqués de Almazán. Sucedió su hijo del segundo matrimonio:
Andrés López-Pacheco y Osorio de Moscoso (1710-27 de junio de 1747), X marqués de Villena, X duque de Escalona, XIII marqués de Aguilar de Campoo, XVII conde de Castañeda, XVI conde de San Esteban de Gormaz y VIII marqués de la Eliseda.
Casó en primeras nupcias el 27 de octubre de 1727, en Madrid, con Ana María de Toledo Portugal Monroy y Ayala, XI condesa de Oropesa. Contrajo un segundo matrimonio el 16 de julio de 1731, en Madrid, con Isabel María Pacheco y Téllez-Girón, sin descendencia de este matrimonio. Su hija primogénita del primer matrimonio, María Ana Catalina López Pacheco Toledo y Portugal, XIV marquesa de Aguilar de Campoo, grande de España, casó con su tío, Juan Pablo López Pacheco y Moscoso quien, después de pleitear y casar con su sobrina, sucedió en los otros títulos:
Juan Pablo López-Pacheco y Moscoso (Madrid, 1716-Madrid, 27 de abril de 1951), XI marqués de Villena, XI duque de Escalona, señor de Belmonte y de Garganta la Olla, coronel del regimiento real de infantería de la reina, teniente general de los reales ejércitos, caballero de San Genaro de Nápoles, comendador de Alcuesta en la Orden de Santiago, director perpetuo de la Real Academia Española y gentilhombre de los reyes Felipe V y Fernando VI de España.
Casó con su sobrina, María Ana Catalina López Pacheco Toledo y Portugal (1727-1768), XIV marquesa de Aguilar de Campoo, VIII marquesa de Frechilla, VIII marquesa de la Eliseda, XVII condesa de Castañeda, XI condesa de Alcaudete y XIII condesa de San Esteban de Gormaz. Sin descendencia, sucedió su primo carnal:
Felipe López-Pacheco y de la Cueva (1727-24 de julio de 1798), XII marqués de Villena, XII duque de Escalona, XVI marqués de Aguilar de Campoo, XI marqués de la Eliseda, XX conde de Castañeda, XIII marqués de Moya, XVII conde de San Esteban de Gormaz, V conde de Villanova, XV marqués de Villanueva del Fresno y Barcarrota, comendador de la Orden de Santiago, VII marqués de Bedmar y caballero del Toisón de Oro. Era hijo de Mariano López Pacheco Cabrera y Bobadilla, XIII marqués de Moya, —hijo del VIII marqués de Villena—, y de su esposa María Francisca de la Cueva y Acuña, VI marquesa de Bedmar.
Casó el 21 de febrero de 1750, en Madrid, con su sobrina, María Luisa Centurión Velasco y López de Ayala, , VIII marquesa de Estepa, con la que no tendrá hijos. Le sucede:
Diego Fernández de Velasco (1754-1811), XIII marqués de Villena, XIII duque de Escalona, VIII duque de Uceda, XIII duque de Frías, V marqués de Menas Albas, X marqués de Frómista, VIII marqués de Belmonte, XIII marqués de Berlanga, VII marqués de Toral, VI marqués de Cilleruelo, X marqués de Jarandilla, VIII conde de Pinto, VII marqués del Fresno, XI marqués de Frechilla y Villarramiel, X marqués del Villar de Grajanejos, XV conde de Haro, XVII conde de Castilnovo, XVIII conde de Alba de Liste, VII conde de la Puebla de Montalbán, X conde de Peñaranda de Bracamonte, XVIII conde de Luna, XVI conde de Fuensalida, IX conde de Colmenar, XV conde de Oropesa, XIV conde de Alcaudete, XIV conde de Deleytosa, conde de Salazar de Velasco.
Casó con Francisca de Paula de Benavides y Fernández de Córdoba, hija de Antonio de Benavides y de la Cueva II duque de Santisteban del Puerto, etc. Le sucedió su hijo:
Bernardino Fernández de Velasco (1783-1851), XIV marqués de Villena, XIV duque de Escalona, IX duque de Uceda, XIV duque de Frías, VI marqués de Menas Albas, IX marqués de Belmonte, XI marqués de Frómista, IX marqués de Caracena, XIV marqués de Berlanga, VIII marqués de Toral, VII marqués de Cilleruelo, IX conde de Pinto, VIII marqués del Fresno, XIV marqués de Jarandilla, XII marqués de Frechilla y Villarramiel, XI marqués del Villar de Grajanejos, XVI conde de Haro, XVIII conde de Castilnovo, conde de Salazar de Velasco, XIX conde de Alba de Liste, VIII conde de la Puebla de Montalbán, XI conde de Peñaranda de Bracamonte, conde de Luna, XVII conde de Fuensalida, X conde de Colmenar, XVI conde de Oropesa, XV conde de Alcaudete, XIX conde de Deleytosa, conde de Villaflor.
Casó con María Ana Teresa de Silva Bazán y Waldstein, hija de José Joaquín de Silva-Bazán, IX marqués de Santa Cruz de Mudela, X marqués del Viso, marqués de Bayona, VI marqués de Arcicóllar y conde de Pie de Concha. Sin descendientes de este matrimonio. Contrajo un segundo matrimonio con María de la Piedad Roca de Togores y Valcárcel, hija de Juan Nepomuceno Roca de Togores y Scorcia, I conde de Pinohermoso, XIII barón de Riudoms. Casó (en matrimonio desigual, post festam, legitimando la unión de hecho), con Ana Jaspe y Macías. Le sucedió su nieto, hijo de Bernardina María Fernández de Velasco Pacheco y Roca de Togores (1815-1869), su hija del segundo matrimonio, y de su esposo Tirso María Téllez-Girón y Fernández de Santillán, hijo de Pedro de Alcántara Téllez-Girón y Pimentel IX marqués de Jabalquinto y nieto del IX duque de Osuna:
Francisco de Borja Téllez-Girón y Fernández de Velasco (1839-8 de agosto de 1897), XV marqués de Villena, XV duque de Escalona, XI duque de Uceda, XX conde de Alba de Liste, IX conde de la Puebla de Montalbán, XI conde de Pinto, senador del reino por derecho propio, caballero de la Orden de Santiago, Gran Cruz de Carlos y gentilhombre de la cámara del rey Alfonso XII y de la reina regente de España.
Casó, el 15 de octubre de 1867, con Ángela María de Constantinopla Fernández de Córdoba y Pérez de Barradas, hija de Luis Tomás de Villanueva Fernández de Córdoba Figueroa y Ponce de León, XV duque de Medinaceli. Sucedió su hijo:
Luis Téllez-Girón y Fernández de Córdoba Madrid, 3 de marzo de 1870-1 de abril de 1909), XVI marqués de Villena, XIV duque de Osuna, XII duque de Uceda, XVIII conde de Ureña, maestrante de Sevilla, diputado a Cortes por Talavera de la Reina y gentilhombre de cámara del rey.
Soltero, sin descendencia, sucedió su hermano:
Mariano Téllez-Girón y Fernández de Córdoba (1887-1931), XVII marqués de Villena, XVI duque de Escalona, XV duque de Osuna y XXI conde de Alba de Liste.
Casó el 10 de noviembre de 1921, en Sevilla, con Petra Duque de Estrada y Moreno (1900-1985), hija de Juan Antonio Duque de Estrada y Cabeza de Vaca, VIII marqués de Villapanés. Le sucede el hijo de su hermana María de los Ángeles Téllez-Girón y Fernández de Córdoba y de su esposo Ricardo Martorell y Fivaller, VIII marqués de Paredes, V duque de Almenara Alta, V marqués de Albranca, diputado a cortes por Mahón en 1884, caballero de la Orden de Santiago y maestrante de Valencia.
Francisco de Borja Martorell y Téllez-Girón (Madrid, 17 de junio de 1898-Paracuellos de Jarama, 30 de noviembre de 1936), XVIII marqués de Villena, XXII conde de Alba de Liste, XVII duque de Escalona, VII duque de Almenara Alta, X marqués de Paredes, XI marqués de Villel, VII marqués de Albranca, XV marqués de la Lapilla, Gentilhombre Grande de España con ejercicio y servidumbre del rey Alfonso XIII.
Casó el 9 de mayo de 1923 con María de los Dolores Castillejo y Wall, hija de Juan Bautista Castillejo y Sánchez de Teruel, IV conde de Floridablanca, y de María de la Concepción Wall y Diego, VII condesa de Armíldez de Toledo. Le sucedió su hija:
María Soledad de Martorell y Castillejo (8 de julio de 1924-Madrid, 6 de agosto de 2022), XIX marquesa de Villena, XI marquesa de Paredes XIII marquesa de Villel, VIII duquesa de Almenara Alta, XII marquesa de Monesterio en 1951, XVI marquesa de la Lapilla, XVIII duquesa de Escalona, VIII marquesa de Albranca y X condesa de Darnius.
Casó en 1948 con Juan Pedro de Soto y Domecq (m. Madrid, 19 de agosto de 2004), caballero de la Real Maestranza de Caballería de Sevilla, hijo de Fernando de Soto y González de Aguilar Ponce de León, XII marqués de Arienzo, IV conde de Puerto Hermoso y XI marqués de Santaella, y de María del Carmen Domecq y Núñez de Villavicencio. En 1990 le sucedió su hijo a quien cedió el título:
Francisco de Borja de Soto y Martorell (1956-1997), XX marqués de Villena, XX duque de Escalona, XXIII conde de Alba de Liste.
Casó con María de la Concepción Moreno Santa María y de la Serna y le sucede a su muerte en accidente a su hijo mayor:
Francisco de Borja de Soto y Moreno-Santamaría (n. 1985), XXI marqués de Villena, XXI duque de Escalona, XIX duque de Frías y conde de Haro con dos Grandezas de España de clase inmemorial.
Marqueses destacados
Juan Pacheco, primer marqués e importante político del . Nacido en Belmonte (Cuenca) pueblo en el que construyó su imponente castillo tras nombrar a la villa capital del marquesado.
Diego López Pacheco y Portocarrero (c. 1443-1529): famoso por su política de mecenazgo y apoyo a los alumbrados, grupos de creyentes cuyas prácticas fueron declaradas heréticas por la Inquisición a partir de 1525. A él va dirigido el tercer Abecedario, de Fray Francisco Osuna, aparecido en Toledo el 31 de agosto de 1527.
Diego López Pacheco y Portugal: virrey de Navarra, (1646-1652)
Juan Manuel Fernández Pacheco, hijo del anterior, fundador y primer director de la Real Academia Española (entre 1713 y su muerte en 1725).
Mercurio Antonio López Pacheco, hijo del anterior, segundo director de la Academia (entre la muerte de su padre, en 1725, y su propia muerte, en 1738).
Véase también
Historia de Villena
Castillo de Belmonte
Referencias
Bibliografía
Marquesado de Villena
Villena | {
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{"url":"https:\/\/codereview.stackexchange.com\/questions\/161473\/for-each-pair-of-strings-eliminate-the-characters-they-have-in-common","text":"# For each pair of strings, eliminate the characters they have in common\n\nIn the below code there are 3 inputs.\n\nFirst line of input is the number of testcases for which the program will run where (1<=testcases<=10) and i is an int.\n\nFor each testcase\nSecond and third input will be a String where (1<=Stringlength<=10^5)\n\nOutput\nNow for the output we need to compare both the strings and remove similar characters from both them. The output will be based on which string encounters 0 length first. if none of them is 0 after completion then it will be a draw.\n\nTime of execution is 1.0 sec for each input but my time for 10^5 strings is 2.0. Is there a way to increase its efficiency based on the time.\n\nimport java.io.*;\nimport java.util.*;\n\npublic class MyProg{\npublic static void main(String[] args) throws IOException\n{\nSystem.out.println(\"Enter the number of testcases\");\nint testcase=Integer.parseInt(ts);\nfor(int i=0;i<testcase;i++)\n{\nSystem.out.println(\"Enter the 2 strings\");\nList<Character> s1 = new ArrayList<Character>();\nList<Character> s2 = new ArrayList<Character>();\nfor(char c : sa.toCharArray())\nfor(char c : sb.toCharArray())\nfor(char c:s2)\n{\ns1.remove((Character)c);\n\n}\n\nfor(char c:sa.toCharArray())\n{\ns2.remove((Character)c);\n}\nif(s1.size()==0 && s2.size()>0)\nSystem.out.println(\"You lose some.\");\nelse if(s1.size()>0 && s2.size()==0)\nSystem.out.println(\"You win some.\");\nelse\nSystem.out.println(\"You draw some.\");\n}\n}}\n\n\u2022 Are there any restrictions on the inputs? E.g. reasonable to assume all printable ASCII characters only? \u2013\u00a0h.j.k. Apr 22 '17 at 10:05\n\u2022 The only restriction is characters of a string is between 'a' to 'z' and it contains nothing else. \u2013\u00a0wiTcH_doCtoR Apr 22 '17 at 15:56\n\nThe cause of your TLE error is this:\n\n for(char c:s2)\ns1.remove((Character)c);\nfor(char c:sa.toCharArray())\ns2.remove((Character)c);\n\n\nYou need to realise that List.remove() is $O(n)$ in the length of the list. And in worst case you do this removal $n$ times which gives you an $O(n^2)$ algorithm which is too slow for this task.\n\nYou can be 100% certain that they have a test case that is the maximal number of characters, all the same in both strings as to trigger this worst case behaviour. For example the following:\n\ns1 = \"aaaaaaaaaa...\" \/\/ repeating 10^5 times\n\ns2 = s1\n\nYou need to do it in $O(n)$ time and to do that you need to figure out a way of doing it without actually removing the characters from the strings. As you didn't link the original question I cannot help you as your description is a bit ambiguous as to how it should work.\n\nI hate this code, but it is faster.\n\nYou said you are only working with strings made of characters from a-z. That means 26 characters. The idea is to use 26 counters, each belonging to a character from a-z.\n\nGo through the first(second) string, and every time you find a character c, you increment(decrement) c's counter by 1.\n\nIf every counter is zero, that means the strings are permutations of each other, i.e. it's a draw.\n\nOtherwise if every counter is non-negative, you'll know that the first string won; if every counter is non-positive, you'll know that the second string won.\n\nFinally, if some counters have different signs, then it's again a draw.\n\nYou can check if all the counters are non-negative like so.\nSet a variable allnonneg to true if the first counter is non-negative. Then loop through the remaining counters.\n\nIf during the $i$-th iteration you find a counter, which is negative, then you change allnonneg to false. Otherwise you keep allnonneg as it is. If in the end allnonneg is true, then you know that every counter was non-negative. If it's false, then you'll know that there was a counter which was negative. This is because the only way the value of allnonneg can change is if there is a counter which is negative.\n\nTo do this manipulation, you need a function f, such that f(allnonneg, charset[i] >= 0) is true precisely when both allnonneg, and charset[i] >= 0 are true. Luckily there's already an operator && which does this, so we get\n\nallnonneg = f(allnonneg, charset[i] >= 0) = allnonneg && (charset[i] >= 0)\n\n\nwhich is the same as allnonneg &= (charset[i] >= 0).\n\nprivate static int decide(String sa, String sb){\nint [] charset = new int[26];\n\nfor(int i = 0; i < sa.length(); charset[sa.charAt(i) - 97] ++, i++);\nfor(int i = 0; i < sb.length(); charset[sb.charAt(i) - 97] --, i++);\n\nboolean allnonneg = charset[i] >= 0;\nboolean allnonpos = charset[i] <= 0;\n\nfor(int i = 1; i < 25; i++) {\nallnonneg &= (charset[i] >= 0);\nallnonpos &= (charset[i] <= 0);\n}\n\nif(allnonneg && allnonpos)\nreturn 0; \/\/ every counter 0 => draw\nif(allnonneg)\nreturn 1; \/\/ 1st won\nif(allnonpos)\nreturn 2; \/\/ 2nd won\nelse\nreturn 0; \/\/ mixed signs => draw\n}\n\n\u2022 It worked fine... Thank you. But can you explain me the use of this for(int i = 0; i < 25; i++) {allnonneg &= (charset[i] >= 0); allnonpos &= (charset[i] <= 0); \u2013\u00a0wiTcH_doCtoR Apr 26 '17 at 14:45\n\u2022 @wiTcH_doCtoR I've edited in an explanation. \u2013\u00a0Andrew Apr 26 '17 at 15:10\n\nBased on your current implementation I'm going to assume that for strings \"ac\" and \"aaa\" we're only removing the first 'a' in both resulting in a draw (\"c\" and \"aa\").\n\nObservation 1: The largest of the 2 input strings will always have at least 1 character left after all the removals. This is trivial since we can only remove the number of letters that the smaller string has from the larger one, and by definition it has more letters.\n\nObservation 2: If both strings are of equal length, this will always result in a draw. Either both strings will be emptied completely at the same time, or both will have at least 1 letter left.\n\nSo let's use those observations to check as little as possible. First let's write a method that checks if the smallest one will become empty after scrapping all the common letters with the largest one:\n\nprivate boolean emptyAfterRemovingAll(String smallest, String largest){\nList<Character> listLargest = new ArrayList<Character>();\n\nfor(char c : smallest.toCharArray()){\nif(!listLargest.remove(c)){\n\/\/smallest string contains a character that is not in the largest\nreturn false;\n}\n}\n\/\/able to remove all characters from largest so smallest ends empty.\nreturn true;\n}\n\n\nNow our for main loop becomes something like this:\n\nfor(int i=0;i<testcase;i++) {\nSystem.out.println(\"Enter the 2 strings\");\nif(sa.length() == sb.length(){\nSystem.out.println(\"you draw some.\");\n} else if(sa.length() < sb.length()){\nif(emptyAfterRemovingAll(sa,sb)){\nSystem.out.println(\"You lose some.\");\n} else {\nSystem.out.println(\"you draw some.\");\n}\n} else {\nif(emptyAfterRemovingAll(sb,sa)){\nSystem.out.println(\"You win some.\");\n} else {\nSystem.out.println(\"you draw some.\");\n}\n}\n}","date":"2020-04-10 20:18:50","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6258005499839783, \"perplexity\": 1780.6296161668947}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-16\/segments\/1585370511408.40\/warc\/CC-MAIN-20200410173109-20200410203609-00158.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.esaral.com\/q\/solve-the-following-61372","text":"# Solve the following :\n\nQuestion:\n\nA circular road of radius $50 \\mathrm{~m}$ has the angle of banking equal to $30^{\\circ}$. At what speed should a vehicle go on this road so that the friction is not used?\n\nSolution:\n\n$\\tan \\theta=\\frac{v^{2}}{R g}$\n\n$\\tan 30^{\\circ}=\\frac{v^{2}}{(50)(10)}$\n\n$\\mathrm{v} \\cong 17 \\mathrm{~m} \/ \\mathrm{s}$","date":"2023-02-02 14:49:24","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2506730556488037, \"perplexity\": 719.1934885559714}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764500028.12\/warc\/CC-MAIN-20230202133541-20230202163541-00788.warc.gz\"}"} | null | null |
Yet again after lots of beta updates and the final of 3.6.0 in Jan and 3.6.1 in March, we have just been informed through one of our friends that Toni Wilen has launched a new beta branch for WinUAE version 4.0.0 with the release of Beta 1. This Amiga emulator has gone through many stages of development through the years and as always Toni Wilen always finds the time to either fix these bugs or add new features. As for what is added or fixed in this version, please see the changelog below.
Replaces old low latency vsync mode.
- Native mode only. Cycle-exact/approximate/fastest possible/JIT supported.
- Direct3D 9 and 11 only.
- Amiga display to monitor position mapping must be border to border vertically (or close enough) or you may see tearing lines.
- Does not gain anything from G-Sync.
- Input is read after each slice.
- Because output is shader based, outputting each slice requires full render pass each time. It technically means same as rendering screen 4 times the frame rate. (for example 50Hz output requires rendering 200 frames) -> don't enable any extra shaders unless you have powerful GPU. Most likely requires GPU with on-board RAM (discrete GPU) because this mode increases VRAM bandwidth requirements heavily. Or reduce resolution.
- END+F9 toggles debug colors when in low latency vsync mode (In normal modes END+F9 changes screens). When debug colors are disabled, useless screen clearing before each slice rendering is also disabled.
Enables multiple virtual Amiga monitors. Amiga monitor = single WinUAE window.
Default mode is unchanged, highest priority Amiga display output appear in single WinUAE window, switches automatically or manually (END+F9).
Optionally any video port display adapter or any RTG board can be disconnected from default monitor and connected to other monitor. (Monitor 1 to 4 select box in GUI, 1 = default). Only one signal source can be connected to non-default monitors. Only default monitor support on the fly switching/END+F9 manual switching.
Native (chipset) video output is always connected to first (default) monitor.
Each active monitor (WinUAE window) content is refreshed in real-time.
For example x86 VGA can be now visible at the same time with WB.
- Fullscreen is not supported and won't be supported.
- Direct 3D 9/11 mode only. DirectDraw won't be supported.
- GUI options adjusts all monitors. If native/video port: native filter and all other native related settings are in use for all windows in native/video port mode, if RTG: GUI RTG settings are used for all monitors in RTG mode.
- Non-default monitors are always opened next to default monitor. Positions are not stored.
- It does not matter which window has focus/captured mouse. All windows listen for input normally.
- Non-default windows don't have status bar or OSD and only have name of monitor in title bar.
- Video port device's window opens immediately at startup, RTG board's window open when board's output is enabled with valid display configuration for the first time.
Supports Casablanca ROM images, none of Casablanca special IO address spaces supported. It is has very unknown custom hardware.
- Set correct ROM, either original 2x512k 1:1 ROM images (ROM scanner supported) or 1x1024M manually merged and byteswapped. (Don't ask me, they contain KS modules, in scrambled format.) If rom starts with "00 00 00 00 00 00 00 18 44 52 42 52 00 01 00 06 ........DRBR...." = correct merged and byteswapped image.
- MMU emulation must be enabled.
- Chipset extra must be set to Casablanca.
- Other chipset options don't matter.
- RAM must be set manually: Select Z3 Fast #1, set size (32M/64M), tick "Manual configuration", set Address range start = 40000000. (End address is set automatically). Casablanca RAM uses Z3 space but does not use autoconfig.
- Log window should be enabled.
It "works" if you see lots of casablanca io access log messages, including MMU enable message. (MMU: TC=109dc enabled=0 page8k=0 PC=00000106). Finally it gets in infinite loop with exec partially initialized.
Because ROM is descrambled and copied to RAM by boot code and MMU is used to remap it to usual $f80000 region, also "zero page" is remapped, you need to enable UAE debugger mmu mapping support (for example "mmu 1" = use current MMU tables to translate user space addresses, 5 = super space) or you most likely get random garbage when using debugger commands. | {
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{"url":"https:\/\/forum.allaboutcircuits.com\/threads\/problems-in-100w-wireless-power-transfer-project.180260\/#post-1646065","text":"# Problems in 100W wireless power transfer project\n\n#### myaeaindrathein1996\n\nJoined Jun 11, 2021\n16\nI made an experiment for 100W wireless power transfer for my research. I used IR21844S for half bridge converter using IRFP360 MOSFETs. I designed the transmitter and receiver coils. I used full bridge rectifier using 1N4002 diodes and 2.2uF filter capacitor. I tested 10.5 ohms as a load by using an electronic load and measure voltage and current. I gave 24V dc supply for MOSFETs and 15V for gate driver. But the problem is that there is no current from the supply for MOSFETs and the power at the load is not even 0.1W. I planned to use schottky diodes in parallel with MOSFETs to reduce voltage spike and change schottky diodes in the rectifier of the receiver circuit. I used the frequency around 80kHz. I have no idea where I have the problems. I also simulated using LT spice and the simulation results are not that bad. Can someone help me or suggest any ideas?\n\n#### Attachments\n\n\u2022 31 KB Views: 25\n\n#### Deleted member 115935\n\nJoined Dec 31, 1969\n0\nI made an experiment for 100W wireless power transfer for my research. I used IR21844S for half bridge converter using IRFP360 MOSFETs. I designed the transmitter and receiver coils. I used full bridge rectifier using 1N4002 diodes and 2.2uF filter capacitor. I tested 10.5 ohms as a load by using an electronic load and measure voltage and current. I gave 24V dc supply for MOSFETs and 15V for gate driver. But the problem is that there is no current from the supply for MOSFETs and the power at the load is not even 0.1W. I planned to use schottky diodes in parallel with MOSFETs to reduce voltage spike and change schottky diodes in the rectifier of the receiver circuit. I used the frequency around 80kHz. I have no idea where I have the problems. I also simulated using LT spice and the simulation results are not that bad. Can someone help me or suggest any ideas?\n\n#### Martin_R\n\nJoined Aug 28, 2019\n103\nSurely need ultrafasr rectifier diodes, UF4002 for example.\n\n#### myaeaindrathein1996\n\nJoined Jun 11, 2021\n16\nIt says measure speed for current and voltage up to 50kHz so I don't think it can measure for around 80kHz. Instead of that one, which one should I use?\n\n#### myaeaindrathein1996\n\nJoined Jun 11, 2021\n16\nSurely need ultrafasr rectifier diodes, UF4002 for example.\nI ordered schottky diodes 1N5819 and MBR1645tg. Can I use them?\n\n#### Papabravo\n\nJoined Feb 24, 2006\n17,624\nI ordered schottky diodes 1N5819 and MBR1645tg. Can I use them?\nYou will want to check the datsheets for any candidate diodes for the parameter named \"Reverse Recovery Time\", sometimes abbreviated:\n$$t_{rr}$$\nDiodes will not block current in the reverse direction during this time, when the bias switches from forward to reverse.\nAlso make sure they can handle the forward current and the Peak Inverse Voltage.\n\n#### myaeaindrathein1996\n\nJoined Jun 11, 2021\n16\nYou will want to check the datsheets for any candidate diodes for the parameter named \"Reverse Recovery Time\", sometimes abbreviated:\n$$t_{rr}$$\nDiodes will not block current in the reverse direction during this time, when the bias switches from forward to reverse.\nAlso make sure they can handle the forward current and the Peak Inverse Voltage.\nI cannot check from both diodes that I ordered. It says extremely fast switching and high frequency operation.\n\n#### Papabravo\n\nJoined Feb 24, 2006\n17,624\nI cannot check from both diodes that I ordered. It says extremely fast switching and high frequency operation.\nI don't quite understand what you are saying. You can find a datasheet for anything you can order online and save a copy for printing or future reference.\nFamiliarizing yourself with a part's datasheet is a useful thing to do. This presumes that the manufacturer puts this information in the datasheet. I'll look for one that does.\n\nLast edited:\n\n#### myaeaindrathein1996\n\nJoined Jun 11, 2021\n16\nI don't quite understand what you are saying. You can find a datsheet for anything you can order online and save a copy for printing or future reference.\nLow drop power Schottky rectifier (st.com)\nMBR1635 - Switch-mode Power Rectifiers 16 A, 35 and 45 V (onsemi.com)\nFamiliarizing yourself with a part's datasheet is a useful thing to do.\nYes I already checked datasheets but they don't mention about the exact reverse recovery time. They mention that the diodes are extremely fast switching. I think it's enough for my work. Isn't it?\n\n#### Papabravo\n\nJoined Feb 24, 2006\n17,624\nYes I already checked datasheets but they don't mention about the exact reverse recovery time. They mention that the diodes are extremely fast switching. I think it's enough for my work. Isn't it?\nThat's a really good question. The datasheets that I found are abbreviated, which often happens with parts that are no longer manufactured or obsolete. If the information is not on the datasheet or the part comes from a secondary source you may not be getting what you think you are getting. On the Digi-Key site, both diodes are claimed to have a \"switching speed\", whatever that is, of \u2264 500 ns. IMHO that is a pretty slow recovery time. I'm not certain that those two things are the same. The datasheet does not mention either \"Revers Recovery Time\" or \"switching speed\", so I am at a loss on how to advise you, except that you can measure this parameter if you have a mind to do it.\n\nIn your application of \"Wireless Power Transfer\", every source of loss is potentially important. It is kind of like building a fire in a fireplace to heat your cabin, and opening the front door to improve the draft. One problem you are facing is that many discrete, leaded parts are obsolete and no longer manufactured. They have been replaced by Pb-Free surface mount parts. Going forward your choices are going to be further limited.\n\nI have some simulations of this you might find useful. It surprised me that the small signal diode was the fastest, the Schottky was in 2nd place, and the supposedly Fast Recovery Rectifiers brought up the rear.\n\nLast edited:\n\n#### myaeaindrathein1996\n\nJoined Jun 11, 2021\n16\nThat's a really good question. The datasheets that I found are abbreviated, which often happens with parts that are no longer manufactured or obsolete. If the information is not on the datasheet or the part comes from a secondary source you may not be getting what you think you are getting. On the Digi-Key site, both diodes are claimed to have a \"switching speed\", whatever that is, of \u2264 500 ns. IMHO that is a pretty slow recovery time. I'm not certain that those two things are the same. The datasheet does not mention either \"Revers Recovery Time\" or \"switching speed\", so I am at a loss on how to advise you, except that you can measure this parameter if you have a mind to do it.\n\nIn your application of \"Wireless Power Transfer\", every source of loss is potentially important. It is kind of like building a fire in a fireplace to heat your cabin, and opening the front door to improve the draft. One problem you are facing is that many discrete, leaded parts are obsolete and no longer manufactured. They have been replaced by Pb-Free surface mount parts. Going forward your choices are going to be further limited.\n\nI have some simulations of this you might find useful. Stay tuned.\nThanks for your advice. So I better look for small reverse recovery time diodes for rectifiers that would be suitable for my work. What do you suggest besides UF4002?\n\n#### Papabravo\n\nJoined Feb 24, 2006\n17,624\nThanks for your advice. So I better look for small reverse recovery time diodes for rectifiers that would be suitable for my work. What do you suggest besides UF4002?\nI am currently retired and have not looked at specific components for more than a decades so my knowledge is somewhat out of date. I can take a look at the UF4002. BTW I'm not saying the parts you are considering won't work at all, I'm just saying you need to know what your are dealing with because efficiency is critical and you really can't afford to use parts that will defeat your purpose.\n\nEDIT: the datasheet is encouraging, and it lists the trr as 50 ns. going from 0.5 amp forward to 1 Amp reverse. There was a time (ca. 1987), that I would have killed for that level of performance.\n\nUF4001-UF4007 Fast Rectifiers (onsemi.com)\n\nI could not find a model for the UF4002, but there was on for the UF4007\n\nLast edited:\n\n#### Alec_t\n\nJoined Sep 17, 2013\n12,479\nI used IR21844S for half bridge converter\nYour schematic is missing a diode from the 15V supply to the VB pin of the IC.\n\nJoined Jan 15, 2015\n6,324\nI made an experiment for 100W wireless power transfer for my research. I used IR21844S for half bridge converter using IRFP360 MOSFETs. I designed the transmitter and receiver coils. I used full bridge rectifier using 1N4002 diodes and 2.2uF filter capacitor. I tested 10.5 ohms as a load by using an electronic load and measure voltage and current. I gave 24V dc supply for MOSFETs and 15V for gate driver. But the problem is that there is no current from the supply for MOSFETs and the power at the load is not even 0.1W. I planned to use schottky diodes in parallel with MOSFETs to reduce voltage spike and change schottky diodes in the rectifier of the receiver circuit. I used the frequency around 80kHz. I have no idea where I have the problems. I also simulated using LT spice and the simulation results are not that bad. Can someone help me or suggest any ideas?\nThe diodes you show in your drawing should be fine and with a Google of \"wireless charging circuits\" you will see the 1N4000 series used extensively. There are a wide range of circuits used as the oscillator source. The Tx and Rx coils need to be identical and with 100 Watts you are asking quite a bit. Circuits I have seen average between 70% and 80% efficient and the latter is really reaching. Magnetic induction transfer of energy relying on air has quite a bit of loss even with the coils tightly packed together. The greater the distance the higher the number of inductor turns needed. 12 Volts 100 Watts you are looking at greater than 8 Amps on the secondary and even with a 12 Volt 8 Amp primary drive at 70% efficiency you would only get about 70 Watts out and I have never seen a wireless power transfer through an air core yet. If you could do it your secondary diodes would need chosen to handle the load. Anything 1N4000 is an amp.\n\nRon\n\n#### myaeaindrathein1996\n\nJoined Jun 11, 2021\n16\nI am currently retired and have not looked at specific components for more than a decades so my knowledge is somewhat out of date. I can take a look at the UF4002. BTW I'm not saying the parts you are considering won't work at all, I'm just saying you need to know what your are dealing with because efficiency is critical and you really can't afford to use parts that will defeat your purpose.\n\nEDIT: the datasheet is encouraging, and it lists the trr as 50 ns. going from 0.5 amp forward to 1 Amp reverse. There was a time (ca. 1987), that I would have killed for that level of performance.\n\nUF4001-UF4007 Fast Rectifiers (onsemi.com)\n\nI could not find a model for the UF4002, but there was on for the UF4007\n\nView attachment 242634\nThank you so much for your simulations and suggestions. I will firstly test with the diodes that I have (1N5819, Mbr1645). If not work, I will change with the ones you recommend.\n\n#### myaeaindrathein1996\n\nJoined Jun 11, 2021\n16\nThe diodes you show in your drawing should be fine and with a Google of \"wireless charging circuits\" you will see the 1N4000 series used extensively. There are a wide range of circuits used as the oscillator source. The Tx and Rx coils need to be identical and with 100 Watts you are asking quite a bit. Circuits I have seen average between 70% and 80% efficient and the latter is really reaching. Magnetic induction transfer of energy relying on air has quite a bit of loss even with the coils tightly packed together. The greater the distance the higher the number of inductor turns needed. 12 Volts 100 Watts you are looking at greater than 8 Amps on the secondary and even with a 12 Volt 8 Amp primary drive at 70% efficiency you would only get about 70 Watts out and I have never seen a wireless power transfer through an air core yet. If you could do it your secondary diodes would need chosen to handle the load. Anything 1N4000 is an amp.\n\nRon\nI used 2mm diameter solid copper wire, 13 turns and the ansys maxwell simulations show that coil self inductance is 18uH and mutual is 4uH. I used acrylic to fix the coils and the coils are almost touched (no air gap distance). The problem is that even though I increase the dc supply voltage to MOSFETs, the current is not increased at all (0.0mA). I don't know where my circuit has the problems.\n\n#### myaeaindrathein1996\n\nJoined Jun 11, 2021\n16\nS\na resistor, or more likely a pile of resistors is the answer.\n\nThese are normally inside a metal \"box\" so as not to break local rules and radiate,\nlocal authorities take very badly to jamming,\n\nthere even used to be one that every one used to us\nbut alas now long gone\n\n#### myaeaindrathein1996\n\nJoined Jun 11, 2021\n16\nYour schematic is missing a diode from the 15V supply to the VB pin of the IC.\nYour schematic is missing a diode from the 15V supply to the VB pin of the IC.\nI used Mbr1645 schottky diodes for boot strap.\n\n#### Martin_R\n\nJoined Aug 28, 2019\n103\nThere's a shut down pin on the ic shown on the datasheet. Is it connected correctly? I can't see reference to it on your circuit diagram","date":"2022-01-28 00:32:48","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.44840890169143677, \"perplexity\": 1459.1230031555344}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-05\/segments\/1642320305317.17\/warc\/CC-MAIN-20220127223432-20220128013432-00075.warc.gz\"}"} | null | null |
{"url":"http:\/\/experiment-ufa.ru\/derivative_of_7\/ln(x)","text":"# Derivative of 7\/ln(x)\n\n## Derivative of 7\/ln(x). Simple step by step solution, to learn. Simple, and easy to understand, so dont hesitate to use it as a solution of your homework.\n\nIf it's not what You are looking for type in the derivative calculator your own function and let us solve it.\n\n## Derivative of 7\/ln(x):\n\n(7\/ln(x))'((7)'*ln(x)-(7*(ln(x))'))\/((ln(x))^2)(0*ln(x)-(7*(ln(x))'))\/((ln(x))^2)(0*ln(x)-(7*(1\/x)))\/((ln(x))^2)(-7*x^-1)\/((ln(x))^2)`\nThe calculation above is a derivative of the function f (x)\n\n## Related pages\n\n12.25 as a fractionlog3x 4what is the hcf of 90 and 1209x 2-16prime factors of 3652sinxcosx5h 5tsinx cosx cos2x100-55common multiples of 2 and 5tan 2 x derivative3x 4y 16cos 2x sin x 030 000 pounds in dollarswhat is the derivative of sinxcos72solutions to inequalities calculator2cosx 1 04 5x6the prime factorization of 80yexpfraction subtraction calculatorsin 5xwrite 0.625 as a fraction in simplest form2sinxsimplify 2x-1what is the prime factorization of 205x3 y3simplify the square root of 147how to write a prime factorization3x2 x 43.14r2solve 2x2 12x 10keiseruniversity blackboard com5t lbgcf of 46 and 69finding least common denominator calculatorlcd of fractions calculatory 3sin 2x104-203-158gcf of 72 and 90factor x2-x-12roman numerals 1-100000what is the derivative of cos 2x12x squaredeasy 97.9prime factorization of 244derivative of tan2xgraph 3x 4y 12prime factorization of 728roman numeral 1995log5x 4factoring calculator with stepswhat is the prime factorization of 914 5x1 1 6 answercsc2x-1300-229the greatest common factor of 36 and 48fog equationsquadratic formula solver with stepswhat is the prime factorization of 252dividing fractions by fractions calculatorroman numerals 10000log02xy x yx 2y 5 graphlcm of four numberscospix 2 y 2 factorisewhat is 6.25 as a fraction in simplest form9x-7i 3 3x-7u solve for iprime factorization for 126square root of 1025lowest common multiple finderln918x5derive ln 2xprime factorization for 196prime factorization of 44what is the gcf of 60 and 72prime factorization for 125is902log base2","date":"2017-10-20 01:32:57","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5896347761154175, \"perplexity\": 9748.039954662396}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-43\/segments\/1508187823605.33\/warc\/CC-MAIN-20171020010834-20171020030834-00348.warc.gz\"}"} | null | null |
Кадриа́на Сагайда́к (; ) — канадская кёрлингистка из города Гимли, провинция Манитоба.
Участвует в соревнованиях смешанных пар с Колтоном Лоттом. Серебряный призёр Чемпионата Канады среди смешанных пар.
Достижения
: серебро (, ), бронза ().
Карьера
Кадриана Сагайдак добилась успеха в кёрлинге смешанных пар с бойфрендом Колтоном Лоттом. Их первым соревнованием стал Чемпионат Манитобы по кёрлингу среди смешанных пар 2018 года, который они выиграли и получили место на Чемпионате Канады по кёрлингу среди смешанных пар 2018. Этот дуэт был самым молодым на турнире и единственным, который не проиграл по групповом этапе. Однако в финале они проиграли со счетом 8–7 паре Лора Крокер и Кирк Майерс.
В сезоне 2018-19 команда Сагайдак / Лотт была представителем Канады на третьем этапе Кубка мира. Они выиграли турнир, получив право на участие в Гранд Финале. На Чемпионате Канады по кёрлингу среди смешанных пар 2019 команда вышла в полуфинал, в котором проиграла со счетом 7–6 команде Nancy Martin / Тайрел Гриффит.
Частная жизнь
Кадриана Сагайдак работает ассистентом врача-оптометриста в Oakley Vision Center. Она состоит в отношениях со своим партнером по смешанным парам Колтоном Лоттом.
Команды
Примечания
Ссылки
Кёрлингисты по алфавиту
Кёрлингисты Канады
Чемпионы Канады по кёрлингу | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,596 |
Q: ParseLiveQuery can't access Pointer object Hi I'm trying to fetch my object via ParseLiveQuery
I think ParseLiveQuery is not support Pointer Object.
Here is snippet my code.
Post.swift
import Foundation
import Parse
class Post: PFObject, PFSubclassing {
@NSManaged var postBy: PFUser?
@NSManaged var postText: String?
@NSManaged var postImg: PFFile?
static func parseClassName() -> String {
return "Post"
}
override class func query() -> PFQuery<PFObject>? {
//1
let query = PFQuery(className: Post.parseClassName())
query.whereKeyExists("objectId")
//2
query.includeKeys(["postBy"])
//3
query.order(byDescending: "createdAt")
return query
}
}
extension Post: FeedCellSupport {
var username:String?{
return postBy?["username"] as? String
}
var userImg:PFFile?{
return postBy?["profileImg"] as? PFFile
}
FeedVC.swif
let liveQueryClient = ParseLiveQuery.Client()
protocol FeedCellSupport {
var username:String?{ get }
var userImg:PFFile?{ get }
var postText: String? { get }
}
class FeedVC: UITableViewController, ShopDetailDelegate {
private var subscription: Subscription<Post>!
//Add friends and me
var postLiveQuery: PFQuery<Post> {
return (Post.query()?
.whereKeyExists("objectId")
.includeKeys(["postBy", "commentBy", "commentBy.commentBy"])
.order(byAscending: "createdAt")) as! PFQuery<Post>
}
var results = [Post]()
override func viewDidLoad() {
super.viewDidLoad()
subscription = liveQueryClient.subscribe(postLiveQuery).handleSubscribe { [weak self] (_) in
// Fetch the objects on subscription to not miss any
self?.fetchObjects()
}.handleEvent { [weak self] (_, event) in
self?.handleEvent(event: event)
}
}
I have a 2 questions.
1. ParseLiveQuery has returned PFObject like an REST results.
When I fetch object first time It works fine.
I mean I can get username and userImg data via findObjectBackground.
<Post: 0x6180000b43a0, objectId: w5qcfMCByF, localId: (null)> {
likeCount = 0;
postBy = "<PFUser: 0x6180000f4600, objectId: rgG7XfAYWj, localId: (null)>";
postImg = "<PFFile: 0x618000246ba0>";
postText = nice2MeetYous121;
sell = 0;
}
After received updated event then..I got an different style PFObject.
<Post: 0x6100000b3020, objectId: w5qcfMCByF, localId: (null)> {
"__type" = Object;
className = Post;
createdAt = "2016-11-19T12:37:30.896Z";
likeCount = 0;
postBy = {
"__type" = Pointer;
className = "_User";
objectId = rgG7XfAYWj;
};
postImg = {
"__type" = File;
name = "92aa66bfdcf5f70d1d277556bbd9d7ca_post.jpg";
url = "https://parsefiles.back4app.com/PlY72cbRxsOIXQ1qbJjaQtudZQU9HA8U2RIg2oE1/92aa66bfdcf5f70d1d277556bbd9d7ca_post.jpg";
};
postText = nice2MeetYous1211;
sell = 0;
updatedAt = "2016-11-21T14:34:11.338Z";
}
So I got an error message because Parse LiveQuery returned like REST.
2. When I had tried branch of "fix-object-decode" then It returned PFObject not REST style. But It also can't retrieve my Pointer Data directly.
ios ParseLiveQuery link branch->fix-object-decode
I had tested "fix-object-decode" branch.
It returned well formatted PFObject but It seems different results.
It is my original PFObject when I request via findObjectInBackGround()
<Post: 0x6080000b0800, objectId: w5qcfMCByF, localId: (null)> {
likeCount = 0;
postBy = "<PFUser: 0x6080000e3100, objectId: rgG7XfAYWj, localId: (null)>";
postImg = "<PFFile: 0x60800024c150>";
postText = nice2MeetYous1211;
sell = 0;
}
When I change postText then I got update event via live query but different.
<Post: 0x6100000b1be0, objectId: w5qcfMCByF, localId: (null)> {
likeCount = 0;
postBy = "<PFUser: 0x6100000e6900, objectId: rgG7XfAYWj, localId: (null)>";
postImg = "<PFFile: 0x61000025d1f0>";
postText = nice2MeetYous;
sell = 0;
}
As you can see..PFUser:0x6080000e3100 and PFFile: 0x60800024c150 has changed to PFUser: 0x6100000e6900, PFFile: 0x61000025d1f0
Anyway I can't fetchObject when I received events.
Is this problem about live query or parse-server side problem?
Terminating app due to uncaught exception 'NSInternalInconsistencyException', reason: 'Key "username" has no data. Call fetchIfNeeded before getting its value.'
I added some code to avoid fetchIfNeeded errors.
Here is my snippet code.
extension Post: FeedCellSupport {
var username:String?{
do {
try postBy?.fetchIfNeeded()
} catch _ {
print("There was an error")
}
return postBy?["username"] as? String
}
var userImg:PFFile?{
do {
try postBy?.fetchIfNeeded()
} catch _ {
print("There was an error")
}
return postBy?["profileImg"] as? PFFile
}
Now It works fine but...system says "Warning: A long-running operation is being executed on the main thread. "
I think it is not bestway..
Could you anyone helping me?
A: I noticed that parse server is not support includekey.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,771 |
\section{Introduction}
\label{sec:introduction}
Missing data is a common problem in data analysis. For instance, respondents in a survey may refuse to fill in the income, or sensors may fail and need to be replaced. These imply missing data challenges.
Most of the existing methods \cite{marivate2007autoencoder, buuren2010mice, kim2005missing, mazumder2010spectral, candes2009exact, rahman2016missing, burgette2010multiple, costa2018missing} require revisiting the data multiple times before yielding convergence and are computationally expensive in high-dimensional settings.
In this paper, we introduce a novel approach, namely DPER (\textit{Direct Parameter Estimation for Randomly Missing Data}), that can compute the maximum likelihood estimators (MLEs) for both mean and covariance matrices of a one-class/multiple-class data set. For a multiple-class data set, we develop solutions for both cases when all classes' covariance matrices are assumed to be equal or not. Since the computation is direct, our approach does not require many iterations through the data, promising a faster estimation speed. For the same reason, unlike many other imputations methods that may run slower when there are more missing entries, our approach is more rapid when there are more missing entries. Yet, experiments show that the resulting estimates are far superior to many state-of-the-art methods. In addition, we do not assume multivariate normality as presented in \cite{NGUYEN20211}. Instead, we use a milder assumption of bivariate normality in each pair of features. Lastly, it is worth noting that normal distribution is a widely used approximator due to the Central Limit Theorem when the data's distribution is unknown. Therefore, even under the fore-mentioned mild assumption, our approach is robust enough to be applied in various applications, as illustrated in our experiments later.
Finally, the contributions of our work can be summarized as follows:
\begin{enumerate}[(i)]
\item We compute the MLEs directly for the mean and covariance matrix of one-class/multiple-class randomly missing data. Therefore, we provide an approximation to the underlying distribution of the data.
\item We provide algorithms to compute the MLEs from the data that are suitable for both small and large data sets.
\item The experimental results show that our algorithms can outperform state-of-the-art methods in error rates, speed, and memory requirements.
\item Our experiments on large data sets show that while iterative methods may not handle the missing data problem for big data sets, our approach can still find the parameter rapidly without requiring extensive memory and computation time.
We discuss the potential drawbacks of our methods and future research directions.
\end{enumerate}
The rest of this paper can be organized as follows. Section \ref{sec:related_work} introduces an overview of the current researches related to the problem. In Section \ref{sec: without}, we present the formulas and algorithms for computing the means and covariance matrix for a randomly missing data set that only consists of a single class and when there are multiple classes without assuming the equal covariance matrices are equal. Next, we present the estimation of the parameters under the assumption of equal covariance matrices in a multiple-class setting. Finally, we illustrate the power of our approach via experiments in Section \ref{exper} and discuss the implications of the experimental results. The paper ends with our conclusion and future works in Section \ref{sec:conclusion}.
\section{Related works}
\label{sec:related_work}
Various methods have been developed to tackle the problem of missing data. They can be divided into several subcategories. The first category includes all techniques that are based on matrix completion such as Polynomial Matrix Completion \cite{fan2020polynomial}, SOFT-IMPUTE \citep{mazumder2010spectral}, and Nuclear Norm Minimization \citep{candes2009exact}.
The second category consists of regression-based and least-square techniques, such as, CBRL and CBRC \cite{m2020cbrl},
multiple imputation by chained equation (MICE)\citep{buuren2010mice}, local least squares imputation \citep{kim2005missing}, and least trimmed squares imputation \citep{templ2011iterative}.
The third one consists of tree-based techniques such as sequential regression trees \citep{burgette2010multiple}, missForest \cite{stekhoven2012missforest}, DMI algorithm \cite{rahman2013missing}, and C4.5 algorithm \citep{fortes2006inductive} that are applied for this problem. Next, the fourth category contains clustering-based techniques such as Fuzzy c-means clustering \citep{aydilek2013hybrid}, K-nearest neighbor imputation (KNN)\citep{garcia2010pattern}, kEMI and $\text{kEMI}^+$ \citep{razavi2020similarity}, imputation using fuzzy neighborhood density-based clustering \citep{razavi2016imputation}, imputation using Hybrid K-Means and Association Rules\citep{chhabra2018missing}, and evolutionary clustering method \cite{gautam2015data}.
Also, one can find techniques that are based on extreme learning, for example, AAELM \cite{gautam2015data}, extreme learning machine multiple imputation \cite{sovilj2016extreme}, or Bayesian approaches, which are Naive Bayesian imputation \citep{garcia2005naive}, Bayesian network imputation \citep{hruschka2007bayesian}, and Bayesian principal component analysis-based imputation\citep{audigier2016multiple}.
In addition, deep learning techniques also form another dominant class of imputation methods. Those techniques include multiple imputations using Deep Denoising Autoencoders \citep{gondara2017multiple}, imputation via Stacked Denoising Autoencoders \citep{costa2018missing}, imputation via Adversarially-trained Graph Convolutional Networks \citep{spinelli2020missing}, a Swarm Intelligence-deep neural network \citep{leke2016missing}, combining Gravitational search algorithm with a deep-autoencoder \citep{garg2018dl}, Generative Adversarial Multiple Imputation Network \cite{yoon2020gamin}, etc. Hence, they are not applicable to small data sets.
Last but not least, the final category consists of fuzzy imputation techniques
such as the evolving granular fuzzy-rule-based model
\cite{garcia2019evolvable}, \cite{garcia2019incremental}, fuzzy c-means clustering \citep{aydilek2013hybrid},
fuzzy clustering-based EM imputation\citep{rahman2016missing}, decision trees and fuzzy clustering with iterative learning (DIFC) \cite{nikfalazar2020missing},
and imputation using fuzzy neighborhood density-based clustering \citep{razavi2016imputation}.
Up to now, there have been several attempts to estimate the parameters directly from the data \citep{anderson1957maximum,fujisawa1995note, NGUYEN20211}. Yet, to our knowledge, these approaches rely on the assumption that the data follow a multivariate normal distribution and can only be used for monotone missing data. On the other hand, our works only assume pairwise normality (i.e., each pair of features follows a bivariate normal distribution) and work for randomly missing data in general.
For the rest of this paper, $\hat{\theta}$ denotes the maximum likelihood estimate of a parameter $\theta$, $A$' denotes the transpose of a matrix $A$, $B^{-1}$ indicates the inverse of a square matrix $B$.
\section{Methodology}\label{sec: without}
This section will describe our proposed approaches to find the maximum likelihood estimators for a randomly missing data set that only consists of a single class and for a multiple-class data set without the assumption of equal covariance matrices.
\subsection{Single-class DPER algorithm}\label{sec:1class-method}
First, we have the following results:
\begin{theorem}\label{bivariatemle_single}
Assume that we have a set of i.i.d observations from a bivariate normal distribution with mean
\begin{equation}
\boldsymbol {\mu } = \begin{pmatrix}
\mu_1\\ \mu_2
\end{pmatrix}
\end{equation}
and covariance matrix
\begin{equation}
\boldsymbol {\Sigma } = \begin{pmatrix}
\sigma_{11}&\sigma_{12}\\
\sigma _{21} & \sigma _{22}
\end{pmatrix}.
\end{equation}
and arrange the data into the following pattern
\begin{equation}\label{blform}
\boldsymbol{x} = \begin{pmatrix}
{x}_{11} & ... & {x}_{1m}&{x}_{1m+1}&...&{x}_{1n}&*&...&*\\
{x}_{21}&...&{x}_{2m}& *& ...& *& {x}_{2n+1}&...&{x}_{2l}
\end{pmatrix}.
\end{equation}
Note that each column represents an observation, and $x_{ij} \in \mathbb{R}$ is an entry, i.e., each observation has two features.
Let $L$ be the likelihood of the data and
\begin{align}
s_{11} &= \sum_{j=1}^{m}(x_{1j}-\hat{\mu}_1)^2 ,\\
s_{12} &= \sum_{j=1}^{m}(x_{2j}-\hat{\mu}_2)(x_{1j}-\hat{\mu}_1),\\
s_{22} &= \sum_{j=1}^{m}(x_{2j}-\hat{\mu}_2)^2.
\end{align}
Then, the resulting estimators obtained by maximizing $L$ w.r.t $\mu_1, \sigma_{11},\mu_2, \sigma_{22}$, and $\sigma_{12}$ are:
\begin{align*}
\hat{\mu}_1 & = \frac{1}{n}\sum_ {j=1}^{n}x_{1j},\;\;
\hat{\mu}_2 = \frac{\sum_ {j=1}^{m}x_{2j}+ \sum_ {j=n+1}^{l}x_{2j}}{m+l-n}, \\
\hat{\sigma}_{11} & = \frac{\sum_ {j=1}^n(x_{1j}-\hat{\mu}_1)^2}{n},\\
\hat{\sigma}_{22} & = \frac{\sum_ {j=1}^{m}(x_{2j}-\hat{\mu}_2)^2+ \sum_ {j=n+1}^{l}(x_{2j}-\hat{\mu}_2)^2}{m+l-n},
\end{align*}
and $\hat{\sigma} _{12}$, where $\hat{\sigma} _{12}$ is the maximizer of:
\begin{equation}\label{etacov-sing}
\eta = C-\frac{1}{2}m\log \left(\sigma_{22}-\frac{\sigma_{12}^2}{\sigma_{11}}\right)
- \frac{1}{2} \left( s_{22} - 2\frac{\sigma_{12}}{\sigma_{11}} s_{12}+\frac{\sigma_{12}^2}{\sigma _{11}^2}s_{11}\right)\left(\sigma_{22}-\frac{\sigma_{12}^2}{\sigma_{11}}\right)^{-1}.
\end{equation}
\end{theorem}
It is important to note that the estimates for $\mu_1, \mu_2,\sigma_{11}, \sigma_{22}$ are the corresponding sample means and uncorrected sample variance (where the denominator is divided by the sample size) of the first/second feature after dropping the missing entries. We have the following theorem related to the existence of $\hat{\sigma}_{12}$.
\begin{theorem}\label{unique-single}
In Equation (\ref{etacov-sing}), solving
\begin{equation}\label{der01}
\frac{d\eta}{d\sigma_{12}} = 0
\end{equation}
can be reduced to solving the following third-degree polynomial
\begin{equation}\label{eqExist0}
\small
s_{12} \sigma_{11} \sigma_{22} + {\left( \sum_{g=1}^Gm_g\sigma_{11} \sigma_{22} - s_{22}\sigma_{11} - s_{11}\sigma_{22} \right)}\sigma_{12} + s_{12}\sigma_{12}^2- (\sum_{g=1}^Gm_g)\sigma_{12}^3,
\end{equation}
which has at least one real root. In addition, the global maximum is a real solution to that equation, provided that
\begin{equation}
-\frac{s_{22}\sigma_{11}+s_{11}\sigma_{22}}{2\sqrt{\sigma_{11}\sigma_{22}}} \neq
s_{12} \neq \frac{s_{22}\sigma_{11}+s_{11}\sigma_{22}}{2\sqrt{\sigma_{11}\sigma_{22}}}.
\end{equation}
\end{theorem}
The proof of Theorems \ref{bivariatemle_single} and \ref{unique-single} follow directly as corollaries of Theorems \ref{bivariatemle} and \ref{unique-multiple}, the proofs of which are given in \ref{existence} and \ref{proof2mle}, respectively. Based on the above theorem, we have the following algorithm:
\begin{Algorithm}{(DPER algorithm for single-class randomly missing data)}
\textit{Input:} a data set of $p$ features.
\textit{Ouput:} $\hat{\boldsymbol {\mu}}$ and $\hat{\boldsymbol {\Sigma}}=(\sigma_{ij})_{i,j=1}^p$.
\begin{enumerate}
\item Estimate $\boldsymbol{\mu}$: $\hat{\mu}_i$ is the sample mean of all the available entries in the $i^{th}$ feature.
\item Estimate the diagonal elements of $\boldsymbol {\Sigma}$: $\hat{\sigma}_{ii}$ is the uncorrected sample variance of all the available entries in the $i^{th}$ feature.
\item For $1\le i\le p$:
\;\;\; For $1\le j\le i$:
\;\;\;\;\;\; Compute $\hat{\sigma}_{ij}$ based on Equation (\ref{der01}). If there are two solutions maximizing the function, choose the one closest to the estimate based on case deletion method.
\end{enumerate}
\end{Algorithm}
Recall that in the \textit{case deletion method}, the sample that has one or more missing values is deleted. In this setting, during the estimation of $\hat{\sigma}_{ij}$, we delete any $(i,j)^{th}$ pair that has at least one missing entry.
\subsection{Multiple-class DPER algorithm without the assumption of equal covariance matrices}\label{sec: multiple-class-DPER-without}
When the covariance matrices of all classes are not assumed to be equal, the mean and covariance matrix for each class can be estimated separately by applying the \textit{DPER algorithm for single class randomly missing data} to the data from each class.
\subsection{Multiple-class DPER algorithm under the assumption of equal covariance matrices}\label{mgmle}
In the previous section, we have described our proposed approaches to find the maximum likelihood estimators for a randomly missing data set that only consists of a single class and a multiple-class data set without the assumption of equal covariance matrices. Yet, in many cases, for a multiple-class data set, it may be more desirable to assume that the covariance matrices are equal. Those cases may happen when the number of samples per class is small or in linear discriminant analysis. In what follows, we tackle the multiple-class problem under the assumption of equal covariance matrices.
\begin{theorem}\label{bivariatemle}
Assume that there is a data set with $G$ classes, where each sample from class $g^{th} \;( 1\le g\le G)$ follows a bivariate normal distribution with mean
\begin{equation}
\boldsymbol {\mu }^{(g)} = \begin{pmatrix}
\mu_1^{(g)}\\ \mu_2^{(g)}
\end{pmatrix},
\end{equation}
and covariance matrix
\begin{equation}
\boldsymbol {\Sigma } = \begin{pmatrix}
\sigma_{11}&\sigma_{12}\\
\sigma _{21} & \sigma _{22}
\end{pmatrix}.
\end{equation}
We arrange the data from each class into the following pattern
\begin{equation}\label{blform}
\boldsymbol{x}^{(g)} = \begin{pmatrix}
{x}_{11}^{(g)} & ... & {x}_{1m_g}^{(g)}&{x}_{1m_g+1}^{(g)}&...&{x}_{1n_g}^{(g)}&*&...&*\\
{x}_{21}^{(g)}&...&{x}_{2m_g}^{(g)}& *& ...& *& {x}_{2n_g+1}^{(g)}&...&{x}_{2l_g}^{(g)}
\end{pmatrix}.
\end{equation}
Note that each column represents an observation and $x_{ij} \in \mathbb{R}$, i.e., each observation has only two features.
Let $L$ be the likelihood of the data and
\begin{align}
A &= \sum_{g=1}^Gm_g,\\
s_{11} &= \sum_{g=1}^G\sum_{j=1}^{m_g}(x_{1j}^{(g)}-\hat{\mu}_1^{(g)})^2
,\\
s_{12} &= \sum_{g=1}^G\sum_{j=1}^{m_g}(x^{(g)}_{2j}-\hat{\mu}_2^{(g)})(x_{1j}^{(g)}-\hat{\mu}_1^{(g)}),\\
s_{22} &= \sum_{g=1}^G\sum_{j=1}^{m_g}(x^{(g)}_{2j}-\hat{\mu}_2^{(g)})^2.
\end{align}
Then, the resulting estimators obtained by maximizing $L$ w.r.t $\mu_1^{(g)}, \sigma_{11},\mu_2^{(g)}$, $\sigma_{22},\sigma_{12}$ are:
\begin{align*}
\hat{\mu}_1^{(g)} & = \frac{1}{n_g}\sum_ {j=1}^{n_g}x_{1j}^{(g)},\;\;
\hat{\mu}_2^{(g)} = \frac{\sum_ {j=1}^{m_g}x_{2j}^{(g)}+ \sum_ {j=n_g+1}^{l_g}x_{2j}^{(g)}}{m_g+l_g-n_g}, \\
\hat{\sigma}_{11} & = \frac{\sum_{g=1}^G\sum_ {j=1}^{n_g}(x_{1j}^{(g)}-\hat{\mu}_1^{(g)})^2}{\sum_{g=1}^G n_g},\\
\hat{\sigma}_{22} & = \frac{\sum_{g=1}^G[\sum_ {j=1}^{m_g}(x_{2j}^{(g)}-\hat{\mu}_2^{(g)})^2+ \sum_ {j=n_g+1}^{l_g}(x_{2j}^{(g)}-\hat{\mu}_2^{(g)})^2]}{\sum_{g=1}^G(m_g+l_g-n_g)},
\end{align*}
$\hat{\sigma} _{12}$, where $\hat{\sigma} _{12}$ is the maximizer of:
\begin{equation}\label{etacov}
\eta(\sigma_{12}) = C-\frac{A}{2}\log \left(\sigma_{22}-\frac{\sigma_{12}^2}{\sigma_{11}}\right)
- \frac{s_{22} - 2\frac{\sigma_{12}}{\sigma_{11}} s_{12}+\frac{\sigma_{12}^2}{\sigma _{11}^2}s_{11}} {2\left(\sigma_{22}-\frac{\sigma_{12}^2}{\sigma_{11}}\right)}.
\end{equation}
\end{theorem}
This means the estimate for $\mu_1^{(g)}, \mu_2^{(g)},\sigma_{11}, \sigma_{22}$ are the corresponding sample means and uncorrected sample variance of the first/second feature after dropping the missing entries. We also have the following theorem regarding $\hat{\sigma}_{12}$,
\begin{theorem}\label{unique-multiple}
For Equation (\ref{etacov}), solving
\begin{equation}\label{der02}
\frac{d\eta}{d\sigma_{12}} = 0
\end{equation}
can be reduced to finding the roots of the following third-degree polynomial
\begin{equation}\label{eqExist}
s_{12} \sigma_{11} \sigma_{22} + {\left( \sigma_{11} \sigma_{22} A - s_{22}\sigma_{11} - s_{11}\sigma_{22} \right)}\sigma_{12} + s_{12}\sigma_{12}^2- A\sigma_{12}^3,
\end{equation}
which has at least one real root. Moreover, the global maximum is a real solution to that equation, provided that
\begin{equation}
-\frac{s_{22}\sigma_{11}+s_{11}\sigma_{22}}{2\sqrt{\sigma_{11}\sigma_{22}}} \neq
s_{12} \neq \frac{s_{22}\sigma_{11}+s_{11}\sigma_{22}}{2\sqrt{\sigma_{11}\sigma_{22}}}.
\end{equation}
\end{theorem}
The proof of this theorem can be given in \ref{existence}. In addition, the proof of Theorem \ref{bivariatemle} is provided in \ref{proof2mle}. It makes use of the following lemma, whose proof is available in \ref{sec:appendix_A}.
\begin{lemma}\label{lem1}
Suppose that we have a data set that comes from $G$ classes, where the observations from the $g^{th}$ class follow multivariate normal distribution with mean $\tau^{{(g)}}$ and covariance matrix $\Delta$. Let the observations of the $g^{th}$ class be $\boldsymbol{u}^{(g)}_1,\boldsymbol{u}^{(g)}_2,...,\boldsymbol{u}^{(g)}_{n_g}$. Then, the MLEs of $\tau^{{(g)}}$ is the sample class mean $\bar{\mathbf{u} }^{(g)}$, and the MLE of $\Delta$ is
\begin{equation}
\hat{\Delta} = \frac{1}{\sum_{g=1}^G n_g} \sum_{g=1}^G \sum_{j=1}^{n_g}
(\boldsymbol{u} _j^{(g)}-\bar{\boldsymbol{u}}^{(g)})
(\boldsymbol{u} _j^{(g)}-\bar{\boldsymbol{u}}^{(g)})'.
\end{equation}
\end{lemma}
Based on Theorem \ref{bivariatemle}, we have the following algorithm.
\begin{Algorithm}{(DPER algorithm for multiple -class randomly missing data)}
\textit{Input:} a data set of $G$ classes, $p$ features.
\textit{Ouput:} $\hat{\boldsymbol{\mu}}^{(g)}, \hat{\boldsymbol{\Sigma}}=(\sigma_{ij})_{i,j=1}^p$
\begin{enumerate}
\item Estimate $\boldsymbol{\mu}^{(g)}$: $\hat{\mu}_i^{(g)}$ is the mean of all the available entries in the $i^{th}$ feature.
\item Estimate the diagonal elements of $\boldsymbol{\Sigma}$: $\hat{\sigma}_{ii}$ is the uncorrected sample variance of all the available entries in the $i^{th}$ feature.
\item For $1\le i\le p$:
\;\;\; For $1\le j\le i$:
\;\;\;\;\;\; Compute $\hat{\sigma}_{ij} = \hat{\sigma}_{ji}$ based on Equation (\ref{der02}). If there are two solutions maximizing the function, choose the one that is closest to the estimate based on the case deletion method.
\end{enumerate}
\end{Algorithm}
\begin{Remarks}
We have the following remarks about our estimates:
\begin{itemize}
\item The computation is done on each pair of features. Therefore, we only need the assumption of bivariate normality on each pair of features instead of multivariate normality on each observation as in EPEM \cite{NGUYEN20211}.
\item The computation is done separately for each $\sigma_{ij}$. As a result, our method is also applicable to the problems where the number of features is much higher than the sample size.
\item Since maximum likelihood estimates are asymptotic (see \cite{casella2002statistical}), we can ensure that the resulting estimates of the our algorithm are asymptotic, i.e.,
\begin{equation}
\hat{\boldsymbol {\mu } }\overset{p}{\rightarrow} \boldsymbol {\mu }, \text{and} \;\;\; \hat{\boldsymbol {\Sigma } }\overset{p}{\rightarrow} \boldsymbol {\Sigma },
\end{equation}
where $\overset{p}{\rightarrow}$ denotes convergence in probability for each element of the matrix $\hat{\boldsymbol {\mu }}$ or $\hat{\boldsymbol {\Sigma }}$.
\end{itemize}
\end{Remarks}
\section{Experiments}\label{exper}\FloatBarrier
This section describes all data sets, the implementation of the proposed techniques, and experimental results in detail.
\subsection{Settings}
To illustrate the efficiency of our algorithm, we compare the results of the proposed method the following methods: SOFT-IMPUTE \citep{mazumder2010spectral}, by Nuclear Norm Minimization \citep{candes2009exact}, MissForest \citep{stekhoven2012missforest}
and Multiple Imputation by Chained Equation (MICE) \citep{buuren2010mice}.
We implement these methods via packages \textit{fancyimpute}\footnote{\url{https://pypi.org/project/fancyimpute/}}, \textit{impyute}\footnote{\url{https://pypi.org/project/impyute/}}, \textit{missingpy}\footnote{\url{https://pypi.org/project/missingpy/}}, and \textit{scikit-learn}\footnote{\url{https://scikit-learn.org/}}.
When using iterative methods for small data sets, we use the default options in the packages \textit{fancyimpute, sklearn} and \textit{impyute}. Specifically, the maximum number of iterations is 100 for SOFT-IMPUTE, MICE, Nuclear Norm Minimization, and 10 for MissFores
. For big data sets (MNIST \& Fashion MNIST), the maximum number of iterations for MICE and Nuclear Norm Minimization are reduced to 10 instead due to expensive memory and time requirements.
The experiments on small data sets are ran directly on \textit{Google Colaboratory}\footnote{\url{https://colab.research.google.com/}}. Meanwhile, the experiments on large data sets are run on a Linux machine with 130 GB RAM, 40 processing units. We terminate an experiment if no result is produced after five hours of running or when having out-of-memory issues, and denote this as NA in the result tables (Tables \ref{table2} and \ref{table3}).
\subsection{Datasets}
\begin{table}
\caption{Descriptions of data sets used in the experiments}
\centering
\label{tab1}
\scalebox{0.82}{
\begin{tabular}{|c|c|c|c|}
\hline
\textbf{data set} & \textbf{\# Classes} & \textbf{ \# Features} & \textbf{\# Samples} \\\cline{1-4}
{Iris}& 3 & 4 & 150 \\ \hline
{Wine}& 3 & 13 & 178 \\ \hline
{Seeds} & 3 & 7 & 210 \\ \hline
{Inosphere} & 2 & 34 {($32^*$)} & 351 \\
\hline
{{MNIST}} & 10 & {$784(649^*)$} & 70000\\
\hline {{Fashion MNIST}} & 10 & $784$ & 70000\\
\hline
\end{tabular}}
\end{table}
We perform the experiments on the following data sets from the Machine Learning Database Repository at the University of California, Irvine \citep{Dua:2019}: Iris, Wine, Seeds, and Ionosphere. Besides, we do experiments on two large data sets: Fashion MNIST \cite{xiao2017fashion} and MNIST\cite{lecun1998mnist}. Fashion MNIST is a large data set of clothing images, consisting of 60000 training images and 10000 testing images of size $28\times 28$, and MNIST is a data set of handwritten digits, also having 60000 training images and 10000 testing images of size $28\times 28$. Each of these two data sets has ten labels.
Table \ref{tab1} shows a summary of all data sets used in the experiment. For each data set, we normalize by removing the mean and scaling to unit variance all features. We delete the first column for Ionosphere, where the values are the same within one of the classes, and the second column, where all entries are 0. Lastly, for the MNIST, we delete 135 columns with no more than ten nonzero values (Note that we have ten classes. If one class has a column of all zeros, then the sample covariance matrix for that class is a degenerate matrix.)
\subsection{Evaluation Metrics}
For evaluation, we use the following metric \cite{NGUYEN20211}, which is the sum of the average difference of each entry in the mean/common covariance matrix.
\begin{equation}
r = \frac{||\boldsymbol {\mu } -\boldsymbol {\hat{\mu}}||_F }{n_{\boldsymbol {\mu } }}
+\frac{||\boldsymbol {\Sigma
} -\boldsymbol {\hat{\Sigma}}||_F }{n_{\boldsymbol {\Sigma } }},
\end{equation}
where $||.||$ is the Frobenius norm; $\hat{\boldsymbol {\mu } }, \hat{\boldsymbol {\Sigma } }$ are estimated values derived from DPER for $\boldsymbol {\mu } , \boldsymbol {\Sigma } $ respectively; ${n_{\boldsymbol {\mu } }}$, ${n_{\boldsymbol {\Sigma } }}$ are the corresponding number of entries in $\boldsymbol {\mu }, \boldsymbol {\Sigma }$ and the ground truth $\boldsymbol {\mu }, \boldsymbol {\Sigma }$ are calculated from the full data without missing values (because we do not know the true value of $\boldsymbol {\mu }, \boldsymbol {\Sigma }$). Note that unlike the mean square error, this evaluation measure takes into account the number of entries in the means and the covariance matrix instead.
\begin{table}
\caption{Parameters estimation errors without equal covariance matrix assumption}\label{table2}
\centering
\scalebox{0.82}{
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
\textbf{data set} & \textbf{\makecell{Missing\\Rate(\%)}} & \textbf{DPER} & \textbf{MICE} & \textbf{\makecell{SOFT-\\IMPUTE}} & \textbf{\makecell{Nuclear\\Norm}} & \textbf{MissForest} \\\hline
Seeds & \makecell{20\%\\35\%\\50\%\\65\%\\80\%} & \makecell{{\bf0.004}\\{\bf0.008}\\{\bf0.007}\\{\bf0.009}\\{\bf0.009}} &
\makecell{{\bf0.004}\\0.009\\0.01\\0.017\\0.025} & \makecell{0.007\\0.015\\0.016\\0.025\\0.028} & \makecell{0.522\\0.517\\0.459\\0.489\\0.486} & \makecell{0.52\\0.543\\0.504\\0.607\\0.647} \\ \hline
Iris & \makecell{20\%\\35\%\\50\%\\65\%\\80\%} & \makecell{{\bf0.007}\\{\bf0.009}\\{\bf0.006}\\{\bf0.013}\\{\bf0.024}} &
\makecell{0.009\\0.015\\0.017\\0.033\\0.035} & \makecell{0.013\\0.025\\0.026\\0.049\\0.049} & \makecell{0.693\\0.665\\0.597\\0.672\\0.616} & \makecell{0.71\\0.857\\0.812\\0.998\\0.951} \\ \hline
Wine & \makecell{20\%\\35\%\\50\%\\65\%\\80\%} & \makecell{{\bf0.005}\\{\bf0.009}\\{\bf0.008}\\{\bf0.012}\\{\bf0.013}} &
\makecell{{\bf0.005}\\0.01\\0.011\\0.014\\0.018} & \makecell{0.006\\0.012\\0.016\\0.023\\0.025} & \makecell{0.27\\0.256\\0.239\\0.229\\0.215} & \makecell{0.288\\0.277\\0.276\\0.304\\0.286} \\ \hline
Ionosphere & \makecell{20\%\\35\%\\50\%\\65\%\\80\%} & \makecell{{\bf0.003}\\{\bf0.004}\\0.006\\0.007\\{\bf0.008}} &
\makecell{0.004\\0.005\\{\bf0.005}\\{\bf0.006}\\0.01} & \makecell{{\bf0.003}\\0.005\\{\bf0.005}\\0.007\\0.009} &
\makecell{0.67\\0.615\\0.57\\0.531\\0.511} & \makecell{0.717\\0.704\\0.693\\0.688\\0.682} \\ \hline
MNIST & \makecell{20\%\\35\%\\50\%\\65\%\\80\%} &
\makecell{{\bf0.4e-4}\\{\bf0.5e-4}\\{\bf0.7e-4}\\{\bf0.8e-4}\\{\bf0.9e-4}}& \makecell{NA\\NA\\NA\\NA\\NA} &
\makecell{0.5e-4\\0.9e-4\\1.4e-4\\2e-4\\2.5e-4} &
\makecell{NA\\NA\\NA\\NA\\NA} &
\makecell{NA\\NA\\NA\\NA\\NA} \\ \hline
Fashion MNIST & \makecell{20\%\\35\%\\50\%\\65\%\\80\%} &
\makecell{{\bf0.3e-4}\\{\bf0.4e-4}\\{\bf0.5e-4}\\{\bf0.6e-4}\\{\bf0.8e-4}}& \makecell{NA\\NA\\NA\\NA\\NA} &
\makecell{0.4e-4\\0.7e-4\\0.9e-4\\1.3e-4\\1.6e-4} &
\makecell{NA\\NA\\NA\\NA\\NA} &
\makecell{NA\\NA\\NA\\NA\\NA} \\ \hline
\end{tabular}}
\end{table}
\begin{table}
\caption{Parameters estimation errors under the equal covariance matrix assumption}\label{table3}
\centering
\scalebox{0.82}{
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
\textbf{data set} & \textbf{\makecell{Missing\\Rate(\%)}} & \textbf{DPER} & \textbf{MICE} & \textbf{\makecell{SOFT-\\IMPUTE}} & \textbf{\makecell{Nuclear\\Norm}} & \textbf{MissForest} \\\hline
Seeds & \makecell{20\%\\35\%\\50\%\\65\%\\80\%} & \makecell{0.004\\0.007\\{\bf0.009}\\{\bf0.008}\\{\bf0.014}} &
\makecell{{\bf0.003}\\{\bf0.006}\\0.013\\0.014\\0.034} & \makecell{0.005\\0.01\\0.02\\0.024\\0.033} & \makecell{0.005\\0.01\\0.019\\0.023\\0.025} & \makecell{0.004\\0.008\\0.011\\0.016\\0.019} \\ \hline
Iris & \makecell{20\%\\35\%\\50\%\\65\%\\80\%} & \makecell{{\bf0.008}\\{\bf0.01}\\{\bf0.012}\\{\bf0.01}\\{\bf0.016}} &
\makecell{{\bf0.008}\\0.018\\0.029\\0.03\\0.049} & \makecell{0.014\\0.029\\0.043\\0.045\\0.069} & \makecell{0.014\\0.028\\0.04\\0.042\\0.061} & \makecell{0.01\\0.017\\0.021\\0.037\\0.042} \\ \hline
Wine & \makecell{20\%\\35\%\\50\%\\65\%\\80\%} & \makecell{{\bf0.005}\\{\bf0.006}\\{\bf0.009}\\{\bf0.009}\\{\bf0.012}} &
\makecell{0.006\\0.009\\0.01\\0.014\\0.021} & \makecell{0.007\\0.011\\0.016\\0.021\\0.025} & \makecell{0.007\\0.011\\0.015\\0.02\\0.023} & \makecell{{\bf0.005}\\0.007\\0.01\\0.013\\0.017} \\ \hline
Ionosphere & \makecell{20\%\\35\%\\50\%\\65\%\\80\%} & \makecell{0.004\\0.005\\0.006\\0.008\\{\bf0.008}} & \makecell{{\bf0.003}\\{\bf0.004}\\0.006\\{\bf0.007}\\0.01} &
\makecell{{\bf0.003}\\{\bf0.004}\\0.006\\0.008\\0.009} & \makecell{{\bf0.003}\\{\bf0.004}\\0.006\\{\bf0.007}\\0.009} &
\makecell{{\bf0.003}\\{\bf0.004}\\{\bf0.005}\\{\bf0.007}\\{\bf0.008}} \\ \hline
MNIST & \makecell{20\%\\35\%\\50\%\\65\%\\80\%} &
\makecell{0.4e-4\\0.5e-4\\{\bf0.6e-4}\\0.8e-4\\1e-4}&
\makecell{NA\\NA\\NA\\NA\\NA} &
\makecell{{\bf0.3e-4}\\{\bf0.4e-4}\\{\bf0.6e-4}\\{\bf0.7e-4}\\{\bf0.9e-4}} &
\makecell{NA\\NA\\NA\\NA\\NA} &
\makecell{NA\\NA\\NA\\NA\\NA} \\ \hline
Fashion MNIST & \makecell{20\%\\35\%\\50\%\\65\%\\80\%} &
\makecell{{\bf0.3e-4}\\{\bf0.4e-4}\\{\bf0.5e-4}\\{\bf0.6e-4}\\{\bf0.7e-4}}& \makecell{NA\\NA\\NA\\NA\\NA} & \makecell{0.4e-4\\0.7e-4\\1e-4\\1.3e-4\\1.7e-4} &
\makecell{NA\\NA\\NA\\NA\\NA} &
\makecell{NA\\NA\\NA\\NA\\NA} \\ \hline
\end{tabular}}
\end{table}
\subsection{Results and Discussion}
Noticeably, we do not conduct any experiment about single class randomly missing data. The reason is that the multiple-class problem assuming equal covariance matrices problem boils down to one-class sub-problems as explained in Section \ref{sec: without}.
Table~\ref{table2} shows that without the assumption of equal covariance matrices, DPER gives the best result on every data set except for the Ionosphere. Interestingly, there is little distinction between DPER with MICE and SOFT-IMPUTE at lower missing rates, but the higher the missing rate, the better DPER performs against its peers. Considering the Seeds data set, for example, at $20\%$ missing rate, DPER gives the same best $0.004$ error rate as MICE, but at $80\%$ missing rate, the $0.009$ error rate of DPER is less than half of the others.
From Table~\ref{table3}, we see that under the equal covariance assumption, DPER gives the best results on all of the missing rates on every data sets except for Ionosphere and MNIST. Still, for Ionosphere and MNIST, DPER's performance is competitive against other approaches. When it does not perform best, the best method can only improve slightly than DPER (the maximum difference is $0.001$ for Ionosphere and $0.1e-4$ for MNIST). Again, there is little distinction between DPER with other approaches at lower missing rates, but the higher the missing rate, the better DPER performs against its peers. For instance, at $20\%$ missing rate in the Iris data set, the best error rate $0.008$ of DPER is equal to MICE, but at $80\%$ missing rate, the $0.016$ error rate of DPER is less than half of the rest.
It is worth noting whether to assume the covariance matrices are equal or not depends on the application and the nature of data sets. Demonstratively, from Tables~\ref{table2} and ~\ref{table3}, one can also see how this assumption affects the algorithms. First, the assumption seems to benefit DPER at high missing rates ($65\%, 80\%$) on small data sets (Seeds, Iris). For example, at $80\%$ of missing values on Iris, there is a $1/3$ reduction in the $0.024$ error rate of DPER with the equal covariance assumption. Yet, improvement may not happen in all small data sets with lower missing rates. For the Wine dataset, at $50\%$, the experiment with the assumption gives the error rate about $0.009$. Meanwhile, it is approximately $0.008$ without this assumption. There is no clear pattern on the effects of the equal covariance assumption for MICE and SOFT-IMPUTE datasets.
Meanwhile, Nuclear Norm and MissForest datasets have a significantly better performance with the assumption. As an indication, with $20\%$ missing rate in the Ionosphere data set, the $0.717$ error rate of MissForest reduces over $99\%$ to $0.005$ in Table~\ref{table3}. The result suggests that for smaller data sets, the equal covariance matrix assumption benefits Nuclear Norm and MissForest significantly. It may be due to the number of samples used for the covariance estimation is lower without the assumption.
The parameter estimation on large data sets such as MNIST and Fashion MNIST, DPER gives small error rates. Since the populational means and covariance matrix are unknown, one can evaluate the estimation on the complete data sets (i.e., the data sets before the missing data simulation). It implies that with DPER, we can approximate means and covariance matrices with almost identical results with the complete data set. This result is reasonable since the Multivariate Central Limit Theorem suggests the maximum likelihood parameter approximation gets better with the increment of sample size, and these data sets are large.
Remarkable, only the results for DPER and SOFT-IMPUTE are available for these two data sets. Among the available methods, DPER is the fastest one with minimum run-time for parameter estimation on MNIST at $69.54$s, while SOFT-IMPUTE is the second fastest ($165.15$s), respectively. For other approaches, the corresponding outcomes are not available due to memory-bound or running-time bound. Therefore, we can deduce that DPER and SOFT-IMPUTE are more suitable than MICE, Nuclear Norm, and MissForest for large data sets.
\section{Conclusion}\label{sec:conclusion}
In this paper, we have derived formulas and provided algorithms to compute the mean and covariance matrices from the data suitable for both small and large data sets, hence providing an approximation to the data's underlying distribution(s). We illustrate the power of our methods by experiments, which show that while iterative methods may not handle the missing data problem for big data sets, our approach can still find the parameter rapidly without requiring extensive memory and computation time. As the estimation is done for each pair of features, the proposed method is also applicable to problems where the number of features is much higher than the sample size.
Yet, our methods still have several drawbacks and room for improvement.
First, when the distribution of the data is highly skewed \cite{mardia1970measures}, the bivariate normal distribution might not be a good approximator. Therefore, when the pair of features is highly skewed, other methods rather than DPER may be utilized for that pair of features.
Second, the computation is done separately for each $\sigma_{ij}$ that only requires the data of the $i$th and $j$th features. It also means we have not used the extra information from the data set's other features. Also, separate computation for each of $\sigma_{ij}$ means we could parallelize the algorithm even further. These will be the topics for our future research. We also publish all codes related to the experiments in one Github repository\footnote{\url{https://github.com/thunguyen177/DPER}}.
\section*{Acknowledgments}
We want to thank the University of Science, Vietnam National University in Ho Chi Minh City, and AISIA Research Lab in Vietnam for supporting us throughout this paper. This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number C2021-18-03.
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module.exports = class CommandsRegistry {
constructor(container) {
this.container = container;
this.commands = new Set();
}
addCommand(command) {
// @todo How to check if the command is container aware?
if (typeof command.setContainer === "function") {
command.setContainer(this.container);
}
this.commands.add(command);
}
getCommands() {
return this.commands;
}
};
| {
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{"url":"https:\/\/algebra-calculators.com\/laplace-formulas\/","text":"## laplace formulas\n\n### Introduction\n\nThe Laplace transform is an integral transform perhaps second only to the Fourier transform in its utility in solving physical problems. The Laplace transform is particularly useful in solving linear ordinary differential equations such as those arising in the analysis of electronic circuits.","date":"2023-04-02 05:07:17","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9704415202140808, \"perplexity\": 284.3931427003861}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296950383.8\/warc\/CC-MAIN-20230402043600-20230402073600-00135.warc.gz\"}"} | null | null |
'''
Author: Dr. John T. Hwang <hwangjt@umich.edu>
This package is distributed under New BSD license.
'''
try:
import cPickle as pickle
except:
import pickle
import hashlib
import contextlib
@contextlib.contextmanager
def cached_operation(inputs_dict, data_dir, desc=''):
"""
Context manager for an operation that may be cached.
Arguments
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inputs_dict : dict
Dictionary containing the inputs of the operation.
data_dir : None or str
Directory containing the cached data files; if None, do not load or save.
desc : str
Optional descriptive prefix for the filename.
Yields
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outputs_dict : dict
Dictionary containing the outputs of the operation.
"""
checksum = _caching_checksum(inputs_dict)
filename = '%s/%s_%s.dat' % (data_dir, desc, checksum)
try:
with open(filename, 'rb') as f:
outputs_dict = pickle.load(f)
load_successful = True
except:
outputs_dict = {}
load_successful = False
yield outputs_dict
if not load_successful and data_dir:
with open(filename, 'wb') as f:
pickle.dump(outputs_dict, f)
def _caching_checksum(obj):
"""
Compute the hex string checksum of the given object.
Arguments
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obj : object
Object to compute the checksum for; normally a dictionary.
Returns
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str
Hexadecimal string checksum that was computed.
"""
try:
tmp = obj['self'].printer
obj['self'].printer = None
except:
pass
self_pkl = pickle.dumps(obj)
checksum = hashlib.md5(self_pkl).hexdigest()
try:
obj['self'].printer = tmp
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pass
return checksum
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<?php
/**
* System settings resolver
*
* @author Ivan Klimchuk <ivan@klimchuk.com>
* @package Slackify
* @subpackage build
*/
if (!$object->xpdo && !$object->xpdo instanceof modX) {
return true;
}
switch ($options[xPDOTransport::PACKAGE_ACTION]) {
case xPDOTransport::ACTION_INSTALL:
if (isset($options['slackify_entrypoint'])) {
$ss = $object->xpdo->getObject('modSystemSetting', ['key' => 'slackify_entrypoint'])
?: $object->xpdo->newObject('modSystemSetting');
$ss->fromArray([
'namespace' => 'slackify',
'xtype' => 'textfield',
'key' => 'slackify_entrypoint',
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if (isset($options['slackify_channel'])) {
$ss = $object->xpdo->getObject('modSystemSetting', ['key' => 'slackify_channel'])
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$ss->fromArray([
'namespace' => 'slackify',
'xtype' => 'textfield',
'key' => 'slackify_channel',
'value' => $options['slackify_channel'],
], '', true, true);
$ss->save();
}
break;
case xPDOTransport::ACTION_UPGRADE:
break;
case xPDOTransport::ACTION_UNINSTALL:
$object->xpdo->removeCollection('modSystemSetting', ['key:LIKE' => 'slackify\_%']);
break;
}
return true;
| {
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} | 3,333 |
Shut down in Egypt: One artist's story of struggle and oppression
Photo by Abdelrhman Zin Eldin
Becky Hagan-Egyir
DURING THE 2011 REVOLUTION in Egypt (commonly referred to as the January 25th Revolution), artists in Egypt began to express themselves in ways they never had before. Their work caught the world's attention, inspiring us all to believe in change. Ganzeer was one of those artists whose work covered the walls of Cairo, documenting the spirit of the revolution, supporting its call for "bread, social dignity, and justice."
Fast forward 3+ years, and artists and revolutionaries in Egypt are facing uncertain times. On May 29, after a two-day election, a new leader — Abdel Fattah-Sisi, head of the Supreme Council of the Armed Forces (SCAF) — was elected Egypt's president. Support for SCAF has created divisions between revolutionaries in Egypt, and the leaders of SCAF have often been a focus of Ganzeer's work.
Today, Egypt is undergoing a counter-revolution driven by the supporters of the Egyptian Muslim Brotherhood, which believes former President Morsi's ouster — as demanded by many Egyptians in July 2013 and enforced by the army — was unwarranted. This accusation has led them to be labelled as "terrorists" who are now facing mass trials and much worse. In addition, the government has been widely criticized by human rights groups for the mass arrests of protesters and members of the media.
But the ongoing revolution hasn't stopped Ganzeer from fighting for positive changes in Egypt's future. I interviewed him to discuss the role of art in Egypt's struggles. He also talks about his childhood pleasures and the daily issues he faced as a resident of one of the world's largest metropolises, Cairo.
Tank vs. Biker is a mural by Ganzeer which clearly shows in black and white stenciling his opinion about the relationship between the army and the people. On the left, a huge tank rolls forward aiming at a young man riding his bike on the right. He carries the city on his head in place of a loaf of bread. The Arabic word for bread sounds similar to that for life. Photo: Mehri Khalil
BHE: Did you grow up in Cairo, and what were some of the best things about growing up in the city?
Ganzeer: Yeah, I grew up in Cairo, in a little neighborhood in Heliopolis called Ard El-Golf, which is right behind the abandoned Baron Empain Palace constructed in 1911. It's far from the hustle and bustle of Downtown Cairo, or even Egypt's lifeline — the Nile River. I feel like I never really got a taste of "city life" till much later. Today Ard El-Golf is a go-to hangout area, with many popular cafes, sushi spots, high cake-like buildings and what have you. But back in the 80s / 90s it was pretty much a semi-quiet residential neighborhood with many stray dogs befriended by me and other kids my age. My school was around the block and the couple friends I made were in the neighborhood.
I feel like I only really faced the city — understood the scope of the city and all that — when I had to go to college which was in a town called Banha, a 30-minute train ride from Cairo. I would have to spend roughly an hour and half in public transportation just to get to the train station. I don't think I'm a big city kinda guy. I find myself much more comfortable in more intimate communities that are more connected with nature. But don't get me wrong! I am fascinated by cities, and megacities, and how they function. Cairo's crazy in just the layers of history that are apparent in every facet of the city. The architecture, the food, the conversations, it's such a culturally rich city but it's also one that carries a lot of baggage.
What are some of the most important things that are needed for a better quality of living in Cairo and Egypt right now?
This design entitled "Evil Military" by Ganzeer references "the girl in the blue bra." After a video was released online during a December 2011 protest showing the brutal beating of a female protester – whose shirt during the beating was opened, revealing her blue bra underneath – by soldiers, the video became a rallying call for protesters demanding an end to the military's power. Photo: Ganzeer
First off, about seventy-five percent less people! There's no way any city on the planet can accommodate [over] twenty million people. The number of people living in Cairo are having such a huge toll on the transportation system, the architecture, the environment. On the urban planning front, the city just can't keep up — it's always much, much behind. I'd put most of the development money into the rest of the country's towns and villages, get people to decentralize and spread out.
Secondly, private cars need to be banned. Of course, it's difficult to get around a city and spread out in Cairo without a car, but seriously, it's just out of hand. I understand that it's easier for the government in the short run to let people buy cars (making money in the process), but in the long run, it becomes unbearable for everyone. The city really needs to ban cars and focus entirely on developing its public transportation options to reach capacity and maintenance.
Thirdly, all this stuff should be running on solar energy or electricity or whatever. I've seen solar energy panels cladding the roofs of farm houses in freakin' Germany. GERMANY… it's cloudy most of the year. But in Cairo, the sun shines bright even in winter. It's just dumb to depend on gas the way we [all] do. It's the only way if we don't want our people [in Egypt] to all drop dead and die from lung disease, which by the way, a lot of us already suffer from.
And lastly, water canals. It's ridiculous to grow up in some part of the city two hours away from the Nile, yet have no direct access to it, and to only read about the Nile and its significance in history books. If they expect to teach us the importance of the Nile and our historical connection to it, then whenever a new extension of the city is planned, a Nile artery should be the first thing in that plan. Plus, it would offer a good alternative to getting around the city, much better than overcrowded asphalt roads (which discharge so much heat throughout Egypt's extended summer months).
Did you ever join the sit-ins in Tahrir or any protest gathering points in Cairo? What was it like for you?
I just so happened to be there on January 25, 2011, when the revolution first broke out, and boy it was the most thrilling and exhilarating time of my life. Seeing people band together and sacrifice themselves in the face of armed troops, with nothing but their voices, and all for what? For other people, people they don't even know, future generations they will never meet. It was such a glorious thing to experience, the closest thing I've ever experienced to seeing God or something. Indescribable.
When did you first realize that you enjoyed art?
[When] I was about four or five years old. My older brothers had lots of Dungeons and Dragons catalogs, and Nintendo game cartridges, and superhero comic books, and I was just always fascinated by the art in those things and would spend many hours trying to copy them.
What's the first work you did on the walls of Cairo as part of the Revolution?
The very first thing I did was not at all planned. Nor was it an artwork at all really. But being in Tahrir Square on January 25th when the revolution broke out, and just so happening to have a can of spray paint, I climbed an NDP (Mubarak's National Democratic Party) billboard in the middle of Tahrir Square and spray painted what people were chanting: "Down with Mubarak." The crowd erupted with cheers and whistles.
The first "artwork" I created, however, was on February 2nd — a black stencil of visual symbols that pretty much visually stated that Mubarak does not equal Egypt. This was after Mubarak's second public speech since the revolution broke out — a highly emotionally charged one that many, many, people were actually starting to fall for.
A citizen holds up one of Ganzeer's stencils which expresses that "Mubarak does not equal Egypt" on February 11th, 2011, in Cairo. This was the day when Vice President Omar Suleiman announced that former President Hosni Mubarak's three-decade presidency in Egypt had come to an end. Photo: Ganzeer
Was street art common in any part of Cairo before the revolution? How did people react to it before the Revolution?
Not really. Just a handful of rather content-less stuff in Heliopolis and Alexandria [Egypt's second largest city]. Very cool and pretty to look at but without much meaning to it.
Egyptian jail cells have gained a notoriously bad reputation in the world's eyes since the Revolution began in January 2011. For your work as a multi-medium artist helping the Revolution you were briefly arrested. Would you be able to tell me about your experience and how it happened?
So far, I've been lucky enough to not have to set foot in a jail cell at all. When I was detained, I was welcomed into the office of a high-ranking military officer who offered me a soda and later in the day a Nescafé. They were all eerily very nice and I was released on the very same day.
Read more about the incident in Ganzeer's own words here.
Much of your work is critical of (SCAF) or establishments — e.g., political, religious, and art establishments — that oppose freedom or change and growth. Have you faced a lot of negative reaction to your work by these groups?
All the time. Hardly anything I do is not met with a negative reaction from someone [such as Ibn Salaama].
On his blog on March 16, 2011, Ganzeer wrote this about his project to create murals of martyrs of the Revolution: "The goal is to, on one hand, honor the martyrs, and on another hand provide passers-by with a reminder of Egypt's struggle for freedom, democracy, and equality." This particular mural by Ganzeer depicts 16-year-old Seif Allah Mustafa. On streets with murals such as this, flowers and prayers can be seen resting against the base of walls in memory of faces staring out at those who walk by. Photo: Mostafa Hussein
Has the SCAF or any other group in your opinion taken the Revolution away from the people and their goals of gaining "bread, social justice, and dignity?"
Yes. Particularly SCAF and the Muslim Brotherhood, as well as Salafist groups.
How do you feel about the proposed law to ban graffiti in Egypt and send accused artists to jail for four years? Do you fear being a target?
Well, it's not like the revolution itself was ever legal. It was illegal but we did it anyway. And it's not like doing graffiti was a totally safe game up to this point either. One could easily have been charged with plotting against the state with the type of graffiti we've been doing so y'know…we'll always try and do what we think is the right thing to do even if the government oppresses us. It's always been that way anyway.
Check out Ganzeer's recent projects and activities here.
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,263 |
Victor William (Peter) Watson (14 September 1908 – 3 May 1956) was a wealthy English art collector and benefactor. He funded the literary magazine, Horizon, edited by Cyril Connolly.
Life and work
Watson was the son of William George Watson, later Sir George Watson, 1st Baronet, and was the youngest of three children—his brother Norman was born in 1897 and sister Florence in 1894. He was educated at Lockers Park School, Eton College and St John's College, Oxford.
Watson was an avid art collector acquiring works by such artists as Miró, Klee, and Pablo Picasso, which were displayed in his Paris apartment in the 1930s. He was the principal benefactor of the Institute of Contemporary Arts in London and also provided financial assistance to English and Irish painters including Francis Bacon, Lucian Freud and John Craxton. In 1930, society photographer, artist and set designer Sir Cecil Beaton began a lifelong obsession with Watson, though the two never became lovers. One chapter from Hugo Vickers' authorized biography of Cecil Beaton is titled "I Love You, Mr. Watson".
In 1940 Watson provided funding for Cyril Connolly's Horizon and became its arts editor. Stephen Spender was also involved with the magazine initially. Watson was art editor for the magazine between 1940 and 1949. He rarely contributed articles, but gave many opportunities for his friends to have their pictures reproduced in the magazine, and also encouraged Horizon to look beyond British Art, particularly to Paris. Watson commissioned articles on artists barely known at the time in England, such as Balthus, Morandi and Klee. He persuaded Picasso's dealer, Daniel Kahnweiler, to comment on the contemporary art market; and he also got Michel Leiris to write about Giacometti. Spender recalled to Connolly's biographer, Clive Fisher, that Watson hated "priggishness, pomposity and almost everything to do with public life," and he suspected that he had educated himself "through a love of beautiful works and of people in whom he saw beauty ...". He added "When I think of him then, I think of his clothes, which were beautiful, his general neatness and cleanness, which seemed almost those of a handsome young Bostonian."
Fisher writes that Peter Watson "was a figure of striking attractiveness; women in particular seem to have found his manners irresistible... almost everyone appears to have liked him." One of Watson's lovers was the American male prostitute and socialite Denham Fouts, whom he continued to support even after they separated as a result of Fouts's drug addiction
Watson was found drowned in his bath on 3 May 1956 at his home in Knightsbridge, London. Some have suggested that he was murdered by his young American lover, Norman Fowler (11 May 1927– March 23, 1971). Fowler inherited the bulk of Watson's estate and died 14 years later in the West Indies; he was also found drowned in his bathtub.
Watson's sister, Florence Nagle, was a race horse breeder and trainer. His brother Sir Norman Watson, Baronet, (1897 - 1989), provided funding for the early development of Lake Louise, a ski resort in Alberta, Canada.
Notes and references
English art collectors
1908 births
1956 deaths
English LGBT people
People educated at Eton College
People educated at Lockers Park School
Deaths by drowning
20th-century LGBT people | {
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box-shadow: none;
}
#widgets-left .inactive-sidebar.first {
margin-top: 40px;
}
/* Not sure what this is for... */
div#widgets-left .inactive-sidebar .widget.expanded {
left: auto;
}
.widget-title-action {
float: right;
position: relative;
}
div#widgets-left .inactive-sidebar .widgets-sortables {
min-height: 42px;
padding: 0;
background: transparent;
margin: 0;
position: relative;
}
/* Widgets Right */
div#widgets-right .sidebars-column-1,
div#widgets-right .sidebars-column-2 {
max-width: 450px;
}
div#widgets-right .widgets-holder-wrap {
margin: 10px 0 0 0;
}
div#widgets-right .sidebar-description {
min-height: 20px;
margin-top: -5px;
}
div#widgets-right .sidebar-name h2,
div#widgets-right .sidebar-name h3 {
padding: 15px 7px;
}
div#widgets-right .sidebar-name .sidebar-name-arrow:before {
top: 2px;
}
div#widgets-right .widget-top {
padding: 0;
}
div#widgets-right .widgets-sortables {
padding: 0 8px;
margin-bottom: 9px;
position: relative;
min-height: 123px;
}
div#widgets-right .closed .widgets-sortables {
min-height: 0;
margin-bottom: 0;
}
.sidebar-name .spinner,
.remove-inactive-widgets .spinner {
float: none;
position: relative;
top: -2px;
margin: -5px 5px;
}
/* Dragging a widget over a closed sidebar */
#widgets-right .widgets-holder-wrap.widget-hover {
border-color: #72777c;
box-shadow: 0 1px 2px rgba(0,0,0,0.3);
}
/* Accessibility Mode */
.widgets_access #widgets-left .widget .widget-top {
cursor: auto;
}
.widgets_access #wpwrap .widgets-holder-wrap.closed .sidebar-description,
.widgets_access #wpwrap .widgets-holder-wrap.closed .widget,
.widgets_access #wpwrap .widget-control-edit {
display: block;
}
.widgets_access #widgets-left .widget .widget-top:hover,
.widgets_access #widgets-right .widget .widget-top:hover {
border-color: #ddd;
}
#available-widgets .widget-control-edit .edit,
#widgets-left .inactive-sidebar .widget-control-edit .add,
#widgets-right .widget-control-edit .add {
display: none;
}
.widget-control-edit {
display: block;
color: #666;
background: #EEE;
padding: 0 15px;
line-height: 43px;
border-left: 1px solid #DDD;
}
#widgets-left .widget-control-edit:hover,
#widgets-right .widget-control-edit:hover {
color: #fff;
background: #444;
border-left: 0;
outline: 1px solid #444;
}
.widgets-holder-wrap .sidebar-name,
.widgets-holder-wrap .sidebar-description {
-webkit-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none;
}
.editwidget {
margin: 0 auto;
}
.editwidget .widget-inside {
display: block;
padding: 0 15px;
}
.editwidget .widget-control-actions {
margin-top: 20px;
}
.js .widgets-holder-wrap.closed .widget,
.js .widgets-holder-wrap.closed .sidebar-description,
.js .widgets-holder-wrap.closed .remove-inactive-widgets,
.js .widgets-holder-wrap.closed .description,
.js .closed br.clear {
display: none;
}
.js .widgets-holder-wrap.closed .widget.ui-sortable-helper {
display: block;
}
/* Hide Widget Settings by Default */
.widget-inside,
.widget-description {
display: none;
}
.widget-inside {
background: #fff;
}
/* Dragging widgets over the available widget area show's a "Deactivate" message */
#removing-widget {
display: none;
font-weight: 400;
padding-left: 15px;
font-size: 12px;
line-height: 1;
color: black;
}
.js #removing-widget {
color: #00a0d2;
}
.widget-control-noform,
#access-off,
.widgets_access .widget-action,
.widgets_access .sidebar-name-arrow,
.widgets_access #access-on,
.widgets_access .widget-holder .description,
.no-js .widget-holder .description {
display: none;
}
.widgets_access .widget-holder,
.widgets_access #widget-list {
padding-top: 10px;
}
.widgets_access #access-off {
display: inline;
}
.widgets_access .sidebar-name,
.widgets_access .widget .widget-top {
cursor: default;
}
/* Widgets Area Chooser */
.widget-liquid-left #widgets-left.chooser #available-widgets .widget,
.widget-liquid-left #widgets-left.chooser .inactive-sidebar {
transition: opacity 0.1s linear;
}
.widget-liquid-left #widgets-left.chooser #available-widgets .widget,
.widget-liquid-left #widgets-left.chooser .inactive-sidebar {
/* -webkit-filter: blur(1px); */
opacity: 0.2;
pointer-events: none;
}
.widget-liquid-left #widgets-left.chooser #available-widgets .widget-in-question {
/* -webkit-filter: none; */
opacity: 1;
pointer-events: auto;
}
.widgets-chooser ul,
#widgets-left .widget-in-question .widget-top,
#available-widgets .widget-top:hover,
div#widgets-right .widget-top:hover,
#widgets-left .widget-top:hover {
border-color: #999;
box-shadow: 0 1px 2px rgba(0,0,0,0.1);
}
.widgets-chooser ul.widgets-chooser-sidebars {
margin: 0;
list-style-type: none;
max-height: 300px;
overflow: auto;
}
.widgets-chooser {
display: none;
}
.widgets-chooser ul {
border: 1px solid #ccc;
}
.widgets-chooser li {
padding: 10px 15px 10px 35px;
border-bottom: 1px solid #ccc;
background: #fff;
margin: 0;
cursor: pointer;
outline: none;
position: relative;
transition: background 0.2s ease-in-out;
}
/* @todo looks like these hover/focus states are overridden by .widgets-chooser-selected */
.widgets-chooser li:hover,
.widgets-chooser li:focus {
background: rgba(255,255,255,0.7);
}
.widgets-chooser li:focus:before {
content: "\f147";
display: block;
-webkit-font-smoothing: antialiased;
font: normal 26px/1 dashicons;
color: #555d66;
position: absolute;
top: 7px;
left: 5px;
}
.widgets-chooser li:last-child {
border: none;
}
.widgets-chooser li.widgets-chooser-selected {
background: #00a0d2;
color: #fff;
}
.widgets-chooser li.widgets-chooser-selected:before,
.widgets-chooser li.widgets-chooser-selected:focus:before {
content: "\f147";
display: block;
-webkit-font-smoothing: antialiased;
font: normal 26px/1 dashicons;
color: #fff;
position: absolute;
top: 7px;
left: 5px;
}
.widgets-chooser .widgets-chooser-actions {
padding: 10px 0 12px 0;
text-align: center;
}
.widgets-chooser button {
margin-right: 5px;
}
#available-widgets .widget .widget-top {
cursor: pointer;
}
#available-widgets .widget.ui-draggable-dragging .widget-top {
cursor: move;
}
/* =Specific widget styling
-------------------------------------------------------------- */
.text-widget-fields {
position: relative;
}
.text-widget-fields [hidden] {
display: none;
}
.text-widget-fields .wp-pointer.wp-pointer-top {
position: absolute;
z-index: 3;
top: 100px;
right: 10px;
left: 10px;
}
.text-widget-fields .wp-pointer .wp-pointer-arrow {
left: auto;
right: 15px;
}
.text-widget-fields .wp-pointer .wp-pointer-buttons {
line-height: 1.4em;
}
/* =Media Queries
-------------------------------------------------------------- */
@media screen and (max-width: 480px) {
div.widget-liquid-left {
width: 100%;
float: none;
border-right: none;
padding-right: 0;
}
#widgets-left .sidebar-name {
margin-right: 0;
}
#widgets-left #available-widgets .widget-top {
margin-right: 0;
}
#widgets-left .inactive-sidebar .widgets-sortables {
margin-right: 0;
}
div.widget-liquid-right {
width: 100%;
float: none;
}
div.widget {
margin: 0 auto 10px !important;
max-width: 480px;
}
}
@media screen and (max-width: 320px) {
div.widget {
max-width: 320px;
}
}
@media only screen and (min-width: 1250px) {
#widgets-left #available-widgets .widget {
width: 49%;
float: left;
}
.widget.ui-draggable-dragging {
min-width: 49%;
}
#widgets-left #available-widgets .widget:nth-child(even) {
float: right;
}
#widgets-right .sidebars-column-1,
#widgets-right .sidebars-column-2 {
float: left;
width: 49%;
}
#widgets-right .sidebars-column-1 {
margin-right: 2%;
}
#widgets-right.single-sidebar .sidebars-column-1,
#widgets-right.single-sidebar .sidebars-column-2 {
float: none;
width: 100%;
margin: 0;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,299 |
{"url":"http:\/\/libros.duhnnae.com\/2017\/jul7\/15008002447-Optimal-Gathering-in-Radio-Grids-with-Interference.php","text":"# Optimal Gathering in Radio Grids with Interference\n\nOptimal Gathering in Radio Grids with Interference - Descarga este documento en PDF. Documentaci\u00f3n en PDF para descargar gratis. Disponible tambi\u00e9n para leer online.\n\n1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications CRISAM - Inria Sophia Antipolis - M\u00e9diterran\u00e9e , COMRED - COMmunications, R\u00e9seaux, syst\u00e8mes Embarqu\u00e9s et Distribu\u00e9s 2 School of Computing Science\n\nAbstract : We study the problem of gathering information from the nodes of a radio network into a central node. We model the network of possible transmissions by a graph and consider a binary model of interference in which two transmissions interfere if the distance in the graph from the sender of one transmission to the receiver of the other is $d I$ or less. A {\\em round} is a set of non-interfering transmissions. In this paper, we determine the exact number of rounds required to gather one piece of information from each node of a square two-dimensional grid into the central node. If $d I = 2k-1$ is odd, then the number of rounds is $kN-1-c k$ where $N$ is the number of nodes and $c k$ is a constant that depends on $k$. If $d I = 2k$ is even, then the number of rounds is $k+\\frac{1}{4}N-1-c- k$ where $c- k$ is a constant that depends on $k$. The even case uses a method based on linear programming duality to prove the lower bound, and sophisticated algorithms using the symmetry of the grid and non-shortest paths to establish the matching upper bound. We then generalize our results to hexagonal grids.\n\nKeywords : Radio communication interference grids gathering\n\nAutor: Jean-Claude Bermond - Joseph Peters -\n\nFuente: https:\/\/hal.archives-ouvertes.fr\/\n\nDESCARGAR PDF","date":"2018-03-21 15:25:56","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7867069244384766, \"perplexity\": 772.8429238705562}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-13\/segments\/1521257647660.83\/warc\/CC-MAIN-20180321141313-20180321161313-00409.warc.gz\"}"} | null | null |
Q: What is this object serialization pattern? Have you ever taken a close look at some of the urls produced as you browse around www.amazon.com? Here's a typical one:
http://www.amazon.com/s/ref=sr_nr_p_n_age_range_2?rh=i%3Aaps%2Ck%3Abumblebee%2Cp_n_age_range%3A165890011%7C165936011&keywords=bumblebee&ie=UTF8&qid=1373589657&rnid=165794011
After you urldecode it, you get:
http://www.amazon.com/s/ref=sr_nr_p_89_2?rh=i:aps,k:bumblebee,p_n_age_range:165890011|165936011,p_89:Pillow Pets&keywords=bumblebee&ie=UTF8&qid=1373589678&rnid=2528832011
I'm particularly interested in this portion:
rh=i:aps,k:bumblebee,p_n_age_range:165890011|165936011,p_89:Pillow Pets
It looks like some kind of object serialization that reduces down even smaller than JSON. There are no quotes around strings, and arrays are bracketless and delimited by pipes.
Ebay does something similar, particularly the array pipes. Have you ever seen this format? Is this a common pattern you recognize? Or is it just some exotic hand-rolled solution that they both happened to arrive at independently? Any idea why they do it, as opposed to just straight JSON?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,562 |
Q: Quotient Ring multiplication Please help I'm very confused about this.
If $[r]$ and $[s]$ are two cosets of the set $R/A$ (Where $A$ is an ideal of the ring $R$) why are we allowed to define $[r]*[s]=[rs]$ when we only know that $[r]*[s]$ is a subset of $[rs]$?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,879 |
Q: Xamarin Forms - How to create custom render to give TableSection the default iOS Footer? I want to add the default iOS footer to the tablesection in the tableview in Xamarin Forms. How can I go about doing this? I assume a customer renderer but I'm only reading that this can be done for Tableview?
To show an example, the following image is from Xcode storyboards when I enter the footer text on a static cell.
A: A Custom renderer is right, but you will have to use a custom renderer for the entire TableView. From there, you will need to override the TableViewModelRenderer and then the GetViewForFooter method in that ModelRenderer. Here's something that might help get you started:
public class FooterTableViewRenderer : TableViewRenderer
{
protected override void OnElementChanged(ElementChangedEventArgs<TableView> e)
{
base.OnElementChanged(e);
if (Control == null)
return;
var tableView = Control as UITableView;
var formsTableView = Element as TableView;
tableView.WeakDelegate = new CustomFooterTableViewModelRenderer (formsTableView);
}
private class CustomFooterTableViewModelRenderer : TableViewModelRenderer
{
public CustomFooterTableViewModelRenderer(TableView model) : base(model)
{
}
public override UIView GetViewForFooter(UITableView tableView, nint section)
{
return new UILabel()
{
Text = TitleForFooter(tableView, section), // or use some other text here
TextAlignment = UITextAlignment.Center
};
}
}
}
As mentioned in my comments below, you can alternatively override other methods in your TableViewModelRenderer:
public override nfloat GetHeightForFooter(UITableView tableView, nint section)
{
return 10;
}
public override string TitleForFooter(UITableView tableView, nint section)
{
return "This is the title for this given section";
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 637 |
{"url":"https:\/\/hygprogramming.wordpress.com\/test-cases\/branin-hoo\/","text":"# Branin-Hoo\n\nIn this case the true underlying function HyGP had to approximate is the 2D Branin-Hoo function (Viana and Haftka 2009):\n\n$f(z_{1}, z_{2})=\\left( z_{2} - 5.1\\dfrac{z_{1}^2}{4\\pi^2} + 5\\dfrac{z_{1}}{\\pi} - 6\\right)^{2} + 10\\left(1 - \\dfrac{\\pi}{8}\\right) cos(z_{1}) + 10$\n\nBUILDING DATA SET:\n30-point Optimal Latin Hypercube DoE in [-5, 10] x [0, 15]\nAvailable here: braninhoo_input_file\n\nVALIDATION DATA SET:\n1369-point Full Factorial DoE\u00a0 [-6.5 : 0.5 : 11.5] x [-1.5 : 0.5 : 16.5]\nAvailable here: braninhoo_test_dataset\n\nHyGP hyperparameters (see braninhoo_input_file):\nPopulation size: 200\nGenerations: 50\nPrimitives: +, -, *, \/ (protected), ^2, ^3, sin, cos, exp\n\nResults:\nThe experiment done with 10 random initial guesses for numerical coefficients (10-guesses approach) returned as best model the following symbolic expression:\n\n$\\tilde{f}(z_{1},z_{2}) = 9.60209703926\\, cos \\left(1.00000053842\\, \\mathrm{z_{1}}\\right) - 12.0000255964\\, \\mathrm{z_{2}} - 19.0985885529\\, \\mathrm{z_{1}} + 3.1830982295\\, \\mathrm{z_{1}}\\, \\mathrm{z_{2}} - 0.258368814492\\, {\\mathrm{z_{1}}}^2\\, \\mathrm{z_{2}} + 4.08324072854\\, {\\mathrm{z_{1}}}^2 - 0.411206971382\\, {\\mathrm{z_{1}}}^3 + 0.0166886394138\\, {\\mathrm{z_{1}}}^4 + 1.00000121669\\, {\\mathrm{z_{2}}}^2 + 46.0001253703$\n\ncharacterised by a coefficient of determination R2=1 on the validation data. The returned expression\u00a0$\\tilde{f}$ is as a matter of fact the original underlying Branin-Hoo function, if minor errors on the numerical coefficients are neglected.\n\nIn the video below the evolution leading to the correct identification of the Branin-Hoo function is shown:\n\nReferences:\n\n\u2022 F.A.C. Viana and R.T. Haftka. Cross validation can estimate how well prediction variance correlates with error. AIAA Journal, 47(9):2266\u20132270, 2009.\nAdvertisements","date":"2018-09-20 12:50:16","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 3, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5617833733558655, \"perplexity\": 11117.390224952063}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-39\/segments\/1537267156471.4\/warc\/CC-MAIN-20180920120835-20180920141235-00025.warc.gz\"}"} | null | null |
\section{Introduction} \label{sec:intro}
How and when metal enrichment happened in the epoch of reionization (EoR) is one of the most fundamental questions in modern astronomy. Recent \textit{Planck} results suggest that the cosmic reionization occurred at an instantaneous reionization redshift of
$z_\mathrm{re} = 7.68 \pm 0.79$ \citep{Planck18},
and the latest \textit{Hubble Space Telescope} (\HST{}) surveys have revealed more than a hundred of candidate $z \gtrsim 8$ Lyman break galaxies \citep[LBGs, e.g.,][see \citealt{Stark16} for a review]{Bouwens15, Ishigaki18} out to $z = 11.1^{+0.08}_{-0.12}$ \citep{Oesch16}.
Furthermore, based on the samples of $z \gtrsim 8$ LBGs, \citet{Oesch18} reported a strong evolution of the ultraviolet (UV) luminosity function by one order of magnitude from $z \sim 10$ to $\sim 8$, implying a rapid increase of the cosmic star-formation rate density by an order of magnitude within a very short time-scale ($\lesssim 200$~Myr). It is likely that this steep evolution compared to lower-$z$ can be explained by the fast build-up of the dark matter halo mass function at $z > 8$ \citep{Oesch18}.
However, it is still a challenge to characterize baryonic physics of the $z > 8$ galaxies.
One of the major obstacles is that these LBGs are yet to be confirmed through spectroscopy; since the rest-frame UV continuum is typically not sufficiently bright for detection with current instruments, it is often assumed that the Lyman-$\alpha$ (Ly$\alpha$) emission line might be the best tool for spectroscopic confirmation. A large amount of 8--10~m telescope time have been invested in Ly$\alpha$ searches for $z > 8$ candidates, but so far this resulted in only a few detections \citep[$z = 8.683$, 8.38, 9.11,][respectively]{Zitrin15, Laporte17, Hashimoto18}, likely indicating that the Ly$\alpha$ signal is substantially attenuated by the largely-neutral intergalactic medium at this epoch.
Alternative UV indicators such as \textsc{C~iii]} $\lambda\lambda$1907,1909~\AA{} serve as a workhorse for redshift identification \citep[e.g.,][]{Zitrin15a, Stark15a}. These lines, in addition to the rest-frame optical oxygen and nitrogen lines, are also useful for characterizing the metal enrichment of interstellar medium (ISM) and stellar components of the galaxies \citep[e.g.,][]{Stark15a, Stark15b, Stark17, Mainali18}.
These diagnostic lines will provide a unique insight into the physical properties of ionized gas in the $z > 8$ Universe when the \emph{James Webb Space Telescope} (\emph{JWST}) comes online, although their use is currently limited to bright galaxies in a certain redshift range, because most of the lines are intrinsically faint and/or are redshifted outside the wavelength range where the atmospheric transmittance is good for ground-based facilities.
With this in mind, \citet{Inoue14} have investigated the potential use of redshifted nebular emission lines in the rest-frame far-infrared (FIR) in determining spectroscopic redshift of $z \sim 8$ galaxies. The \oiii{} 88~$\micron$ line, which is often observed as the brightest FIR line in local \textsc{H~ii} regions \citep[e.g.,][]{Takami87, Kawada11}, can be used as an instantaneous tracer of massive star formation, since ionization of O$^{+} \rightarrow$ O$^{++}$ requires hard ($E >35.1$~eV) ionizing photons from hot, short-lived O-type stars.
\citet{Inoue14} predicted the line fluxes from high-$z$ galaxies on the basis of a cosmological hydrodynamic simulation of galaxy formation \citep{Shimizu14} by incorporating an \oiii{} emission line model as a function of metallicity calibrated by \textit{ISO}, \textit{AKARI} and \Herschel{} observations of local galaxies \citep[][see also \citealt{Cormier15}]{Brauher08, Kawada11, Madden12, Madden13}.
Since the metallicity of a typical galaxy with $H_{\rm 160} = 26$\,mag (AB) reaches $\sim 0.2$ $Z_{\odot}$ even at $z \gtrsim 8$, the \oiii{} line of such galaxies is as bright as 1--5~mJy, which is bright enough to be detected with existing submillimeter facilities, such as the Atacama Large Millimeter/submillimeter Array (ALMA).
Indeed, it is becoming clear that galaxies at $z > 6$ are bright in \oiii{} 88~$\micron$ \citep{Inoue16, Carniani17, Laporte17, Marrone18, Hashimoto18, Hashimoto18b, Hashimoto18c, Walter18}. The first detection in the EoR has been made for a $z = 7.212$ Ly$\alpha$ emitter, SXDF-NB1006-2 \citep{Inoue16}, in which only 2~hr integration of ALMA Band 8 was invested, implying the \oiii{} line as a promising tool to pin down the spectroscopic redshift even for $z > 8$ galaxies.
More recently, two LBGs, A2744\_YD4 at $z = 8.38$ \citep{Laporte17} and MACS1149-JD1 at $z = 9.1096 \pm 0.0006$ \citep{Hashimoto18}, have been confirmed in \oiii{} at $4.0\sigma$ and $7.4\sigma$, respectively. A2744\_YD4 was also detected in 850-$\micron$ continuum with $S_\mathrm{850\,\mu m} = 0.1$~mJy, suggesting the presence of a chemically-evolved ISM. It should also be noted that MACS1149-JD1 was identified without any prior information of a redshift inferred from a spectral line, demonstrating the \oiii{} line as the redshift indicator complementing the role of the Ly$\alpha$ and other UV lines.
In addition, the \oiii{} 88~$\micron$ flux places a unique constraint on the stellar and ISM properties, since the \oiii{} line is extinction-free and sensitive to the electron density, ionization parameter, and gas-phase oxygen abundance of the ionized media, which also depend on the global properties such as the star-formation rate (SFR) and stellar age. \citet{Inoue16} have carried out comprehensive modeling of the UV-to-FIR spectral energy distribution (SED) of SXDF-NB1006-2, in which the \oiii{} flux and submillimeter continuum upper limits are taken into account. They found this to be a young ($< 30$~Myr) star-forming ($\approx 300~M_{\odot}$~yr$^{-1}$) galaxy with a somewhat high best-fitting metallicity of 0.05--1 $Z_{\odot}$. In contrast, \citet{Hashimoto18} revealed that MACS1149-JD1 has a more evolved (290~Myr) stellar component with a metallicity of $0.2Z_{\sun}$, suggesting a formation redshift of $z_\mathrm{f} \approx 15$.
The non-detection of dust continuum in both galaxies suggests low dust-to-metal mass ratios in their ISM \citep{Inoue16} compared to the Milky Way's value \citep[$\sim 0.5$, e.g.,][]{Inoue11b}, which could indicate that a substantial fraction of ISM metals is not stored in grains.
In this paper, we report the detections of the \oiii{} 88~$\micron$ line and dust continuum in a modestly-magnified $Y$-dropout LBG, confirming the spectroscopic redshift to be $z = 8.3118 \pm 0.0003$, i.e., corresponding to an epoch when the age of the Universe was only 600 Myr. This is one of the furthest galaxies ever identified spectroscopically by exploiting the brightness of the \oiii{} line. This paper is organized as follows:
\S~\ref{sec:target} explains how the target was selected.
\S~\ref{sec:obs} describes the ALMA and VLT/X-shooter observations.
\S~\ref{sec:result} demonstrates the detection of dust and \oiii{} emission in \target{}.
In \S~\ref{sec:sed}, we perform an analysis of the SED to constrain the physical properties of \target{}.
In \S~\ref{sec:discussion}, we discuss the model prediction of the dust mass, whereby we demonstrate that some parameter degeneracies obtained in the SED analysis can be resolved by incorporating a dust mass evolution model.
Finally, our conclusions are presented in \S~\ref{sec:conclusion}.
Throughout this paper, we adopt a concordance cosmology with $\Omega_\mathrm{m} = 0.3$, $\Omega_{\Lambda} = 0.7$ and $H_0 = 70$ km\,s$^{-1}$\,Mpc$^{-1}$. An angular scale of $1''$ corresponds to the physical scale of 4.7~kpc at $z = 8.312$. A redshift $z = 8.312$ corresponds to an age of the Universe of 0.60~Gyr.
\begin{deluxetable*}{cccccc}[ht!]
\tablecaption{The parameters of ALMA observations. \label{tab:log}}
\tablecolumns{6}
\tablewidth{0pt}
\tablehead{
\colhead{UT start time\tablenotemark{$\sharp$}} &
\colhead{Baseline lengths} &
\colhead{} &
\colhead{Center frequency} & \colhead{Integration time} & \colhead{PWV} \\
\colhead{(YYYY-MM-DD hh:mm:ss)} & \colhead{(m)} & \colhead{$N_\mathrm{ant}$\tablenotemark{$\dagger$}} &
\colhead{(GHz)} & \colhead{(min)} & \colhead{(mm)}
}
\startdata
2016-10-25 05:11:40 & 19--1399 & 43 & 351.40 (T2) & 32.76 & 0.62 \\
2016-10-26 09:25:43 & 19--1184 & 46 & 351.40 (T2) & 32.76 & 0.30 \\
2016-10-28 09:15:52 & 19--1124 & 39 & 355.00 (T3) & 38.30 & 0.35 \\
2016-10-29 07:10:42 & 19--1124 & 41 & 347.80 (T1) & 33.77 & 1.27 \\
2016-10-30 07:36:05 & 19--1124 & 39 & 355.00 (T3) & 38.30 & 0.93 \\
2016-10-30 08:55:42 & 19--1124 & 40 & 347.80 (T1) & 33.77 & 0.78 \\
2016-11-02 04:23:49 & 19--1124 & 40 & 358.60 (T4) & 30.23 & 0.64 \\
2016-11-02 05:31:01 & 19--1124 & 40 & 358.60 (T4) & 30.23 & 0.97 \\
2016-12-17 05:37:41 & 15--460 & 44 & 347.80 (T1) & 33.77 & 0.90 \\
2016-12-18 05:21:55 & 15--492 & 47 & 347.80 (T1) & 33.77 & 1.29 \\
2017-04-28 21:51:39 & 15--460 & 39 & 355.00 (T3) & 38.30 & 0.72 \\
2017-07-03 12:28:53 & 21--2647 & 40 & 358.60 (T4) & 30.23 & 0.24 \\
2017-07-04 12:40:06 & 21--2647 & 40 & 358.60 (T4) & 30.23 & 0.41 \\
\enddata
\tablenotetext{\sharp}{At integration start.}
\tablenotetext{\dagger}{The number of antenna elements.}
\end{deluxetable*}
\section{Target} \label{sec:target}
Among a hundred of $z \gtrsim 8$ candidates from treasury \HST{} programs (e.g., BoRG, CANDELS, CLASH, HFF, HUDF), we carefully selected a bright ($H_{160} < 26$, AB) galaxy candidate with an accurate photometric redshift ($z_\mathrm{phot}$) which is accessible from ALMA ($\delta_{\rm J2000} < +30^{\circ}$) with good atmospheric transmission. The criteria finally leave \target{} \citep[$H_{160} = 25.92 \pm 0.02$,][]{Laporte15, Infante15}.
\target{} lies behind the MACS\,J0416.1$-$2403 cluster, one of the \Hubble{} Frontier Fields \citep[HFF,][]{Lotz17}, while the magnification of the LBG is moderate \citep[e.g., magnification factor, $\mu_\mathrm{g} = 1.43 \pm 0.04$,][]{Kawamata16}. Thanks to the deepest \HST{} and \textit{Spitzer} photometry, the photo-$z$ is well constrained by six independent studies to be
$z_{\rm phot} = 8.478^{+0.062}_{-0.056}$ \citep{Infante15},
$8.57^{+0.3}_{-0.4}$ \citep{Laporte15},
$8.42$ \citep{Laporte16},
$8.6^{+0.1}_{-0.1}$ \citep{McLeod15},
8.66 \citep{Castellano16} and
$8.4^{+0.9}_{-0.9}$ \citep{Kawamata16}.
The most-likely redshift interval $8.3 < z < 8.7$ can be covered by four tunings of ALMA Band~7, which offer a wide redshift coverage of $\Delta z \approx 0.72$ for \oiii{} 88~$\micron$.
\begin{figure*}[th]
\includegraphics[width=\textwidth]{fig1_alma.pdf}
\caption{
(Left) The ALMA 850~$\micron$ continuum image of \target{} (contours) overlaid on the \HST{}/WFC3 near-infrared pseudo-color image in the F160W band. The contours are drawn at $-2\sigma$, $2\sigma$, $3\sigma$, ..., $7\sigma$, where $\sigma = 10.9$~$\mu$Jy~beam$^{-1}$. The negative contour is indicated by the dotted line. The synthesized beam size is indicated at the bottom-left corner.
(Center) The ALMA \oiii{} 88~$\micron$ integrated intensity image (contours) overlaid on the \HST{}/F160W image. The contours are drawn in the same manner as the Left panel, but $\sigma = 55$~mJy~beam$^{-1}$~km~s$^{-1}$.
(Right) The false-color \HST{}/WFC3 image taken with F160W (red), F140W (green) and F125W (blue) bands. The letters `E', `C' and `W' denote the positions of the eastern, central, and western clumps seen in the rest-frame UV, respectively. The physical scale of 1~kpc on the image plane is indicated by the bar at the bottom-left corner.
\label{fig:image}}
\end{figure*}
\section{Observations} \label{sec:obs}
\subsection{ALMA Observations and Reduction}
The ALMA observations were carried out from 2016 October to December and 2017 May to July as a Cycle~4 program (program ID: 2016.1.00117.S). The observation log is given in Table~\ref{tab:log}. Four different tunings were assigned to cover contiguous frequency range between 340.0 and 366.4~GHz. The local oscillators of the Band~7 receivers were tuned at 347.80, 351.40, 355.00, and 358.60 GHz, and we hereafter denote these tunings as T1, T2, T3, and T4, respectively. The correlator was configured with the frequency-division mode, in which the four spectral windows (SPWs) cover 7.5~GHz with respect to the central frequencies with a channel spacing of 7.8125 MHz. The phase tracking center was set to the LBG position, $\rm (\alpha_{J2000}, \delta_{J2000}) = (04^h16^m09\fs4010, -24\arcdeg 05' 35\farcs 470)$, which was determined by the \HST{} observations \citep{Laporte15,Infante15}. The on-source time was 436~min in total.
Two quasars, J0348$-$2749 and J0453$-$2807, were used for complex gain calibration. J0522$-$3627 was used for bandpass calibration.
Flux was scaled using J0522$-$3627 (for the tunings T2 and T3, $S_\mathrm{850\,\mu m} \simeq 3$--4~Jy) and J0334-4008 (for the tunings T1 and T4, $S_\mathrm{850\,\mu m} \simeq 0.3$~Jy), yielding an absolute accuracy better than 10\%.
The calibration and flagging were made using a standard pipeline running on \textsc{casa} \citep{McMullin07} version 4.7.2, while manual flagging was needed for some outlier antennas.
Four tuning data are combined to make the continuum image using the \textsc{casa} task, \texttt{clean}, with the natural weighting. Note that spectral channels where the \oiii{} line is detected were not used for continuum imaging. The resulting synthesized beam size in full width at half maximum (FWHM) is $0\farcs 26 \times 0\farcs 21$ (position angle PA = $-82\arcdeg$). Synthesized beam deconvolution is made down to $2\sigma$.
Each tuning data set was also imaged to produce a cube with a frequency resolution of 31.25~MHz ($\approx 26$~km~s$^{-1}$) to search for the \oiii{} line. As the data sets were obtained in different array configurations and some SPWs with long baselines may resolve out the emission, we optimally-taper the image with a $0\farcs 35$ Gaussian kernel to maximize the signal-to-noise ratio (SNR) of the emission.
The resulting beam size and r.m.s.\ noise level measured at 364~GHz are $0\farcs 38 \times 0\farcs 36$ (PA = $-79\arcdeg$) and $\sigma = 0.5$~mJy~beam$^{-1}$, respectively (Figures~\ref{fig:image} and \ref{fig:spectrum2}).
\subsection{ALMA and Hubble Astrometry} \label{sec:astrometry}
The position of the LBG was originally determined by the HFF \HST{} images which are aligned to the existing CLASH catalogs \citep{Postman12}; the CLASH astrometry was based on Subaru's Suprime-Cam catalogs which are registered onto the Two-Micron All Sky Survey (2MASS) frame. We find, however, that the optical-to-NIR astrometry does not fully match the International Celestial Reference System (ICRS), on which ALMA relies. In order to correct the astrometry of the \HST{} images, we use four positions of objects (3 stars and 1 cluster elliptical) accurately measured in the \Gaia{} first data release (DR1) catalog \citep{Gaia16a, Gaia16b}. We also compare the positions of the three quasars used as ALMA phase calibrators, J0348$-$2749, J0453$-$2807 and J0522$-$3627, which are determined by the \Gaia{} DR1 catalog and by phase solutions from our ALMA calibration.
We find that the relative offsets between the ALMA and \Gaia{} coordinates are typically $< 10$ mas. All of the \HST{} images are corrected for astrometry on the basis of the \Gaia{} coordinates using the \textsc{iraf} \citep{Tody93} task, \texttt{ccsetwcs}, confirming those two frames coincide with each other down to the accuracy of $\lesssim 30$ mas. The resulting centroid of the LBG in the ICRS coordinate is at $\rm (\alpha_{ICRS}, \delta_{ICRS}) = (04^h 16^m 09\fs 415, -24\arcdeg 05' 35\farcs54)$. We hereafter use this coordinate as the formal position of \target{}.
\subsection{X-shooter Observations and Reduction}
To verify the redshift of \target{} we aimed to detect the redshifted UV emission lines from either Ly$\alpha$, C{\sc\,iv}~$\lambda\lambda$1548,\,1550~\AA{}, C{\sc\,iii}]~$\lambda\lambda$1907,1909~\AA{} or
O{\sc\,iii}]~$\lambda\lambda$1661,\,1666~\AA{}.
We observed \target{} with VLT/X-shooter \citep{Vernet11} for a total of 10 hours on target. The observations were carried out at 10 different nights between 2017 December 8 and 2018 January 21 (Program ID: 0100.A-0529(A), PI: Zackrisson). A blind offset from a neighboring star was used to place the slit on the galaxy using the coordinates from \emph{HST} images. A $1\farcs 2$ wide slit was chosen at optical and near-IR wavelengths in order to capture the rest-frame UV emission from the galaxy, and the slit was aligned along the parallactic angles (between 95$\arcdeg$--100$\arcdeg$ East of North). The observations were carried out in an ABBA nodding mode pattern with $4 \times 900$~s integrations. During the observations, the sky transmission was clear or photometric and the seeing varied between $0\farcs 4$ and $0\farcs 8$, yielding the best possible conditions for detecting faint emission lines.
The data were reduced with {\sc esorex} scripts \citep{Modigliani10} using adjacent positions in the nodding sequence for sky background subtraction. Corrections for telluric absorption lines were applied from models with {\sc Molecfit} \citep{Kausch15} applied to observations of hot stars following the science integrations. Errors were propagated throughout the data processing stpdf. Since the seeing FWHM was smaller than the slit widths, we measured the spectral resolutions from telluric absorption lines, yielding effectively $R=5600$ in the near-IR spectra. Observations of spectrophotometric standard stars on each of the 10 nights were used to flux calibrate each spectrum before they were co-added.
\begin{figure*}[ht!]
\includegraphics[angle=-90,width=1.0\textwidth]{fig2_spectrum_31p25MHz.pdf}
\caption{
The full ALMA spectrum produced by combining four independent tunings
T1--T4. The spectrum is continuum-subtracted. The blue dots with
error bars represent the photometric redshifts with a 68\% confidence
interval measured by six independent studies;
\citet[][denoted as I15]{Infante15},
\citet[][L15]{Laporte15},
\citet[][M15]{McLeod15},
\citet[][L16]{Laporte16},
\citet[][K16]{Kawamata16} and
\citet[][C16]{Castellano16}.
The lower panel shows the atmospheric transmission under a precipitable
water vapor (PWV) of 0.9~mm, a moderate condition at the ALMA site. The
horizontal bars show the coverage of the 4 tunings, T1--T4, each of
which has 4 spectral windows.
\label{fig:spectrum}}
\end{figure*}
\begin{figure}[th!]
\includegraphics[angle=-90,width=0.47\textwidth]{fig3_spectrum2.pdf}
\caption{
The continuum subtracted spectrum showing the \oiii{} line (top) with
the best-fitting Gaussian function (red curve). The lower panel shows
the $1\sigma$ noise level, where an atmospheric absorption line is seen
close to the \oiii{} line.
\label{fig:spectrum2}}
\end{figure}
\section{Results} \label{sec:result}
\subsection{Detection of 850 $\micron$ Dust Continuum}
We detect 850-$\micron$ (i.e., rest-frame 90~$\micron$) continuum emission at the position of \target{} as shown in Figure~\ref{fig:image} (left). The peak ICRS position is $\rm (\alpha_{ICRS}, \delta_{ICRS})= (04^h16^m09\fs423 \pm 0\fs002,\,-24\arcdeg 05' 35\farcs50 \pm 0\farcs01)$.
The r.m.s.\ noise level after combining all of the SPWs is $\sigma = 10.9$~$\mu$Jy~beam$^{-1}$, yielding the significance of $7.6\sigma$ on the resulting image.
The flux density and the image component size deconvolved with the synthesized beam are measured using a \textsc{casa} task \texttt{imfit} with an assumption that the source is 2-dimensional Gaussian and are found to be $S_\mathrm{850\,\mu m} = 137 \pm 26$~$\mu$Jy and $(0\farcs 36 \pm 0\farcs 09) \times (0\farcs 10 \pm 0\farcs 05)$ in FWHM (PA = +84$\arcdeg$), respectively.
This elongation is not likely due to the cluster magnification but the intrinsic shape of the LBG, because its elongation does not align with the lensing shear direction. The overall spatial distribution of the 850~$\micron$ continuum is similar to that of the rest-frame UV emission, while the bulk of dust emission is likely to be associated with the eastern `E' knot (or a gap between the `E' and central `C' knots) seen in the \HST{}/WFC3 image (Figure~\ref{fig:image} right).
We also retrieve a previous 1.14~mm imaging result obtained for the MACS~J0416.1$-$2403 cluster \citep{Gonzalez-Lpez17}. No 1.14 mm emission is found with the $2\sigma$ upper limit of 116~$\mu$Jy. This places an upper limit on the spectral index between 1.14~mm and 850~$\micron$ to be $\alpha > 0.6$ (2$\sigma$), where $\alpha$ is defined such that $S_{\nu} \propto \nu^{\alpha}$. Despite a relatively weak constraint, this could rule out a low-$z$ interloper with non-thermal emission from an active galactic nucleus, where $\alpha \sim -0.7$ is expected.
Instead, the spectral index is consistent with dust continuum emission with a temperature of $\gtrsim 30$~K.
The observed flux density of $S_\mathrm{850\,\mu m} = 137 \pm 26$~$\mu$Jy corresponds to a de-lensed total IR luminosity of
$\Lir = (1.7 \pm 0.3) \times 10^{11} L_\sun$
[$(1.1 \pm 0.2) \times 10^{11} L_\sun$]
and a dust mass of
$\Mdust = (3.6 \pm 0.7) \times 10^{6} M_\sun$
[($8.2 \pm 1.6) \times 10^{6} M_\sun$]
when assuming a dust temperature of $\Tdust = 50$~K (40~K) and the magnification
factor of $\mu_{\rm g} = 1.43 \pm 0.04$ (see Table~\ref{tab:param} for more details).
\begin{figure*}[th]
\begin{center}
\includegraphics[angle=-90,width=0.65\textwidth]{fig4_o3deficit.pdf}
\caption{
The \oiii-to-IR luminosity ratio as a function of IR luminosity. The filled symbols represent the galaxies at $z \gtrsim 7$, i.e.,
\target{} (five-pointed star),
SXDF-NB1006-2 \citep[filled circle with two arrows,][]{Inoue16},
BDF-3299 \citep[filled pentagon,][]{Maiolino15, Carniani17},
A2744\_YD4 \citep[filled square,][]{Laporte17},
MACS1149-JD1 \citep[filled triangle with two arrows,][]{Hashimoto18},
B14-65666 \citep[filled diamond,][]{Hashimoto18b} and
SPT0311$-$58 E/W \citep[filled triangles,][]{Marrone18}.
The open symbols are lower-$z$ galaxies;
local dwarfs \citep[open circles,][]{Madden13, Cormier15},
the SHINING samples of local star-forming galaxies from normal spirals to ultra-luminous IR galaxies (ULIRGs) \citep[small gray open squares,][]{Herrera-Camus18a, Herrera-Camus18b},
the median of local spirals \citep[large black open square with the error bar representing 1.5 times the median absolute deviation,][]{Brauher08} and
$z \sim 2$--4 dusty star-forming galaxies \citep[open triangles,][]{Ferkinhoff10, Ivison10, Valtchanov11, Vishwas18}.
All of the $z > 7$ galaxies, except for SPT0311$-$58 E/W, are assumed to have the dust temperature of $\Tdust = 50$~K; note that $\Lir$ decreases by a factor of 0.7 if assuming $\Tdust = 40$~K. The IR luminosities are corrected for magnification, if any. The blue-to-green color code shown for \target{}, SXDF-NB1006-2, MACS1149-JD1, B14-65666 and local dwarfs indicates the best-fitting oxygen abundances.
\label{fig:o3deficit}}
\end{center}
\end{figure*}
\subsection{Blind Detection of [O\,III] 88 $\micron$}
At the position of the dust emission, we detect an emission line feature at $364.377 \pm 0.012$~GHz, strongly suggesting the \oiii{} 88~$\micron$ emission line at $z = 8.3118 \pm 0.0003$ (Figure~\ref{fig:spectrum}). This redshift is slightly lower than, but yet consistent with, the photometric redshifts. This is a rather common feature seen in LBGs in the reionization era \citep[e.g., MACS1149-JD1][]{Zheng17, Hashimoto18}; the slight offset is likely due to the fact that the largely-neutral interstellar/intergalactic medium attenuates the edge of Lyman break and makes the photo-$z$ estimates higher.
Figure~\ref{fig:image} (center) shows the integrated intensity image where the \oiii{} line is detected at $6.3\sigma$. The intensity peak is associated with the `E'--`C' clumps seen in the \HST{}/F160W image (Figure~\ref{fig:image} right).
The apparent flux is
$F_\mathrm{[O\,III]} = 0.66 \pm 0.16$~Jy~km~s$^{-1}$, corresponding to the de-lensed luminosity of $L_\mathrm{[O\,III]} = (1.2 \pm 0.3) \times 10^{9} L_{\sun}$.
The image may barely be resolved and has a beam-deconvolved size of $\sim 0\farcs 5 \times 0\farcs 3$ (PA = $89^{\arcdeg}$) despite a large uncertainty.
The line width is estimated by a Gaussian fit (Figure~\ref{fig:spectrum2}) and is found to be $\Delta V_\mathrm{[O\,III]} = 141 \pm 21$~km~s$^{-1}$ in FWHM, which is consistent with those predicted for dark halos hosting a bright ($H_{160} \sim 26$) galaxy at $z \sim 8$ in a cosmological hydrodynamic simulation \citep{Shimizu14, Inoue14}.
The line width is also similar to those found in SXDF-NB1006-2 at $z = 7.212$ \citep[$\Delta V_\mathrm{[O\,III]} \approx 80$~km~s$^{-1}$,][]{Inoue16} and MACS1149-JD1 at $z = 9.110$ \citep[$154 \pm 39$~km~s$^{-1}$,][]{Hashimoto18}, but broader than that of A2744-YD4 \citep[$\Delta V_\mathrm{[O\,III]} \simeq 43$~km~s$^{-1}$,][]{Laporte17}. The observed quantities are summarized in Table~\ref{tab:param}.
Figure~\ref{fig:o3deficit} shows the \oiii-to-IR luminosity ratio, $\Loiii/\Lir$, found in local and high-$z$ galaxies as a function of $\Lir$.\footnote{Here we assume $\Tdust = 50$~K for $\Lir$ of $z > 7$ galaxies for which $\Tdust$ is unknown. The $\Loiii/\Lir$ ratio increases by a factor of 1.5 if assuming $\Tdust = 40$~K.}
It is known that the $\Loiii/\Lir$ ratios exhibit a possible weak anti-correlation with $\Lir$ as suggested by earlier studies of local galaxies \citep{DeLooze14, Cormier15, Diaz-Santos17}.
The $\Loiii/\Lir$ of \target{} is estimated to be
$\Loiii/\Lir \approx 7 \times 10^{-3}$ and is comparable to
those found in the \Herschel{} Dwarf Galaxy Survey \citep[$\Loiii/\Lir = 5.0^{+16.6}_{-1.5} \times 10^{-3}$,][]{Cormier15}.
The ratio is as high as those found for $z = 7$--9 UV-selected galaxies,
such as
SXDF-NB1006-2 \citep[$\Loiii/\Lir > 1.3 \times 10^{-2}$,][]{Inoue16},
MACS1149-JD1 \citep[$> 7 \times 10^{-3}$,][]{Hashimoto18},
B14-65666 \citep[$4.6 \times 10^{-3}$,][]{Hashimoto18b},
BDF-3299 \citep[$> 2 \times 10^{-3}$,][]{Carniani17}, and
A2744\_YD4 at $z = 8.38$ \citep[$\sim 1 \times10^{-3}$,][]{Laporte17},
although SXDF-NB1006-2 and MACS1149-JD1 may have much higher values.
The ratio of \target{}, however, exhibits a sharp contrast to
those found in local spirals, ultra-luminous IR galaxies
\citep[][see the gray open squares in Figure~\ref{fig:o3deficit}]{Herrera-Camus18a, Herrera-Camus18b},
$z \sim 2$--7 submillimeter galaxies \citep[$\simeq 1 \times 10^{-3}$ or less,][]{Ferkinhoff10, Valtchanov11, Marrone18, Vishwas18},
and an IR-luminous quasar APM~08279+5255 \citep[$3 \times 10^{-4}$,][]{Ferkinhoff10}.
\begin{deluxetable*}{ccccccccccc}[ht]
\tablecaption{The observed quantities of \target{}. \label{tab:param}}
\tablecolumns{10}
\tablewidth{0pt}
\tablehead{
\colhead{} & \colhead{} &
\multicolumn{2}{c}{$\Tdust = 40$~K} &
\colhead{} &
\multicolumn{2}{c}{$\Tdust = 50$~K} &
\colhead{} & \colhead{} & \colhead{} & \colhead{} \\
\cline{3-4}
\cline{6-7}
\colhead{$S_\mathrm{850\,\mu m}$} &
\colhead{FWHM\tablenotemark{$\dagger$}} &
\colhead{$L_\mathrm{IR}$\tablenotemark{$\sharp$}} &
\colhead{$M_\mathrm{dust}$\tablenotemark{$\sharp$}} &
\colhead{} &
\colhead{$L_\mathrm{IR}$\tablenotemark{$\sharp$}} &
\colhead{$M_\mathrm{dust}$\tablenotemark{$\sharp$}} &
\colhead{$F_\mathrm{[O\,III]}$} &
\colhead{$\Delta V_\mathrm{[O\,III]}$} &
\colhead{$z$} &
\colhead{$L_\mathrm{[O\,III]}$\tablenotemark{$\sharp$}} \\
\colhead{($\mu$Jy)} &
\colhead{(arcsec)} &
\colhead{($10^{11} L_\sun$)} &
\colhead{($10^{6} M_\sun$)} &
\colhead{} &
\colhead{($10^{11} L_\sun$)} &
\colhead{($10^{6} M_\sun$)} &
\colhead{(Jy km s$^{-1}$)} &
\colhead{(km s$^{-1}$)} &
\colhead{} &
\colhead{($10^{9} L_\sun$)}
}
\startdata
$137 \pm 26$ &
$0\farcs 36 \times 0\farcs 10$ &
$1.1 \pm 0.2$ &
$8.2 \pm 1.6$ &
&
$1.7 \pm 0.3$ &
$3.6 \pm 0.7$ &
$0.66 \pm 0.16$ &
$141 \pm 21$ &
$8.3118 \pm 0.0003$ &
$1.2 \pm 0.3$ \\
\enddata
\tablecomments{The error represents the 68\% confidence interval.}
\tablenotetext{\dagger}{
The beam-deconvolved source size measured for the continuum image.}
\tablenotetext{\sharp}{
The value is corrected for lensing magnification of $\mu_\mathrm{g} = 1.43 \pm 0.04$ \citep{Kawamata16}, while the error bar does not include the uncertainty in $\mu_{\rm g}$. The IR luminosity is derived from a modified blackbody defined in the range of 8--1000~$\micron$. Note that no Wien correction is applied when the IR luminosity is derived. The extra heating from the cosmic microwave background is taken into account in deriving the IR luminosity and dust mass according to the formulation by \citet{daCunha13}. The dust emissivity is assumed such that $\kappa_\mathrm{d}(\nu) = \kappa_\mathrm{d}(850~\micron) (\nu/\nu_0)^{\beta}$,
where
$\nu_0 = 353$~GHz,
$\kappa_\mathrm{d}(850~\micron) = 0.15$~m$^2$~kg$^{-1}$ \citep[e.g.,][]{Weingartner01, Dunne03} and
$\beta = 1.5$ are the dust absorption coefficient and the emissivity index, respectively.}
\end{deluxetable*}
\subsection{UV emission line detection limits}
The final 2-dimensional spectrum from X-shooter covering near-IR
wavelengths at 1--2.4~$\micron$ was inspected for emission lines. At
the redshift of \oiii{} 88~$\micron$ from ALMA ($z=8.3118$) no
rest-frame UV emission lines were detected. Furthermore, no emission
lines could be visually identified at other wavelengths. To determine
detection limits, we added artificial emission lines with varying FWHM
at the expected wavelengths and extracted 1-dimensional spectra and
their associated error spectra. To enhance the S/N detection limit, we
binned the data in the spectral dimension by varying factors between 3
and 7 pixels \citep[see][]{Watson15}. To confidently detect an
emission line we require a S/N = 5 detection. Table~\ref{tab:xsh_limits}
summarizes the detection limits for lines with FWHM ranging from 50 to
150~km~s$^{-1}$ for the brighter of the doublet lines. Since
Ly$\alpha$ is a resonance line, we also compute the detection limit
for a larger width of 250 km~s$^{-1}$. Typical limits are of the
order of a few times $10^{-18}$~erg~s$^{-1}$~cm$^{-2}$. The reported
limits have not been corrected for lens magnifications.
\begin{deluxetable}{lccc}[hb!]
\tablecaption{The 5$\sigma$ detection limits of UV emission lines
in X-shooter data assuming redshift $z=8.3118$.
\label{tab:xsh_limits}}
\tablecolumns{4}
\tablewidth{0pt}
\tablehead{
\colhead{} &
\multicolumn{3}{c}{$5\sigma$ detection limits} \\
\cline{2-4}
\colhead{Lines} &
\colhead{250~km~s$^{-1}$} &
\colhead{150~km~s$^{-1}$} &
\colhead{50~km~s$^{-1}$}
}
\startdata
Ly$\alpha$ & $< 8.0$ & $< 5.0$ & $< 3.0$ \\
C{\sc\,iv} $\lambda\lambda$1548,\,1550 \AA{} & $\cdots$ & $< 4.0$ & $< 1.8$ \\
O{\sc\,iii}] $\lambda$1666 \AA{}\tablenotemark{$\dag$} & $\cdots$ & $< 5.2$ & $< 3.0$ \\
C{\sc\,iii}] $\lambda$1907 \AA{}\tablenotemark{$\dag$} & $\cdots$ & $< 6.0$ & $< 2.4$ \\
\enddata
\tablecomments{
The detection limits are measured for line widths (FWHM) of 250, 150 and 50~km~s$^{-1}$. The limits are not corrected for magnification. The flux limits are in units of
$10^{-18}$~erg~s$^{-1}$~cm$^{-2}$.}
\tablenotetext{\dagger}{The detection limit for the brighter of the doublet lines.}
\end{deluxetable}
\section{Physical Properties of \target{}} \label{sec:sed}
The ALMA observations clearly show that \target{} has a substantial amount of dust which exhibits a similar spatial distribution to the rest-frame UV emission on a $\sim$1~kpc scale. This is somewhat surprising because the UV slope is blue ($\beta_\mathrm{UV} \approx -2$) and earlier studies have actually suggested small dust extinction with $A_V \lesssim 0.4$ \citep[e.g.,][]{Laporte15}.
Furthermore, the \Spitzer{}/IRAC photometry shows a red color in the rest-frame optical ($[3.6]-[4.5] > 0.38$; see Table~\ref{tab:photometry}). The attribution includes (i) the stellar population with the Balmer break at $\lambda_\mathrm{obs} \approx 3.7~\micron$ and (ii) a substantial contribution of the optical \oiii{} $\lambda\lambda4959,\,5007$~\AA{} lines to the 4.5~$\micron$ band \citep[e.g.,][]{Labbe13, Smit15}. The former case is expected for a relatively-evolved stellar component, while the latter requires a much younger stellar population where OB stars are dominant in luminosity.
\begin{deluxetable*}{ccccc}[ht!]
\tablecaption{The photometric data of \target{}.\label{tab:photometry}}
\tablecolumns{5}
\tablewidth{0pt}
\tablehead{
\colhead{} &
\colhead{Wavelength} &
\colhead{AB magnitude\tablenotemark{$\dagger$}} &
\multicolumn{2}{c}{Flux density\tablenotemark{$\ddagger$}} \\
\cline{4-5}
\colhead{Instrument} &
\colhead{($\micron$)} &
\colhead{(mag)} &
\colhead{Value} &
\colhead{Unit}
}
\startdata
\textit{HST}/F435W & 0.431 & $>30.07$ & $< 3.40$ & nJy \\
\textit{HST}/F606W & 0.589 & $>30.40$ & $< 2.51$ & nJy \\
\textit{HST}/F814W & 0.811 & $>30.32$ & $< 2.70$ & nJy \\
\textit{HST}/F105W & 1.05 & $>29.83$ & $< 4.25$ & nJy \\
\textit{HST}/F125W & 1.25 & $26.41\pm0.07$ & $99^{+7}_{-6}$ & nJy \\
\textit{HST}/F140W & 1.40 & $26.08\pm0.05$ & $134^{+6}_{-6}$ & nJy \\
\textit{HST}/F160W & 1.55 & $26.04\pm0.05$ & $139^{+7}_{-6}$ & nJy \\
VLT/HAWK-I ($K_S$) & 2.152 & $26.37\pm0.39$ & $103^{+44}_{-31}$ & nJy \\
\textit{Spitzer}/IRAC (ch1) & 3.6 & $>25.32$ & $< 270$ & nJy \\
\textit{Spitzer}/IRAC (ch2) & 4.5 & $24.94 \pm 0.29$ & $384^{+117}_{-90}$ & nJy \\
ALMA/Band 7 & 850 & ... & $137\pm 26$ & $\mu$Jy \\
ALMA/Band 6 & 1140 & ... & $< 116$ & $\mu$Jy \\
\enddata
\tablecomments{All values are not corrected for cluster lensing magnification.}
\tablenotetext{\dagger}{The error bars represent the 68\% confidence interval. The lower limit is given at $2\sigma$, where $\sigma$ is obtained by randomly measuring the sky with PSF diameter apertures. All of the photometry are obtained in this work; see \citet{Laporte15} (\textit{HST} and \textit{Spitzer}) and \citet{Brammer16} (VLT/HAWK-I) for original imaging data.}
\tablenotetext{\ddagger}{The error bars represent the 68\% confidence interval. The upper limit is given at $2\sigma$.}
\end{deluxetable*}
\subsection{Spectral Energy Distribution Model}\label{subsec:SED}
Here we characterize the SED to investigate the physical properties of \target{} by template fits where stellar populations, UV-to-FIR nebular emission, and dust thermal emission are taken into account.
We use the photometric data of the 850~$\micron$ continuum and \oiii{} line in addition to the rest-frame UV-to-optical bands (Table~\ref{tab:photometry}) to model the SED of \target{}.
The model is based on the prescription presented by \citet{Mawatari16} and Mawatari et al.\ in preparation,\footnote{Panchromatic Analysis for Nature of HIgh-$z$ galaxies Tool (PANHIT), \url{http://www.icrr.u-tokyo.ac.jp/~mawatari/PANHIT/PANHIT.html}.} where emission components of a stellar continuum \citep{Bruzual03}, rest-frame UV-to-optical nebular lines \citep{Inoue11}, and dust continuum \citep{Rieke09} are accounted for.
In addition, we take into account the \oiii{} 88~$\micron$ line \citep{Inoue14} and nebular continuum in the UV-to-optical wavelengths \cite{Inoue11}.
We use the stellar population synthesis model from \citet{Bruzual03} with the Chabrier initial mass function (IMF) defined in the range of 0.1--100~$M_\sun$ \citep{Chabrier03}. We assume exponentially declining and rising SFRs expressed as
\begin{eqnarray}\label{eq:sfh}
\mathrm{SFR}(\tau_\mathrm{age}) =
\frac{1}{|\tau_\mathrm{SFH}|}
\exp{\left(-\frac{\tau_\mathrm{age}}{\tau_\mathrm{SFH}}\right)},
\end{eqnarray}
where $\tau_\mathrm{age}$ is the age of the galaxy which ranges from 0.1~Myr to the age of the Universe at $z = 8.312$, $\tau_\mathrm{SFH}$ is the $e$-folding time-scale of SFR and is set to $\pm0.01$, $\pm0.1$, $\pm1$, and $\pm10$~Gyr. The positive and negative time-scales represent declining and rising SFRs, respectively.
For rising SFRs (i.e., $\tau_\mathrm{SFH} < 0$), we just fix
$\mathrm{SFR}(\tau_\mathrm{age}) = \frac{1}{|\tau_\mathrm{SFH}|} \exp{(10)}$
at $\tau_\mathrm{age} > 10\tau_\mathrm{SFH}$ to avoid SFRs diverging.
We also explore five metallicity values of $Z = 0.0001$, 0.0004, 0.004, 0.008, and 0.02 (ranging 1/200--$1\,Z_{\sun}$).
Three extinction laws from \citet{Calzetti00}, Small Magellanic Cloud \citep[SMC,][]{Prevot84, Bouchet85} and Milky Way \citep[MW, ][who fit data obtained by \citealt{Seaton79}]{Fitzpatrick86} are employed in the range of $A_V = 0$--5 to account for dust extinction.
The nebular continuum and lines arising from ionized gas are modeled by relating the Lyman continuum (LyC) photon rate, metallicity and nebular emissivity.
The ionizing photon rate is determined for each grid of stellar age and metallicity in the stellar population synthesis model.
Following \citet{Inoue11}, we derive the electron temperature, the nebular continuum emissivity for a unit LyC photon rate, and the nebular line emissivities for a unit H$\beta$ flux, as a function of metallicity. H$\beta$ flux is derived by assuming the case B recombination. The escape fraction of LyC photons, $f_\mathrm{esc}$, is treated as a free parameter, while that of Ly$\alpha$ photons is fixed to 1. We accordingly attenuate the flux densities at $\lambda_\mathrm{rest} < 912$~\AA{} by a factor of $f_\mathrm{esc}$. We ignored LyC absorption by dust for simplicity.
The intergalactic \textsc{H\,i} transmission model of \citet{Inoue14b} is also adopted with an extrapolation from $z < 6$ to $z = 8.3$. This simply diminishes the flux below the Ly$\alpha$ wavelength including the Ly$\alpha$ emission line.
For \oiii{} 88~$\micron$, we use the prescription of \citet{Inoue14}, where the \oiii{} emissivity for a unit SFR
(i.e., $\Loiii{} / \mathrm{SFR}$) is assumed to be modeled as a function of metallicity. This ($\Loiii{} / \mathrm{SFR}$)-to-metallicity relation is calibrated by \textit{ISO}, \Herschel{} and \textit{AKARI} observations of local dwarfs and spirals \citep{Brauher08, Kawada11, Madden13, DeLooze14, Cormier15}.
We do not use the X-shooter upper limits on the individual UV line fluxes for the model constraint,
because the UV line intensities are sensitive to physical properties of ionized media, such as electron density and ionization parameter \citep[e.g.,][]{Inoue11}, which could induce large uncertainties in the UV nebular line emissivities.
We compute the 5-to-1000 $\micron$ luminosity $L_\mathrm{IR}$ for each stellar model grid and extinction by assuming that $L_\mathrm{IR}$ is equivalent to the luminosity of stellar and nebular emission at 0.01--2.2~$\micron$ absorbed by dust. We then assign an IR-to-millimeter SED for each stellar component and extinction on the basis of $L_\mathrm{IR}$. The shapes of the SEDs were determined for local luminous infrared galaxies (LIRGs) and modeled as a function of $L_\mathrm{IR}$ \citep{Rieke09}.
\begin{figure*}[t]
\includegraphics[width=0.48 \textwidth]{fig5_kensfit_SED_Calzetti.pdf}
\includegraphics[width=0.48 \textwidth]{fig5_kensfit_SED_MW.pdf}\\
\includegraphics[width=0.48 \textwidth]{fig5_kensfit_SED_SMC.pdf}
\caption{
The best-fitting spectral energy distributions (SEDs) for three dust extinction laws.
(a) The SEDs modeled with the Calzetti dust extinction law. The filled and open squares represent the observed photometric data points, while the photometric data at $< 1~\micron$ are not used for SED fits. Those of the rest-frame FIR constraints are shown in the small panels. The solid curve is the best-fitting SEDs. The crosses are flux densities (or flux for the \oiii{} 88~$\micron$ line) predicted from the model.
(b) The same plot, but the Milky Way dust extinction law is used. The overall trend is the same as the Calzetti case, while the $K_s$ band decrement is well explained by the 2175~\AA{} feature of the extinction law.
(c) The same plot, but the SMC extinction law is used.
\label{fig:sed}}
\end{figure*}
\begin{deluxetable*}{cccc}[ht!]
\tablecaption{The best-fitting parameters of the rest-frame ultraviolet to far-infrared spectral energy distribution of \target{}.\label{tab:sedparam}}
\tablecolumns{2}
\tablewidth{0pt}
\tablehead{
\colhead{} &
\multicolumn{3}{c}{Extinction law}\\
\cline{2-4}
\colhead{Items} &
\colhead{Calzetti} &
\colhead{MW} &
\colhead{SMC}
}
\startdata
$\chi^2$
& 7.1
& 6.8
& 8.4 \\
Degree of freedom
& 3
& 3
& 3 \\
Dust attenuation $A_V$ (mag)
& $0.50 ^{+0.09}_{-0.13}$
& $0.50 ^{+0.08}_{-0.16}$
& $0.20 ^{+0.10}_{-0.08}$ \\
Age $\tau_\mathrm{age}$ (Myr)
& $3.5 ^{+0.7}_{-2.3}$
& $4.2 ^{+0.3}_{-3.0}$
& $2.0 ^{+1.6}_{-0.6}$ \\
SFH $\tau_\mathrm{SFH}^{-1}$ (Gyr$^{-1}$)\tablenotemark{$^{\sharp}$}
& $100 ^{+0}_{-200}$
& $-10 ^{+110}_{-90}$
& $100 ^{+0}_{-200}$ \\
Metallicity $Z$ ($Z_{\sun}$)
& $0.20 ^{+0.16}_{-0.18}$
& $0.20 ^{+0.17}_{-0.18}$
& $0.20 ^{+0.54}_{-0.17}$ \\
LyC escape fraction $f_\mathrm{esc}$
& $0.00^{+0.19}_{-0.00}$
& $0.00^{+0.14}_{-0.00}$
& $0.40^{+0.21}_{-0.40}$ \\
Stellar mass $M_\mathrm{star}$ ($10^{8} M_\sun$)\tablenotemark{$^{\dagger}$}
& $2.4 ^{+0.7}_{-0.1}$
& $2.4 ^{+0.6}_{-0.3}$
& $2.2 ^{+0.5}_{-0.2}$ \\
SFR ($M_\sun$ yr$^{-1}$)\tablenotemark{$^{\dagger}$}
& $57 ^{+175}_{-0.2}$
& $60 ^{+168}_{-2}$
& $100 ^{+56}_{-33}$ \\
$L_\mathrm{IR}$ ($10^{11} L_{\sun}$)\tablenotemark{$^{\dagger}$}
& $1.5^{+0.2}_{-0.3}$
& $1.6^{+0.1}_{-0.4}$
& $1.2^{+0.5}_{-0.2}$ \\
\enddata
\tablecomments{The error bars represent the 68$\%$ confidence interval
estimated from probability distribution functions (PDFs) on the basis of a Monte Carlo technique following the prescription presented by \citet{Hashimoto18}.
The probability distributions for the fitting parameters are presented in Appendix~\ref{sec:appendix}.
}
\tablenotetext{\dagger}{The value is corrected for lensing magnification with $\mu_\mathrm{g} = 1.43 \pm 0.04$ \citep{Kawamata16}, while the error bar does not include the uncertainty in $\mu_\mathrm{g}$.}
\tablenotetext{\sharp}{$\tau_\mathrm{SFH}^{-1} = 0$, $\tau_\mathrm{SFH}^{-1} > 0$ and $\tau_\mathrm{SFH}^{-1} < 0$ represent constant, exponentially-declining and rising star-formation histories as defined in Equation~\ref{eq:sfh}.}
\end{deluxetable*}
\subsection{Results}\label{subsec:SEDresults}
The results are shown in Figure~\ref{fig:sed} and Table~\ref{tab:sedparam}\footnote{See also Appendix~\ref{sec:appendix} for the probability distributions for the SED parameters.}. One of the important outcomes is that there exist solutions which reasonably explain the large amount of dust coexisting with the young stellar components.
Regardless of the extinction law, the SED fits favor a young, high-SFR solution, where large equivalent widths of the enhanced \oiii{} $\lambda\lambda$4959,\,5007~\AA{} and H$\beta$ lines contribute to the $[3.6]-[4.5]$ color. The SFR and age are estimated to be $\approx 60\ M_{\sun}$~yr$^{-1}$ and $\approx 4$~Myr, respectively, suggesting that \target{} is at the onset of a starburst phase.
The carbonaceous absorption feature of the MW extinction law at $\lambda_\mathrm{rest} \approx 2175$~\AA{} can explain the blue $H-K_S$ color, although the predicted flat UV spectrum assuming the Calzetti or SMC law is not ruled out because of a large uncertainty in $K_S$ band photometry.
The best-fitting metallicity already reaches $Z \approx 0.2 Z_\sun$ at $z = 8.3$ despite a large uncertainty, suggesting rapid enrichment of heavy elements in the middle of the reionization era.
This does not, however, explain how the galaxy has \emph{obtained} the large amount of dust, even though the SED model explains the energy budget self-consistently if assuming that the dust \emph{preexists}.
The dust-to-stellar mass ratio inferred from the SED fits is $M_\mathrm{dust} / M_\mathrm{star} \sim 1 \times 10^{-2}$. This is 1--2 orders of magnitude higher compared to the median value obtained for 29 local dwarf galaxies from the \Herschel{} Dwarf Galaxy Survey \citep{Madden13, Remy-Ruyer15}, which is
$M_\mathrm{dust} / M_\mathrm{star} = 2^{+12}_{-1.8} \times 10^{-4}$,
where the error bar represents the 90 percentile.
The ratio would even be an order of magnitude higher than those of dusty star-forming galaxies \citep[e.g.,][]{daCunha10, Smith12, Clark15, DeVis17}; for instance, a median of $M_\mathrm{dust}/M_\mathrm{star} = 4.2 \times 10^{-3}$ is observed for 1402 250-$\micron$ selected normal star-forming galaxies at $z < 0.5$ from the \Herschel{}-ATLAS survey \citep{Smith12}.
These facts suggest that the stellar mass of \target{} could significantly be underestimated if only ongoing star-formation is taken into account, implying the presence of a more massive, evolved stellar population. Note that a very high dust temperature (e.g., $\Tdust \sim 100$~K) could only reduce the dust mass by a factor of $\sim 5$ and does not fully explain the high $M_\mathrm{dust} / M_\mathrm{star}$ ratio. The evolved stellar component as a result of past star-formation activity is also expected as the origin of the dust mass, which will be discussed in the following section \S~\ref{sec:discussion}.
\begin{figure*}
\includegraphics[angle=-90, width=1.0 \textwidth]{fig6_dustmodel.pdf}
\caption{
The time evolution of (a) stellar mass, (b) SFR, (c) metallicity, and (d) dust mass predicted in a dust formation model \citep{Asano13a, Asano13b, Asano14, Nozawa15} as a function of galaxy age with an initial gas mass of $M_\mathrm{gas} = 2 \times 10^{10} M_{\sun}$ and a star-formation time-scale of $\tau_\mathrm{SFH} = 0.3$~Gyr.
The open square, filled circle and triangle represent the best-fitting parameters of the physical properties of \target{} estimated by the Calzetti, MW, and SMC extinction laws, respectively (see Table~\ref{tab:sedparam}).
In panel (d) two de-lensed dust mass estimates for $T_\mathrm{dust} = 50$~K (lower symbols) and 40~K (upper symbols) are plotted.
\label{fig:grain}}
\end{figure*}
\begin{figure}
\includegraphics[width=0.47\textwidth]{fig7_youngold.pdf}
\caption{
The stellar SED model (red curve) in which a mature ($\tau_\mathrm{age} = 300$~Myr) component with $M_\mathrm{star} = 3 \times 10^{9}\,M_{\sun}$ built by constant star-formation lasting for 100~Myr (blue curve) is added to the best-fit SED model (pink curve, \S~\ref{subsec:SEDresults}). The symbols are the same as those presented in Figure~\ref{fig:sed}, but the crosses are flux densities predicted from the model in which the mature component is added.
The open squares represent the photometric data at $< 1~\micron$ which are not used for SED fits.
The extinction law is assumed to be \citet{Calzetti00}.
\label{fig:youngold}}
\end{figure}
\section{Discussions} \label{sec:discussion}
The stellar SED analysis presented in \S~\ref{sec:sed} has highlighted
an extremely-young, star-forming stellar component.
The solution also explains the IR luminosity if the dust mass preexists, while it needs to be discussed whether the large dust mass can be attained in the very short duration ($\sim 10^{-3}$~Gyr).
The high $M_\mathrm{dust} / M_\mathrm{star}$ ratio implies the presence of a more massive, evolved stellar component which does not contribute significantly to the rest-frame UV. However, it is not clear how the evolved component plays a role in dust mass assembly.
In this section, we discuss how our current understanding of dust formation and evolution reproduces the dust mass observed in \target{}.
\subsection{Dust mass evolution model} \label{sec:dustmodel}
In the past decade, substantial amounts of dust ranging from $10^6$ to $10^8 M_{\sun}$ have been identified in the $z > 7$ galaxies and quasars \citep[][]{Venemans12, Venemans17, Watson15, Laporte17, Hashimoto18b}, which poses a challenge to the current theory of dust formation \citep{Michalowski15}.
In the local Universe, the origins of dust grains are the stellar winds of asymptotic giant branch (AGB) stars and ejecta of type II supernovae (SNe~II), although accretion of gas-phase metal onto the grains should play a dominant role. In fact, grain growth in dense, metal-polluted ISM is considered to be a major contributor to the dust mass in the MW \citep[e.g.,][]{dwek1998, Zhukovska08, draine2009}.
Furthermore, processes in diffuse gas, such as dust destruction by SN shocks and shattering by grain collisions, control the effective dust yield per SN and the size distribution \citep{Draine79}.
In the $z > 7$ Universe, SNe~II ejecta with a typical dust yield per SN of $\gtrsim 0.1 M_{\sun}$ are claimed to be more important because at least some of intermediate and low-mass stars did not reach the AGB phase.
In fact, large dust masses have been reported in some nearby young SN remnants (SNRs), which could explain the high dust yield \citep[e.g.,][]{Dunne03, Dunne09, Barlow10, Matsuura11, Matsuura15, Indebetouw14, Gomez12, Temim13, DeLooze17}, although the other SNRs typically have much smaller dust masses of $10^{-3}$ to $10^{-2} M_{\sun}$ \citep[][and references therein]{Michalowski15}.
It is likely that the discrepancy is due to the difference in evolutionary phases of SNRs, in which most of dust grains are destroyed by reverse shocks associated with the SN and do not survive in the later SNR phase \citep[][and references therein]{Micelotta18}. If this is the case, it dramatically reduces the yield of dust grains per SN compared to previous beliefs.
A top-heavy IMF is also claimed to explain a high dust yield per unit SFR \citep{Gall11}, although this could lead to a higher rate of dust destruction by more frequent SN shocks.
In recent years, a microscopic process of grain growth in dense ISM has been studied to overcome the problem of explaining the high-$z$ dust reservoirs \citep[e.g.][]{liffman1989, dwek1998, draine2009, jones2011}.
In these models, accretion of gas-phase metal onto dust grains becomes more efficient in dense molecular clouds as the ISM is metal-polluted by stellar ejecta and eventually increases the dust mass for fixed SFR \citep[e.g.][]{Asano13a, zhukovska2014}, allowing one to require neither extreme dust yield per SN nor unusual IMFs.
Here we employ a dust formation model developed by \citet{Asano13a, Asano13b, Asano14} and \citet{Nozawa15} to assess if the dust mass observed in \target{} is reproduced in the stellar age of $\approx 4$~Myr.
In this model, time evolution of masses of stars, ISM, metal and dust are solved by 4 independent equations in which SFR, dust injection into (ejection from) stars, dust destruction by SNe, grain growth in dense ISM are considered. The formation and destruction of dust grains are assumed to be processed in three phases of ISM;
warm neutral media (WNM, $T_\mathrm{gas} = 6000$~K, $n_\mathrm{H} = 0.3$~cm$^{-3}$),
cold neutral media (CNM, $T_\mathrm{gas} = 100$~K, $n_\mathrm{H} = 30$~cm$^{-3}$) and
molecular clouds (MC, $T_\mathrm{gas} = 25$~K, $n_\mathrm{H} = 300$~cm$^{-3}$).
We assume the mass fractions of WNM, CNM and MC to be $(\eta_\mathrm{WNM},\,\eta_\mathrm{CNM},\,\eta_\mathrm{MC}) = (0.5,\, 0.3,\, 0.2)$ following \citet{Nozawa15}.
We use the IMF from \citet{Chabrier03}.
The star formation time-scale is set to $\tau_\mathrm{SFH}$ = 0.3~Gyr, which is well within the 68\% confidence intervals of the best-fitting $\tau_\mathrm{SFH}$ (Table~\ref{tab:sedparam}).
The total baryon mass is scaled to
$M_\mathrm{tot} = 2 \times 10^{10}~M_{\sun}$
such that the model stellar mass and SFR at the galaxy age of
4~Myr roughly match the best-fitting values
$M_\mathrm{star} = 3 \times 10^{8}~M_{\sun}$ and $\mathrm{SFR} = 60~M_{\sun}~\mathrm{yr}^{-1}$,
respectively (Table~\ref{tab:sedparam}). Note that except this scaling, we made no parameter optimization nor fine-tuning with respect to the best-fitting values obtained by the SED fits.
The results are shown in Figure~\ref{fig:grain}.
Although the model does not compute the physical properties at the earliest ages ($< 0.01$~Gyr), the predicted stellar mass and SFR extrapolated from the dust evolution model with a single episode of star-formation (Figure~\ref{fig:grain}a, b) are well aligned with the results from the SED analysis. The predicted metallicity is, however, much lower (Figure~\ref{fig:grain}d), suggesting that the ISM fed to ongoing star formation is already metal-polluted by past star formation.
Furthermore, the model fails to reproduce the dust mass (Figure~\ref{fig:grain}d) if assuming that the observed $\Mdust$ would be produced by the ongoing star formation traced by the rest-frame UV continuum and the \oiii{} 88~$\micron$ line. At the age of $< 0.1$~Gyr, the predicted metallicity and dust mass increase almost linearly with increasing the cumulative number of SNe II. At $> 0.1$~Gyr, the ISM is sufficiently metal-polluted and triggers a rapid interstellar growth of dust grains, resulting in non-linear evolution of $\Mdust$ at $\tau_\mathrm{age} \sim \tau_\mathrm{SFH}$ = 0.3~Gyr. The dust mass evolution peaks at $\tau_\mathrm{age} \sim 0.6$~Gyr and gives $\Mdust/\Mstar \approx 3 \times 10^{-3}$ (similar to low-$z$ normal star-forming galaxies, see also \S~\ref{subsec:SEDresults}), which is followed by a $\Mdust$ decrement due to grain consumption for star-formation at $\gtrsim 1$~Gyr.
The galaxy age of $\approx 4$~Myr is too short to reproduce the observed $\Mdust$, and any reasonable modification of the model cannot explain the dust mass.
\subsection{Potential co-existence of an evolved stellar component} \label{sec:oldcomponent}
Obviously, the disagreement discussed above should be mitigated if assuming the presence of an underlying `old' stellar component assembled in a past star-formation activity.
In what follows, we show that there is at least one solution which reasonably explains the physical properties required to reproduce the observed dust mass without any substantial change in the SED shape.
As for a single episode of star-formation starting with zero metallicity, the time-evolution of metallicity only depends on the elapsed time since the episode started. From Figure~\ref{fig:grain}c, the past star-formation lasting for $\approx 0.1$~Gyr is necessary to reach $Z \approx 0.2\,Z_{\sun}$.
The dust evolution model also predicts that an initial gas mass of $1\times 10^{10}\,M_{\sun}$ will produce a dust mass of $\Mdust \approx 5 \times 10^{6}\,M_{\sun}$ in 0.1~Gyr. This stellar population has a virtually-constant SFR of $\approx 30~M_{\sun}$~yr$^{-1}$ for the duration of 0.1 Gyr and attains a stellar mass of $\Mstar = 3 \times 10^9\,M_{\sun}$.
This massive, old stellar component does not conflict with the best-fitting SED (\S~\ref{subsec:SEDresults}), if the old component has stopped the star-formation activity at a certain point of time in the past and then has been passively evolving for a time duration comparable to the lifetimes of OB stars ($\gtrsim 0.1$~Gyr).
Figure~\ref{fig:youngold} shows the predicted SED of the old component with $\Mstar = 3 \times 10^9\,M_{\sun}$ built by constant star-formation starting 0.3~Gyr ago and lasting for 0.1~Gyr, which exhibits the Balmer break due to the lack of OB stars. The UV continuum of the old component is much fainter than that of the best-fit stellar component presented in \S~\ref{subsec:SEDresults}, suggesting that the addition of the old component does not substantially change the stellar SED in the rest-frame UV-to-optical. A similar star formation history is advocated to account for an excess in the rest-frame optical observed in MACS1149-JD \citep{Hashimoto18} or the presence of dust in B14-65666 \citep{Hashimoto18b}. Therefore, it is likely that the mature (the age of $\sim 0.3$~Gyr) stellar population with no or little ongoing star-formation may be the origin of the very early enrichment of metal and dust.
\section{Conclusions} \label{sec:conclusion}
We report the ALMA detections of the \oiii{} 88~$\micron$ line and the 850~$\micron$ dust continuum emission in the \textit{Y}-dropout LBG \target{} located behind the Frontier Field cluster MACS~J0416.1$-$2403. Four independent tunings of ALMA were assigned to cover the contiguous frequency range between 340.0 and 366.4~GHz (a bandwidth of 26.4~GHz, corresponding to the redshift interval of $\Delta z = 0.72$ around $z \sim 8.5$), which reveals the spectroscopic redshift of $z = 8.3118 \pm 0.0003$.
The observed 850~$\micron$ flux of $137 \pm 26$~$\mu$Jy corresponds to the intrinsic IR luminosity of $\Lir = 1.7 \times 10^{11} L_{\sun}$ if assuming the dust temperature of $T_\mathrm{dust} = 50$~K and an emissivity index of $\beta = 1.5$, suggesting the fast assembly of a dust mass of $M_\mathrm{dust} = 4 \times 10^{6} M_{\sun}$ when the age of the Universe was 600~Myr.
The \oiii{} flux and the de-lensed luminosity are $F_\mathrm{[O\,III]} = 0.66 \pm 0.16$~Jy~km~s$^{-1}$ and $\Loiii{} = (1.2 \pm 0.3) \times 10^9 L_{\sun}$, respectively.
The inferred \oiii{}-to-IR luminosity ratio of $\approx 1 \times 10^{-3}$ is comparable to those found in local dwarf galaxies,
even if the uncertainty in dust temperature is taken into account.
The rest-frame UV-to-FIR SED modeling where the \oiii{} emissivity model is incorporated suggests the presence of a young, but moderately metal-polluted stellar component with $M_\mathrm{star} = 3\times 10^8 M_{\sun}$, $Z = 0.2 Z_{\sun}$, $\tau_\mathrm{age} = 4$~Myr.
The analytic dust mass evolution model with $\tau_\mathrm{SFH} = 0.3$~Gyr, where interstellar grain growth and destruction are fully accounted for, does not reproduce the metallicity and the dust mass in a galaxy age of $\tau_\mathrm{age} = 4$~Myr, suggesting the presence of a past star-formation episode as the origin of dust. We show that if a stellar population with past star formation triggered 0.3~Gyr ago and lasting for 0.1~Gyr is taken into account, it reproduces the metallicity and the dust mass without any substantial change in the observed stellar SED.
Obviously, the ionized and neutral ISM in \target{} are yet to be characterized completely.
The rest-frame FIR and optical fine-structure lines such as \cii{} 158~$\micron$, \textsc{[O\,i]} 146~$\micron$ and \textsc{[N\,ii]} 122/205~$\micron$, \oiii{} 52~$\micron$ and 4959/5007 \AA{}, in addition to multi-wavelength photometry of the continuum emission, will offer a unique opportunity for the better understanding of the fundamental processes of metal/dust enrichment and star-formation activity in \target{}.
Future ALMA and \textit{JWST} observations of them will allow this to be investigated further.
\acknowledgments
We acknowledges the anonymous referee for detailed comments. We thank K.\ Nakanishi, F.\ Egusa, R.\ Kawamata, Y.\ Harikane, M.\ Ouchi, P.\ Papadopoulos and M.\ Micha{\l}owski for fruitful suggestions.
This work was supported by NAOJ ALMA Scientific Research Grant Numbers 2018-09B, 2016-01A, and JSPS/MEXT KAKENHI (Nos.~17H06130, 17H04831, 17KK0098, 17H01110, 18H04333, 17K14252, and 17H01110).
EZ acknowledges funding from the Swedish National Space Board.
TTT is supported by Sumitomo Foundation Grant for Basic Science Projects (180923).
This paper makes use of the following ALMA data: ADS/JAO.ALMA \#2016.1.00117, ADS/JAO.ALMA \#2013.1.00999.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ.
This work is also based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programme 0100.A-0529(A).
Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.
This work has made use of data from the European Space Agency (ESA) mission {\it Gaia} (\url{https://www.cosmos.esa.int/gaia}), processed by the {\it Gaia} Data Processing and Analysis Consortium (DPAC, \url{https://www.cosmos.esa.int/web/gaia/dpac/consortium}). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the {\it Gaia} Multilateral Agreement. IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation.
| {
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USAF prepares for future wars, announces major makeover
Image Credit: Scott 97006/Flickr Creative Commons
US Air Force targeting legacy platforms for cuts in preparation for near-peer competition.
by Erwin Castro
September 5, 2019 at 11:08 AM Updated on September 5, 2019 at 9:03 PM
The US Air Force is now preparing for future battle, announcing some major makeovers to its arsenal. The huge makeover will target legacy platforms or older aircraft that may not be suitable for a future battle against a near-peer adversary like China or Russia. Unfortunately, the latest USAF's decision places the aging A-10 Warthog on the potential chopping block.
As mentioned by Military.com, the USAF is considering divesting legacy capabilities and platforms that are not suited for future war. This means that the service is now ready to chop off older aircraft from its current inventory.
The idea is to stop spending money on programs that simply won't work on the future battlefield.
At the recent 2019 Defense News Conference, the Air Force said that more resources should be spent on advanced programs instead of sustaining legacy platforms During a panel on the USAF program prioritization, Lt. General Timothy Fay, USAF deputy chief of staff for strategy, told the media that the Air Force needs to divest some of its older planes and replace them with brand new and more advanced aircraft. The Air Force general also confirmed that the service is focusing on four major areas. These areas are space, multi-domain command and control, logistics under attack, and generated combat power.
The Air Force will keep the A-10 in its arsenal
The USAF is considering divesting legacy platforms as part of the US Defense Department-wide review directed by Mark Esper, the current Secretary of US Defense Department. As the highest official in the Defense Department, Esper spearheaded a similar night court effort to divert funds from legacy department programs and then refocus those funds on new efforts needed to combat fast-growing rival countries like China and Russia.
Luckily, the aging A-10 Warthog will not be included in the list of the legacy platforms that the Air Force plans to retire or chop off in Air Force's upcoming fiscal year 2021 budget request. A senior Defense official confirmed this story, according to Defense News.
The A-10 Warthog was hit again by "retirement rumors" after acting Air Force Secretary Matt Donovan stoked speculation that the USAF will retire the aging attack plane after a recent announcement that the Air Force's fiscal year 2021 budget request will include "controversial changes" such as divestment of legacy platform or aircraft.
However, Lt. General Timothy Fay confirmed that the aging ground attack plane is not included in the chopping block and that the combat aircraft will stay in service until 2030.
This is not the first time the aircraft has been hit by retirement controversy. There were many unsuccessful requests to retire the attack plane, but US lawmakers rejected every attempt. A major battle was fought in the US Congress for the future of the A-10. Fortunately, US lawmakers prevailed and the Air Force decided to keep the A-10 in its fiscal year 2018 budget request but declined to include the procurement of new wings to its fiscal budget. Instead, the Air Force bumped it into the "unfunded wish list" that it gives to the US Congress every year.
The Air Force restarts a major overhaul for the A-10 fleet
This year, the Air Force has restarted a major overhaul to replace the wings on a portion of the A-10 aircraft. In August, an initial $240 million contract was awarded to Boeing to produce all 27 new wing sets. The Air Force has already placed new wings on 173 A-10 Warthogs, including one that crashed. This was made under the service's previous contract with Boeing. But the Air Force's 109 A-10 Warthogs are still using old wings and replacements for that aircraft, which could cost the service as much as $999 million, according to Defense News.
The Defense News also learned that the USAF are still not committed to replacing the wings on all 281 A-10 Warthogs.
Lt. General Jerry Harris also confirmed this during the 2018 House Armed Services Committee panel. Gen. Harris said that they are not confident that they will be able to fly all of the A-10s that the service currently possesses in its arsenal.
Erwin Castro
Defense updates, technology topics, gaming, startups, and sports. Follow me at Twitter: https://twitter.com/Techchaser.
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Q: How to force children in a tree to go in the right direction? I am drawing a tree and this is my effort below. It works OK except I would like 8 to be the left child of 5 (not drawn straight below it) and 10 to the right child of 8 (not drawn straight below it). How can I do that?
\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[sibling distance=8em,
every node/.style = {shape=circle,
draw, align=center}]]
\node {1}
child { node {3}
child { node {9}}
child { node {7}}}
child { node {5}
child { node {8}
child { node {10}
child { node {12}}
child { node {15}
child { node {20}}
child {node {18}
}}}}};
\end{tikzpicture}
A: Welcome to TeX.SE!!
You want this:
\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[
level 1/.style ={sibling distance=12em},
level 2/.style ={sibling distance=6em},
every node/.style = {shape=circle,
draw, align=center}]
]
\node {1}
child { node {3}
child { node {9}}
child { node {7}}}
child { node {5}
child { node {8}
child {edge from parent[draw=none]} % Added
child { node {10}
child { node {12}}
child { node {15}
child { node {20}}
child {node {18}
}}}}
child {edge from parent[draw=none]} % Added
};
\end{tikzpicture}
\end{document}
It differs from @Zarko's answer because of the left alignment of 8.
A: first version:
ups, after seeing @manooooh answer (+1) I recognize, that I misread the question and of course the resulted tree was wrong (for correct see @manooooh answer)
second version
This tree can be simply drawn with forest package. Hopefull, that this time is correct designed tree:
\documentclass[border=10pt]{standalone}
\usepackage[edges]{forest}
\begin{document}
\begin{forest}
for tree = {draw,
shape=circle,
inner sep=0pt,
minimum size=1.6em,
l sep=6mm,
s sep=9mm
}
[1
[3
[9]
[7]
]
[5
[8
[,phantom]
[10
[12]
[15
[20]
[18]
]
]
]
[,phantom]
]
]
\end{forest}
\end{document}
| {
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{"url":"https:\/\/www.gordonmclean.co.uk\/2010\/08\/31\/13\/?shared=email&msg=fail","text":"# 13 (+1)\n\nUnlucky for some (the future lies ahead).\n\nAs they say (whoever they are).\n\nHad hoped to not to be here when this rolled around (but it\u2019s only a number).\n\nLife goes on (14 years is a long time).\n\nAlways (there are many years ahead).\n\nWithout fail (life goes on).\n\nNothing is truly unlucky (nor is there such a thing as fate).\n\nThings are good (and will get better).\n\nDo not worry (the past will remain, fondly).\n\nThere are many years ahead (always).\n\n### 1 Reply to \u201c13 (+1)\u201d\n\n1. mum says:\n\n13 years + 1 day since gran had her accident -spooky\u2026.","date":"2020-07-04 21:55:45","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8206671476364136, \"perplexity\": 11733.79338776077}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-29\/segments\/1593655886706.29\/warc\/CC-MAIN-20200704201650-20200704231650-00567.warc.gz\"}"} | null | null |
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