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<jats:title>Abstract</jats:title> <jats:p>We consider the body of published distance moduli to the Fornax and Coma galaxy clusters, with specific emphasis on the period since 1990. We have carefully homogenized our final catalogs of distance moduli onto the distance scale established in the previous papers in this series. We assessed systematic differences associated with the use of specific tracers and consequently discarded results based on application of the Tully–Fisher relation and of globular cluster and planetary nebula luminosity functions. We recommend “best” weighted relative distance moduli for the Fornax and Coma clusters with respect to the Virgo cluster benchmark of <jats:inline-formula> <jats:tex-math> <?CDATA ${\rm{\Delta }}(m-M{)}_{0}^{\mathrm{Fornax}-\mathrm{Virgo}}=0.18\pm 0.28$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjsab8562ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> mag and <jats:inline-formula> <jats:tex-math> <?CDATA ${\rm{\Delta }}(m-M{)}_{0}^{\mathrm{Coma}-\mathrm{Virgo}}=3.75\pm 0.23$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjsab8562ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> mag. The set of weighted mean distance moduli (distances) we derived as most representative of the clusters’ distances is <jats:inline-formula id="apjsab8562ueqn1"> <jats:tex-math> <?CDATA \begin{eqnarray*}\begin{array}{c}\begin{array}{c}\begin{array}{rcl}{\left(m-M\right)}_{0}^{{\rm{F}}{\rm{o}}{\rm{r}}{\rm{n}}{\rm{a}}{\rm{x}}} & = & 31.41\pm 0.15\,{\rm{m}}{\rm{a}}{\rm{g}}\,(D={19.1}_{-1.2}^{+1.4}\,{\rm{M}}{\rm{p}}{\rm{c}})\,{\rm{a}}{\rm{n}}{\rm{d}}\\ & = & 31.21\pm 0.28\,{\rm{m}}{\rm{a}}{\rm{g}}\,(D={17.5}_{-2.2}^{+2.4}\,{\rm{M}}{\rm{p}}{\rm{c}}),\\ {\left(m-M\right)}_{0}^{{\rm{C}}{\rm{o}}{\rm{m}}{\rm{a}}} & = & 34.99\pm 0.38\,{\rm{m}}{\rm{a}}{\rm{g}}\,(D={99.5}_{-15.9}^{+19.0}\,{\rm{M}}{\rm{p}}{\rm{c}})\,{\rm{a}}{\rm{n}}{\rm{d}}\\ & = & 34.78\pm 0.27\,{\rm{m}}{\rm{a}}{\rm{g}}\,(D={90.4}_{-10.6}^{+11.9}\,{\rm{M}}{\rm{p}}{\rm{c}}),\end{array}\end{array}\end{array}\end{eqnarray*}?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block" overflow="scroll"> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mtable> <mml:mtr> <mml:mtd columnalign="right"> <mml:msubsup> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>−</mml:mo> <mml:mi>M</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">F</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">o</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">a</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">x</mml:mi> </mml:mrow> </mml:mrow> </mml:msubsup> </mml:mtd> <mml:mtd columnalign="center"> <mml:mo>=</mml:mo> </mml:mtd> <mml:mtd columnalign="left"> <mml:mn>31.41</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.15</mml:mn> <mml:mspace width="0.25em" /> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">a</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">g</mml:mi> </mml:mrow> <mml:mspace width="0.25em" /> <mml:mo stretchy="false">(</mml:mo> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>19.1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.4</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em" /> <mml:mrow> <mml:mi mathvariant="normal">M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> <mml:mspace width="0.25em" /> <mml:mrow> <mml:mi mathvariant="normal">a</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> </mml:mtd> </mml:mtr> <mml:mtr> <mml:mtd columnalign="right" /> <mml:mtd columnalign="center"> <mml:mo>=</mml:mo> </mml:mtd> <mml:mtd columnalign="left"> <mml:mn>31.21</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.28</mml:mn> <mml:mspace width="0.25em" /> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">a</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">g</mml:mi> </mml:mrow> <mml:mspace width="0.25em" /> <mml:mo stretchy="false">(</mml:mo> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>17.5</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2.2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>2.4</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em" /> <mml:mrow> <mml:mi mathvariant="normal">M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> <mml:mo>,</mml:mo> </mml:mtd> </mml:mtr> <mml:mtr> <mml:mtd columnalign="right"> <mml:msubsup> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>−</mml:mo> <mml:mi>M</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">o</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">a</mml:mi> </mml:mrow> </mml:mrow> </mml:msubsup> </mml:mtd> <mml:mtd columnalign="center"> <mml:mo>=</mml:mo> </mml:mtd> <mml:mtd columnalign="left"> <mml:mn>34.99</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.38</mml:mn> <mml:mspace width="0.25em" /> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">a</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">g</mml:mi> </mml:mrow> <mml:mspace width="0.25em" /> <mml:mo stretchy="false">(</mml:mo> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>99.5</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>15.9</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>19.0</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em" /> <mml:mrow> <mml:mi mathvariant="normal">M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> <mml:mspace width="0.25em" /> <mml:mrow> <mml:mi mathvariant="normal">a</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> </mml:mtd> </mml:mtr> <mml:mtr> <mml:mtd columnalign="right" /> <mml:mtd columnalign="center"> <mml:mo>=</mml:mo> </mml:mtd> <mml:mtd columnalign="left"> <mml:mn>34.78</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.27</mml:mn> <mml:mspace width="0.25em" /> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">a</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">g</mml:mi> </mml:mrow> <mml:mspace width="0.25em" /> <mml:mo stretchy="false">(</mml:mo> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>90.4</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>10.6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>11.9</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em" /> <mml:mrow> <mml:mi mathvariant="normal">M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> <mml:mo>,</mml:mo> </mml:mtd> </mml:mtr> </mml:mtable> </mml:mtd> </mml:mtr> </mml:mtable> </mml:mtd> </mml:mtr> </mml:mtable> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjsab8562ueqn1.gif" xlink:type="simple" /> </jats:inline-formula>where the first distance modulus for each cluster is the result of our analysis of the direct, absolute distance moduli, while the second modulus is based on distance moduli relative to the Virgo cluster. While the absolute and relative distance moduli for both clusters are mutually consistent within the uncertainties, the relative distance moduli yield shorter absolute distances by ∼1<jats:italic>σ</jats:italic>. It is unclear what may have caused this small difference for both clusters; lingering uncertainties in the underlying absolute distance scale appear to have given rise to a systematic uncertainty of the order of 0.20 mag.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The Dst index is a commonly geomagnetic index used to measure the strength of geomagnetic activity. The accurate prediction of the Dst index is one of the main subjects of space weather studies. In this study, we use the Bagging ensemble-learning algorithm, which combines three algorithms—the artificial neural network, support vector regression, and long short-term memory network—to predict the Dst index 1–6 hr in advance. Taking solar wind parameters (including the interplanetary total magnetic field, magnetic field <jats:italic>B</jats:italic> <jats:sub> <jats:italic>z</jats:italic> </jats:sub> component, total electric field, solar wind speed, plasma temperature, and proton pressure) as inputs, we establish the Dst index models and complete not only the point prediction but also the interval prediction in forecasting the Dst index. The results show that the root mean square error (rmse) of the point prediction is always lower than 8.0936 nT, the correlation coefficient (<jats:italic>R</jats:italic>) is always higher than 0.8572 and the accuracy of interval prediction is always higher than 90%, implying that our model can improve the accuracy of point prediction and significantly promote the accuracy of interval prediction. In addition, an new proposed metric shows that the Bagging algorithm brings better stability to the model. Our model was also used to predicate a magnetic storm event from 2016 October 12–17. The most accurate prediction of this storm event is the 1 hr ahead prediction, which holds a result with the rmse of 3.7327 nT, the correlation coefficient of 0.9928, and the interval prediction accuracy of 96.69%. Moreover, we also discuss the balance in the Bagging ensemble model in this paper.</jats:p>