Datasets:

mawadalla
/

scientific-figures-captions-context

A novel vision-language dataset of scientific figures taken directly from research papers. We scraped approximately ~150k papers, with about ~690k figures total. We extracted each figure's caption and label from the paper. In addition, we searched through each paper to find references of each figure and included the surrounding text as 'context' for this figure.

All figures were taken from arXiv research papers.

Figure 5: Comparisons between our multifidelity learning paradigm and single low-fidelity (all GPT-3.5) annotation on four domain-specific tasks given the same total 1000 annotation budget. Note that the samples for all GPT-3.5 are drawn based on the uncertainty score.

Figure 3: Problem representation visualization by T- SNE. Our model with A&D improves the problem rep- resentation learning, which groups analogical problems close and separates non-analogical problems.

Usage

The merged.json file is a mapping between the figure's filename as stored in the repository and its caption, label, and context. To use, you must extract the parts located under dataset/figures/ and keep the raw images in the same directory so that they match the image_filename fields. The images are named in the format <paper id>-<figure name> where paper id is the id given by arXiv and figure name is the name of the figure as given in the raw format of each paper.

Contributors

Yousef Gomaa (@yousefg-codes) and Mohamed Awadalla (@mawadalla)

Dataset Summary

This dataset includes ~690,000 figures from ~150,000 scientific papers taken from arXiv papers. Each object in the json file is a single research paper with a list of figures each with their caption and surrounding context.

Category	Count
Figure	690883
Paper	152504

Data Instances

An example of an object in the merged.json file:

{
  [
    {
      'image_filename': 'dataset/figures/example.png' (or .eps or .pdf or other type),
      'label': 'fig_example',
      'caption': 'an example caption for this figure',
      'context': ['example context where this figure was referenced', 'up to 600 characters']
    },
  ...
  ]
}

Dataset Creation

We utilized the bulk access of arXiv's papers.

Curation Rationale

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Source Data

Initial Data Collection and Normalization

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Who are the source language producers?

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Annotations

Annotation process

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Who are the annotators?

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Personal and Sensitive Information

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Considerations for Using the Data

Social Impact of Dataset

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Discussion of Biases

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Other Known Limitations

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Additional Information

Dataset Curators

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image_filename string	context sequence	label string	caption string
dataset/figures/1508.02466_fig1.eps	[ "ique was employed. For these analysis the samples were diluted in alcohol. Magnetic measurements was carried out using a commercial Superconducting Quantum Interference Device (SQUID). Crystal structure and morphologyX-ray powder diffraction of the nanostructures and bulk are shown in the Fig. DRXTODOS; the results confirm the formation of pure Sm$_0.6$Sr$_0.4$MnO$_3$ crystalline phase (space group Pnma ortorhombic system). Those data were refined by the Rietveld method (bottom of Fig. DRXTODOS) and the crystallographic parameters and reliability factors obtained are into Table", "and morphologyX-ray powder diffraction of the nanostructures and bulk are shown in the Fig. DRXTODOS; the results confirm the formation of pure Sm$_0.6$Sr$_0.4$MnO$_3$ crystalline phase (space group Pnma ortorhombic system). Those data were refined by the Rietveld method (bottom of Fig. DRXTODOS) and the crystallographic parameters and reliability factors obtained are into Table crystaldata and are in good agreement with previous results jap/113/11/10.1063/1.4795769. Using the Scherrer equationnosso was possible to estimate the average particle diameter $D$ from the nanopart", "meter $D$ from the nanoparticle and nanotube (note the nanotube wall is composed of nanoparticles) which are 29 nm and 15 nm, respectively (Table crystaldata). width=9cm,angle=-90fig1.epsPowder diffractograms for the Sm$_0.6$Sr$_0.4$MnO$_3$ nanoparticles, nanotubes and bulk samples. DRXTODOSRefined crystallographic data and reliability factors for Sm$_0.6$Sr$_0.4$MnO$_3$ nanoparticle, nanotube and bulk samples. The nanoparticle size $D$ obtained by the X-ray and HRTEM are also presented. crystaldata \|c\|c\|c\|c\|c 2lParameter & 2lSamples\\\\" ]	DRXTODOS	Powder diffractograms for the Sm_0.6Sr_0.4MnO_3 nanoparticles, nanotubes and bulk samples.DRXTODOS
dataset/figures/1508.02466_fig2.eps	[ "th Fe-K$$ ($$ = 1.936087 ) for bulk sample. Data were collected in the 15$^o$ < 2$$ < 85$^o$ range in a Bragg-Brentano geometry, with a step size of 0.02$^o$ and a counting time of 0.1 s per step. To confirm the formation of the nanotubes, high resolution transmission electron microscopy (HRTEM) technique was employed. For these analysis the samples were diluted in alcohol. Magnetic measurements was carried out using a commercial Superconducting Quantum Interference Device (SQUID). Crystal structure and morphologyX-ray powder diffraction of the nanostructures and bulk are shown in", "er diffractograms for the Sm$_0.6$Sr$_0.4$MnO$_3$ nanoparticles, nanotubes and bulk samples. DRXTODOSRefined crystallographic data and reliability factors for Sm$_0.6$Sr$_0.4$MnO$_3$ nanoparticle, nanotube and bulk samples. The nanoparticle size $D$ obtained by the X-ray and HRTEM are also presented. crystaldata \|c\|c\|c\|c\|c 2lParameter & 2lSamples\\\\ & Nanoparticle & Nanotube & Bulk \\\\ $a$ () & 5.4494(6) & 5.4475(9) & 5.4448(8) \\\\ $b$ () & 7.6429(8) & 7.65", "0, 1/4, 0.4924) \\\\ O2 & (0.24994, 0.48939, 0.3133) &(0.4793, -0.0405, 0.1879) &(0.2439, 0.6107, 0.2427) \\\\ $$ & 1.76 & 1.33 & 1.39 \\\\ $D_X-ray (nm)$ & $29 7$ &$15 4$ & - \\\\ $D_HRTEM(nm)$ & $45 8$ & $25 4$ & - \\\\ In order to confirm the formation of the nanotubes, HRTEM image were done. In figure TEM(a) it is possible to see the nanotube diameter of c.a. 200 nm, while figure TEM(b) shows the image of a single nanoparticle that com", "0.2427) \\\\ $$ & 1.76 & 1.33 & 1.39 \\\\ $D_X-ray (nm)$ & $29 7$ &$15 4$ & - \\\\ $D_HRTEM(nm)$ & $45 8$ & $25 4$ & - \\\\ In order to confirm the formation of the nanotubes, HRTEM image were done. In figure TEM(a) it is possible to see the nanotube diameter of c.a. 200 nm, while figure TEM(b) shows the image of a single nanoparticle that composes the nanotube wall. Note the nanotube is formed by an assembly of nanoparticles with average diameter of $25$ nm. This value", "& 1.76 & 1.33 & 1.39 \\\\ $D_X-ray (nm)$ & $29 7$ &$15 4$ & - \\\\ $D_HRTEM(nm)$ & $45 8$ & $25 4$ & - \\\\ In order to confirm the formation of the nanotubes, HRTEM image were done. In figure TEM(a) it is possible to see the nanotube diameter of c.a. 200 nm, while figure TEM(b) shows the image of a single nanoparticle that composes the nanotube wall. Note the nanotube is formed by an assembly of nanoparticles with average diameter of $25$ nm. This value is in good agreement with the o", "$29 7$ &$15 4$ & - \\\\ $D_HRTEM(nm)$ & $45 8$ & $25 4$ & - \\\\ In order to confirm the formation of the nanotubes, HRTEM image were done. In figure TEM(a) it is possible to see the nanotube diameter of c.a. 200 nm, while figure TEM(b) shows the image of a single nanoparticle that composes the nanotube wall. Note the nanotube is formed by an assembly of nanoparticles with average diameter of $25$ nm. This value is in good agreement with the obtained value by XRD refinement data ($154$ nm - see Table crystaldata).", "e is in good agreement with the obtained value by XRD refinement data ($154$ nm - see Table crystaldata). width=5cm,angle=-90fig2.epsTransmission Electron Microscospy for (a) nanotube and (b) high resolution mode used to verify the features of particle that constitutes the wall of the nanotube. TEMMagnetocaloric potential evaluationDue to the different morphology of the pre", "n mode used to verify the features of particle that constitutes the wall of the nanotube. TEMwidth=5cm,angle=-90fig2.epsTransmission Electron Microscospy for (a) nanotube and (b) high resolution mode used to verify the features of particle that constitutes the wall of the nanotube. TEMMagnetocaloric potential evaluationDue to the different morphology of the prepared samples, as detailed before, it is highly expected a different magnetic behavior for those samples; and indeed it was found, as shown on figure MxTtodos-(a), that presents the magnetization curves as a", "reasing of magnetic saturation, as discussed before (see figure MxTtodos-bottom-left). ConclusionsBulk, nanoparticles and nanotubes of Sm$_0.6$Sr$_0.4$MnO$_3$ manganites were successfully produced by the modified sol-gel method. The structural properties were investigated by the DRX and HRTEM techniques, which showed that nanoparticles and nanotubes present average diameter of 29 and 200 nm, respectively. In addition, we also could determine that nanotube wall is composed of nanoparticles with average diameter of 25 nm. Magnetization measurements reveled a possible superparamagnetic" ]	TEM	Transmission Electron Microscospy for (a) nanotube and (b) high resolution mode used to verify the features of particle that constitutes the wall of the nanotube. TEM
dataset/figures/1508.02466_fig3.eps	[ "s of particle that constitutes the wall of the nanotube. TEMMagnetocaloric potential evaluationDue to the different morphology of the prepared samples, as detailed before, it is highly expected a different magnetic behavior for those samples; and indeed it was found, as shown on figure MxTtodos-(a), that presents the magnetization curves as a function of temperature for all samples. Data were collected in zero field cooled (ZFC) and field cooled (FC) regimes. It is possible to observe that the bulk sample shows a thermal hysteresis, as expected and observed in other worksjap/113", "steresis close to $T_c$, presents a peak around 50 K, which is characteristic of superparamagnetic (SPM) systems, and, in addition, the curve is broader than that one of the bulk. This result indicates that the magnetocaloric potential curve ($$ S) for nanostructures will be wider.", ". Bottom-left: magnetization as a function of external magnetic field, at 4 K redFigura 4 entra aqui. Bottom-right: magnetization as a function of $H/T$ presenting an evidence of superparamagnetic behavior for nanotubes and nanoparticles. redFigura 8 entra aqui. blueTirar 'TB and/or Tf'MxTtodoshwidth=10cm,angle=-90fig3.eps(a) Temperature dependence of field-cooled (FC) and zero field-cooled (ZFC) magnetization for nanoparticle, nanotube and bulk of Sm$_0.6$Sr$_0.4$MnO$_3$ manganite. Nanotube magnetization was multiplied by a factor 10 for better visua", "anganite. Nanotube magnetization was multiplied by a factor 10 for better visualization. Bottom-(b): magnetization as a function of external magnetic field, at 4 K. Bottom-(c): magnetization as a function of $H/T$ presenting an evidence of superparamagnetic behavior for nanotubes and nanoparticle. MxTtodosMoreover, figure MxTtodos-(a) shows that the magnetization value at low temperature is very different for all samples, which can be better understood analyzing the magnetization as a function of applied magnetic field at 4 K (see figure MxTtodos-(b)). We can see that the nanostru", "as multiplied by a factor 10 for better visualization. Bottom-(b): magnetization as a function of external magnetic field, at 4 K. Bottom-(c): magnetization as a function of $H/T$ presenting an evidence of superparamagnetic behavior for nanotubes and nanoparticle. MxTtodosMoreover, figure MxTtodos-(a) shows that the magnetization value at low temperature is very different for all samples, which can be better understood analyzing the magnetization as a function of applied magnetic field at 4 K (see figure MxTtodos-(b)). We can see that the nanostructures do not saturate completely", "c behavior for nanotubes and nanoparticle. MxTtodosMoreover, figure MxTtodos-(a) shows that the magnetization value at low temperature is very different for all samples, which can be better understood analyzing the magnetization as a function of applied magnetic field at 4 K (see figure MxTtodos-(b)). We can see that the nanostructures do not saturate completely in fields up to 50 kOe, but using the M vs 1/H curves (not shown), it was possible to obtain the saturation magnetization of 0.4 $_B/FU$, 2 $_B/FU$ and 3.6 $_B/FU$ for the nanotube, nanoparticle and bulk, res", "c evidences in the nanostructured sample, we used a simple criterion for analyzing such behavior: according to Bean and Livingston bean, a system can be considered superparamagnetic if $M$ vs. $H/T$ for several temperatures overlap around $T_B$; and indeed this occurs, as can be seen in figure MxTtodos-(c). Other works indeed agree with this assumptionPhysRevB.45.9778. hwidth=6cmfig4.epsMagnetization as a function of temperature for several values of external magnetic field for (a) bulk, (b) nanoparticle and (c) nanotube. MxTvsHhwidth=5.8cmfig5.epsEntropy chan", "sample. However, a drawback arose: the magnitude of the effect, that decreases from 8.2 J/kg.K for the bulk sample down to 1.2 J/kg.K for the nanoparticles (at 50 kOe of magnetic field change). This decreasing is associated to the decreasing of magnetic saturation, as discussed before (see figure MxTtodos-bottom-left). Indeed, it is not as bad as it seems, because the important quantity for magnetocaloric applications is the relative cooling power (RCP); i.e., the maximum value of magnetic entropy change times the full width at half maximum. Thus, the RCP for the bulk sample is 246 J/kg, wh", "s, the RCP for the bulk sample is 246 J/kg, while it is 132 J/kg for the nanoparticle; and are therefore comparable. Some final words: the decreasing of the maximum magnetic entropy change for the nanoparticles is associated to the decreasing of magnetic saturation, as discussed before (see figure MxTtodos-bottom-left). ConclusionsBulk, nanoparticles and nanotubes of Sm$_0.6$Sr$_0.4$MnO$_3$ manganites were successfully produced by the modified sol-gel method. The structural properties were investigated by the DRX and HRTEM techniques, which showed that nanoparticles and nanotubes pre" ]	MxTtodos	(a) Temperature dependence of field-cooled (FC) and zero field-cooled (ZFC) magnetization for nanoparticle, nanotube and bulk of Sm_0.6Sr_0.4MnO_3 manganite. Nanotube magnetization was multiplied by a factor 10 for better visualization. Bottom-(b): magnetization as a function of external magnetic field, at 4 K. Bottom-(c): magnetization as a function of H/T presenting an evidence of superparamagnetic behavior for nanotubes and nanoparticle. MxTtodos
dataset/figures/1508.02466_fig4.eps	[ "$; and indeed this occurs, as can be seen in figure MxTtodos-(c). Other works indeed agree with this assumptionPhysRevB.45.9778. hwidth=6cmfig4.epsMagnetization as a function of temperature for several values of external magnetic field for (a) bulk, (b) nanoparticle and (c) nanotube. MxTvsHhwidth=5.8cmfig5.epsEntropy change as a function of temperature for some values of external magnetic field for (a) bulk, (b) nanoparticle and (c) nanotube. The error bars were only presented for 5 T curve for clarity purpose. emchwidth=5.6cmfig6.epsArrott plots fo", "nanotube. The error bars were only presented for 5 T curve for clarity purpose. emchwidth=5.6cmfig6.epsArrott plots for different temperatures for all samples analyzed. arrotplotMagnetization as a function of temperature for different applied magnetic fields are shown in figure MxTvsH for (a) bulk, (b) nanoparticles and (c) nanotubes. The magnetic entropy change was determined from the isothermals (M versus H curves transposed of the M(T) presented in figure MxTvsH) using the integral version of a Maxwell relationPRL_78_1997_4494: S=_0^H_f M(T,H) T dHThe obt", "rrotplotMagnetization as a function of temperature for different applied magnetic fields are shown in figure MxTvsH for (a) bulk, (b) nanoparticles and (c) nanotubes. The magnetic entropy change was determined from the isothermals (M versus H curves transposed of the M(T) presented in figure MxTvsH) using the integral version of a Maxwell relationPRL_78_1997_4494: S=_0^H_f M(T,H) T dHThe obtained magnetic entropy change are shown in figure emc for (a) bulk, (b) nanoparticles and (c) nanotubes, for $$H = 10, 20, 30, 40 and 50 kOe. Note indeed one of the goal of this work w", "tube), superparamagnetic behavior is more pronounced (note the valley occurs at the blocking temperature at 50 K)." ]	MxTvsH	Magnetization as a function of temperature for several values of external magnetic field for (a) bulk, (b) nanoparticle and (c) nanotube.MxTvsH
dataset/figures/1508.02466_fig5.eps	[ "d for (a) bulk, (b) nanoparticle and (c) nanotube. MxTvsHhwidth=5.8cmfig5.epsEntropy change as a function of temperature for some values of external magnetic field for (a) bulk, (b) nanoparticle and (c) nanotube. The error bars were only presented for 5 T curve for clarity purpose. emchwidth=5.6cmfig6.epsArrott plots for different temperatures for all samples analyzed. arrotplotMagnetization as a function of temperature for different applied magnetic fields are shown in figure MxTvsH for (a) bulk, (b) nanoparticles and (c) nanotubes. The magnetic entropy c", "otubes. The magnetic entropy change was determined from the isothermals (M versus H curves transposed of the M(T) presented in figure MxTvsH) using the integral version of a Maxwell relationPRL_78_1997_4494: S=_0^H_f M(T,H) T dHThe obtained magnetic entropy change are shown in figure emc for (a) bulk, (b) nanoparticles and (c) nanotubes, for $$H = 10, 20, 30, 40 and 50 kOe. Note indeed one of the goal of this work was reached, since we could make broader the magnetic entropy change of this highlighted Sm$_0.6$Sr$_0.4$MnO$_3$ manganite by producing nanoparticles. In other", "Para ficar igual, precisa tambem ser incluido nessa figura. (2) retirar o ponto em 60 K do bulk. (3) o passo na escala DS para nanotubo deve ser 0.1. (4) os ticks lables estao diferentes no eixo da temperatura. PRECISAM ser iguais. (5) colocar na ordem (a) bulk, (b) nanoparticle e (c) nanotube. emcOther important issue is the character of the magnetic transition. As can be seen in figure arrotplot, which shows the Arrott Plot, the bulk curves present a negative slope ($B$ parameter of the Landau expansionlivromario), for low values of magnetization, which indicates a first-or" ]	emc	Entropy change as a function of temperature for some values of external magnetic field for (a) bulk, (b) nanoparticle and (c) nanotube. The error bars were only presented for 5 T curve for clarity purpose.emc
dataset/figures/1508.02466_fig6.eps	[ "nge as a function of temperature for some values of external magnetic field for (a) bulk, (b) nanoparticle and (c) nanotube. The error bars were only presented for 5 T curve for clarity purpose. emchwidth=5.6cmfig6.epsArrott plots for different temperatures for all samples analyzed. arrotplotMagnetization as a function of temperature for different applied magnetic fields are shown in figure MxTvsH for (a) bulk, (b) nanoparticles and (c) nanotubes. The magnetic entropy change was determined from the isothermals (M versus H curves transposed of the M(T) presented in figure", "sso na escala DS para nanotubo deve ser 0.1. (4) os ticks lables estao diferentes no eixo da temperatura. PRECISAM ser iguais. (5) colocar na ordem (a) bulk, (b) nanoparticle e (c) nanotube. emcOther important issue is the character of the magnetic transition. As can be seen in figure arrotplot, which shows the Arrott Plot, the bulk curves present a negative slope ($B$ parameter of the Landau expansionlivromario), for low values of magnetization, which indicates a first-order magnetic transition according to Banerjee's criterion banerjee; while the two nanostructured samples" ]	arrotplot	Arrott plots for different temperatures for all samples analyzed.arrotplot
dataset/figures/2106.04847_Case_Introduction.png	[ "summarization wang2013domain, pasunuru2018multi, document clustering hulth2006study, information retrieval kim2013applying. !twidth=0.48Case_Introduction.pdfAn example of an input document and its expected keyphrases. Blue and red denote present and absent keyphrases, respectively. fig1:case-studyKeyphrases of a document fall into two categories: present keyphrase that appears continuously in the document, and absent keyphrase which does not exist in the document. Figure fig1:case-study shows an example of a document and its keyphrases. Traditional KP methods are mai", "t and its expected keyphrases. Blue and red denote present and absent keyphrases, respectively. fig1:case-studyKeyphrases of a document fall into two categories: present keyphrase that appears continuously in the document, and absent keyphrase which does not exist in the document. Figure fig1:case-study shows an example of a document and its keyphrases. Traditional KP methods are mainly extractive, which have been extensively researched in past decades witten2005kea, nguyen2007keyphrase, medelyan2009human, lopez2010humb, zhang2016keyphrase, alzaidy2019bi, sun2020joint. These meth", ", which is concatenated of present and absent keyphrases. Therefore, the generative approach can predict both kinds of keyphrases. But these methods treat present and absent keyphrases equally, while these two kinds of keyphrase actually have different semantic properties. As illustrated in Figure fig1:case-study, all the present keyphrases are specific techniques, while the absent keyphrases are tasks or research areas. Thus several integrated methods chen2019integrated, ahmad-etal-2021-select try to perform multi-task learning on present keyphrase extraction (PKE) and absent keyphrase ge", "not trained in an end-to-end fashion, which causes error accumulation in the pipeline. Secondly, integrated methods just adopt a bottom shared encoder to implicitly capture the latent semantic relation between PKE and AKG, while this relation is essential for the KP task. As illustrated in Figure fig1:case-study, the ground truth of PKE are specific techniques, which are all used for the ``singularity detection'' task in the ``traffic data analysis'' area. Such semantic relation between PKE and AKG can bring benefits for KP. Actually, semantic relations like ``technique-task-area'' between", "X I X X I''. We concatenate all the tokenized absent keyphrases into one sequence using a special delimiter “ ; ”. An example of absent keyphrase sequence will like ``peer to peer ; content delivery ; t \\#\\#f \\#\\#rc ; ran \\#\\#su \\#\\#b\". Case Study!twidth=0.4case-study.pdfCase study. fig1:case-study-appendixWe give a case on the KP20k testset in Figure fig1:case-study-appendix. We compare with the original U NILM since our joint models are based on its implementation. Blue and red denote correct present and absent keyphrases, respectively. As shown in Figure fig1:case-st", "sequence using a special delimiter “ ; ”. An example of absent keyphrase sequence will like ``peer to peer ; content delivery ; t \\#\\#f \\#\\#rc ; ran \\#\\#su \\#\\#b\". Case Study!twidth=0.4case-study.pdfCase study. fig1:case-study-appendixWe give a case on the KP20k testset in Figure fig1:case-study-appendix. We compare with the original U NILM since our joint models are based on its implementation. Blue and red denote correct present and absent keyphrases, respectively. As shown in Figure fig1:case-study-appendix, UniKeyphrase successfully catches the deep semantic relatio", "se study. fig1:case-study-appendixWe give a case on the KP20k testset in Figure fig1:case-study-appendix. We compare with the original U NILM since our joint models are based on its implementation. Blue and red denote correct present and absent keyphrases, respectively. As shown in Figure fig1:case-study-appendix, UniKeyphrase successfully catches the deep semantic relation similar to the case in the introduction and gives more accurate results(predicts some applications like \"image restoration\" or \"image reconstruction\"). Evaluation DetailsWe use $F_1$@5 and $F_1$@M as evaluatio" ]	fig1:case-study	An example of an input document and its expected keyphrases. Blue and red denote present and absent keyphrases, respectively.
dataset/figures/2106.04847_visualization_analysis.png	[ "compare the distance between the PKE representation and AKG representation in different settings. In detail, we randomly sample 2000 pairs of PKE representation vector and AKG representation vector on different positions from test data and compute euclidean metric in each pair. As shown in Figure fig:visualization_analysis, the blue points mean the Euclidean metric between PKE and AKG representation vector without SRL layer, while the yellow points mean the Euclidean metric with SRL layer. htwidth=0.4visualization_analysis.pngDistance between PKE representation and AKG representati", "the blue points mean the Euclidean metric between PKE and AKG representation vector without SRL layer, while the yellow points mean the Euclidean metric with SRL layer. htwidth=0.4visualization_analysis.pngDistance between PKE representation and AKG representation on different settings. fig:visualization_analysisFrom the Figure fig:visualization_analysis, we can find that the blue points are under the yellow points, which means the PKE and AKG representation vector without SRL is more similar. In other words, SRL has learned the task-specific representation. Also, the blue po", "een PKE and AKG representation vector without SRL layer, while the yellow points mean the Euclidean metric with SRL layer. htwidth=0.4visualization_analysis.pngDistance between PKE representation and AKG representation on different settings. fig:visualization_analysisFrom the Figure fig:visualization_analysis, we can find that the blue points are under the yellow points, which means the PKE and AKG representation vector without SRL is more similar. In other words, SRL has learned the task-specific representation. Also, the blue points are denser than the yellow points, which m" ]	fig:visualization_analysis	Distance between PKE representation and AKG representation on different settings.
dataset/figures/2106.04847_BWC_Loss.png	[ "n. Also, the blue points are denser than the yellow points, which means the PKE and AKG representation with SRL is more diverse than the one without SRL on different samples. BWC Analysiswidth=0.4BWC_Loss.pngBWC's influence on total training loss (sequence labeling + text generation). fig:bwc_lossLoss Compare: From Figure fig:bwc_loss we can see that the original total loss (labeling and generation) drops more with the help of BWC compared to the vanilla model. BWC actually is an enhancement on the original supervised signal from a global view. It guides the model to learn", "yellow points, which means the PKE and AKG representation with SRL is more diverse than the one without SRL on different samples. BWC Analysiswidth=0.4BWC_Loss.pngBWC's influence on total training loss (sequence labeling + text generation). fig:bwc_lossLoss Compare: From Figure fig:bwc_loss we can see that the original total loss (labeling and generation) drops more with the help of BWC compared to the vanilla model. BWC actually is an enhancement on the original supervised signal from a global view. It guides the model to learn how many to predict and how to allocate pre" ]	fig:bwc_loss	BWC's influence on total training loss (sequence labeling + text generation).
dataset/figures/2106.04847_BWC_Error.png	[ "iginal supervised signal from a global view. It guides the model to learn how many to predict and how to allocate present and absent keyphrases, while original loss only teaches what to predict in each position. width=0.4BWC_Error.pngBag-of-words Error comparison between vanilla and BWC. fig:bow_diffBag-of-words Error: We also calculate the bag-of-words Error between ground truth and model predicted keyphrases, which is how many tokens are incorrectly predicted. As shown in Figure fig:bow_diff, UniKeyphrase with BWC achieves lower BoW Error compared with the vanilla model. It", "osition. width=0.4BWC_Error.pngBag-of-words Error comparison between vanilla and BWC. fig:bow_diffBag-of-words Error: We also calculate the bag-of-words Error between ground truth and model predicted keyphrases, which is how many tokens are incorrectly predicted. As shown in Figure fig:bow_diff, UniKeyphrase with BWC achieves lower BoW Error compared with the vanilla model. It proves that BWC successfully guides the model to learn a better BoW allocation. Joint Framework AnalysisIn our UniKeyphrase model, we adopt pre-trained model U NILM for KP. So it is necessary to ch" ]	fig:bow_diff	Bag-of-words Error comparison between vanilla and BWC.
dataset/figures/2106.04847_case-study.png	[ "X I X X I''. We concatenate all the tokenized absent keyphrases into one sequence using a special delimiter “ ; ”. An example of absent keyphrase sequence will like ``peer to peer ; content delivery ; t \\#\\#f \\#\\#rc ; ran \\#\\#su \\#\\#b\". Case Study!twidth=0.4case-study.pdfCase study. fig1:case-study-appendixWe give a case on the KP20k testset in Figure fig1:case-study-appendix. We compare with the original U NILM since our joint models are based on its implementation. Blue and red denote correct present and absent keyphrases, respectively. As shown in Figure fig1:case-st", "sequence using a special delimiter “ ; ”. An example of absent keyphrase sequence will like ``peer to peer ; content delivery ; t \\#\\#f \\#\\#rc ; ran \\#\\#su \\#\\#b\". Case Study!twidth=0.4case-study.pdfCase study. fig1:case-study-appendixWe give a case on the KP20k testset in Figure fig1:case-study-appendix. We compare with the original U NILM since our joint models are based on its implementation. Blue and red denote correct present and absent keyphrases, respectively. As shown in Figure fig1:case-study-appendix, UniKeyphrase successfully catches the deep semantic relatio", "se study. fig1:case-study-appendixWe give a case on the KP20k testset in Figure fig1:case-study-appendix. We compare with the original U NILM since our joint models are based on its implementation. Blue and red denote correct present and absent keyphrases, respectively. As shown in Figure fig1:case-study-appendix, UniKeyphrase successfully catches the deep semantic relation similar to the case in the introduction and gives more accurate results(predicts some applications like \"image restoration\" or \"image reconstruction\"). Evaluation DetailsWe use $F_1$@5 and $F_1$@M as evaluatio" ]	fig1:case-study-appendix	Case study.
dataset/figures/2009.11347_imgs_FSmethods.png	[ "these features employed in a multilayer perceptron (MLP) as the traffic classifier discussing costs/benefits. Finally, Section sec:conclusions contains some concluding remarks. Feature Selection through Mutual Information!ht\t\twidth=imgs/FSmethods.png\tFeature Selection methods. fig:fsMethods\tFeature Selection methods can be grouped into two broad categories: classifier-independent (filters) and classifier-dependent (wrappers and embedded methods) (see Fig. fig:fsMethods). Filters are based upon classifier-independent metrics such as distance, correlation, mut", "Selection through Mutual Information!ht\t\twidth=imgs/FSmethods.png\tFeature Selection methods. fig:fsMethods\tFeature Selection methods can be grouped into two broad categories: classifier-independent (filters) and classifier-dependent (wrappers and embedded methods) (see Fig. fig:fsMethods). Filters are based upon classifier-independent metrics such as distance, correlation, mutual information and consistency, which are used to rank each feature and remove the least ones. These methods are effective in term of time computation and give robustness to the overfitting p" ]	fig:fsMethods	Feature Selection methods.
dataset/figures/2009.11347_._imgs_metrics.png	[ "d: 46\\width=0.8./imgs/metrics.png SVM metrics during backward feature elimination with the mRMR and MIFS rankings. fig:svmMeanFig. fig:svmMean shows the accuracy, precision and recall metrics calculated during the elimination process from 23 to 5 features, using the mRMR and MIFS rankings. All the performance indicators remain stable above $97\\", "our experiments, we set $=97\\width=0.8./imgs/metrics.png SVM metrics during backward feature elimination with the mRMR and MIFS rankings. fig:svmMeanFig. fig:svmMean shows the accuracy, precision and recall metrics calculated during the elimination process from 23 to 5 features, using the mRMR and MIFS rankings. All the performance indicators remain stable above $97\\" ]	fig:svmMean	SVM metrics during backward feature elimination with the mRMR and MIFS rankings.
dataset/figures/2009.11347_._imgs_errorAE.png	[ "set (46639 samples). The AE training will be performed using the learning and validation sets, whereas the testing set (which is never fed to the network during training) will be used for the final performance tests. ht width=0.8./imgs/errorAE.png Autoencoder reconstruction error. fig:AElossesThe AE is trained for 10 epochs as done in itasec2020 but, from Fig. fig:AElosses, it is possible to see that the model loss (i.e., the data decompression/reconstruction error) converges nicely and the error becomes acceptable from the fourth epoch. Latent AE MTA-KDD'19 features", "on sets, whereas the testing set (which is never fed to the network during training) will be used for the final performance tests. ht width=0.8./imgs/errorAE.png Autoencoder reconstruction error. fig:AElossesThe AE is trained for 10 epochs as done in itasec2020 but, from Fig. fig:AElosses, it is possible to see that the model loss (i.e., the data decompression/reconstruction error) converges nicely and the error becomes acceptable from the fourth epoch. Latent AE MTA-KDD'19 featuresOnce the training is completed with satisfying results, use the AE as a \"feature compr" ]	fig:AElosses	Autoencoder reconstruction error.
dataset/figures/2009.11347_._imgs_avg-DTs.png	[ "ws the AE effect which mixes the distribution of the samples and change the range of values, creating only sporadic small clusters and less outliers than the RRw-Optimized MTA-KDD'19 dataset. It is worth noting that, in the AE MTA-KDD'19 dataset, all the features are now relevant, as shown in Fig. fig:featimp.", "dataset. It is worth noting that, in the AE MTA-KDD'19 dataset, all the features are now relevant, as shown in Fig. fig:featimp. \t\twidth=0.8./imgs/avg-DTs.png\tAverage of Feature Importance with four Decision Trees. fig:featimpNote that, on this kind of dataset, it is now very hard to apply", "tion ability, and thus any of them is relevant given the other. As shown fig. fig:featimp which denote no high variance among the features in terms of importance score in the majority of features. !ht\t\twidth=0.8./imgs/avg-DTs.png\tAverage of Feature Importance with four Decision Trees. fig:featimpNote that, on this kind of dataset, it is now very hard to apply further optimizations (if any), as the connections between the generated features and the original ones is lost, for this reason it is reported in the fig. fig:PPMdsA with anonymous label from $f1$ to $f11$. Experiment" ]	fig:featimp	Average of Feature Importance with four Decision Trees.
dataset/figures/2009.11347_._imgs_dnnMLP2.png	[ "is learning) and its Validation Learning Curve (VLC, showing the loss evolution during the validation phase at the end of each epoch, i.e., how well the model is generalizing). !ht\t\twidth=./imgs/dnnMLP2.png \tTLC and VLC on the Optimized (a) and RRw-Optimized (b) MTA-KDD'19 datasets. fig:dnnRPwThe left side (a) of Fig. fig:dnnRPw shows the learning curves of the MLP trained with the Optimized and RRw-Optimized MTA-KDD'19 datasets. We can see that the model underfits: the loss continues to decrease at the end of the plot, indicating that the model is capable of further lear", "Curve (VLC, showing the loss evolution during the validation phase at the end of each epoch, i.e., how well the model is generalizing). !ht\t\twidth=./imgs/dnnMLP2.png \tTLC and VLC on the Optimized (a) and RRw-Optimized (b) MTA-KDD'19 datasets. fig:dnnRPwThe left side (a) of Fig. fig:dnnRPw shows the learning curves of the MLP trained with the Optimized and RRw-Optimized MTA-KDD'19 datasets. We can see that the model underfits: the loss continues to decrease at the end of the plot, indicating that the model is capable of further learning and therefore that the training proc", "t the model is capable of further learning and therefore that the training process was halted prematurely. With further experiments (not shown here), we determined that the loss stabilizes after 100 epochs. width=" ]	fig:dnnRPw	TLC and VLC on the Optimized (a) and RRw-Optimized (b) MTA-KDD'19 datasets.
dataset/figures/2009.11347_._imgs_AElearning.png	[ "A-KDD'19 dataset. Here the TLC and VLC evolve similarly and the neural network loss stabilizes earlier at an acceptable level. Thus, as expected, re-weighting the dataset helped the classifier. !ht width=./imgs/AElearning.png TLC and VLC on the AE-Generated MTA-KDD'19 dataset. fig:AEtraintestOn the other hand, Fig. fig:AEtraintest shows that with the AE-Generated dataset the error reduction is slower than with the RRw-Optimized one, but at the tenth epoch the loss is almost stable. ht Final metrics on the testing set with the Optimized, RRw-Optimized and AE-Gen", "e similarly and the neural network loss stabilizes earlier at an acceptable level. Thus, as expected, re-weighting the dataset helped the classifier. !ht width=./imgs/AElearning.png TLC and VLC on the AE-Generated MTA-KDD'19 dataset. fig:AEtraintestOn the other hand, Fig. fig:AEtraintest shows that with the AE-Generated dataset the error reduction is slower than with the RRw-Optimized one, but at the tenth epoch the loss is almost stable. ht Final metrics on the testing set with the Optimized, RRw-Optimized and AE-Generated MTA-KDD'19 datasets. \|l\|c\|c\|c\|c\|c\|c" ]	fig:AEtraintest	TLC and VLC on the AE-Generated MTA-KDD'19 dataset.
dataset/figures/2004.08759_Fig_5.eps	[ "in). For instance, Jang et al. studied the impact of currency crises on the MST structure of stock markets Jang-Lee-Chang-2011-PA. Motivated by this, we investigate the evolution of the MSA structure of the Chinese stock market before, during and after two stock market turmoils. As shown in Fig.~Fig:Crash, the two crashes range respectively from 16 October 2007 to 4 November 2008 spanning 259 trading days and from 12 June 2015 to 28 January 2016 spanning 155 trading days. We use the data of the same length of trading days before and after the starting date of a crash as the data sample dur", "trading days and from 12 June 2015 to 28 January 2016 spanning 155 trading days. We use the data of the same length of trading days before and after the starting date of a crash as the data sample during the market turmoils (a bubble followed by a crash), denoted as $C_1,d$ and $C_2,d$ in Fig.~Fig:Crash. In order to analyze and compare the changes of MSTs of the information flow networks, the same time span data before and after the turmoil periods are used as the control data samples, which are denoted as $C_1,b$ and $C_1,a$ for the first case and $C_2,b$ and $C_2,a$ for the sec", "The closing price of Shanghai Stock Exchange Composite Stock Price (SSEC) Index from 04 January 2000 to 29 December 2017. The two gray regions are on behalf of two crashes of the Chinese stock market which from 16 October 2007 to 04 November 2008 and 12 June 2015 to 28 January 2016 respectively. Fig:Crash!htp\t\twidth=15cmFig_6.eps\tThe outgoing MSAs before (left column), during (middle column) and after (right column) the large stock market turmoils around the end of 2007 (top row) and around 2015 (bottom row). Fig:compcr:outflow!htp\t\twidth=15cmFig_7.eps\tThe incom" ]	Fig:Crash	The closing price of Shanghai Stock Exchange Composite Stock Price (SSEC) Index from 04 January 2000 to 29 December 2017. The two gray regions are on behalf of two crashes of the Chinese stock market which from 16 October 2007 to 04 November 2008 and 12 June 2015 to 28 January 2016 respectively.
dataset/figures/2004.08759_Fig_9.eps	[ "rol group, for each year, we randomly select the yearly return time series of non-root sectors to form a control sample $r_t^s$ ($t=2000, , 2017$) and calculate the correlation coefficients between these randomly selected sectors and the Shanghai Composite index. \t\twidth=9cmFig_9.eps\tComparison of the correlation coefficients between the returns of different types of sectors (source, sink and non-root) and the SSEC index. Fig:ret:rootWe use a PDF to show", "width=9cmFig_9.eps\tComparison of the correlation coefficients between the returns of different types of sectors (source, sink and non-root) and the SSEC index. Fig:ret:rootWe use a PDF to show the result of the correlation coefficients between the return time series of the randomly selected non-root sectors and the SSEC in Fig.~Fig:ret:root. It shows that the correlation coefficient between non-root sectors and the Shanghai Composite Index fluctuates", "correlation coefficients between the returns of different types of sectors (source, sink and non-root) and the SSEC index. Fig:ret:rootWe use a PDF to show the result of the correlation coefficients between the return time series of the randomly selected non-root sectors and the SSEC in Fig.~Fig:ret:root. It shows that the correlation coefficient between non-root sectors and the Shanghai Composite Index fluctuates around 0.9 (the black vertical line), indicating that there is a high correlation between different sector indices and the Shanghai Composite Index, which verifies the overal" ]	Fig:ret:root	Comparison of the correlation coefficients between the returns of different types of sectors (source, sink and non-root) and the SSEC index.
dataset/figures/1301.2048_sep_vs_mass.ps	[ "). These three groups correspond to three different detection methods: radialvelocities (RVs), illumination effects, and timing (using either the stellarpulsation or the eclipses as a clock). Figure detectionmethods compares the sensitivities of these different detection methods. The EXOTIME project is primarily oriented to increase the statistics of sdBplanets/BDs in large orbits (third group) and particularly focuses on singlestars which are not part of a binary system. The method is ba", "ination is not known and we report the minimum mass. Horizontallines show 1 Jupiter mass, 13 Jupiter masses (dividing the exoplanet and brown dwarf regimes)and 75 Jupiter masses (dividing the substellar and stellar regimes). The big dots are the twocandidates presented in this paper. *-5mm detectionmethodsData analysisAn O--C diagram is a way to investigate the temporalbehavior of periodic events. In our case, these periodicevents are the intensity variations due to the pulsations ofthe sdB stars. In contrast to the solar-like oscillationswith random phases and short lifet" ]	detectionmethods	Substellar companions around subdwarf B stars (black dots) and comparison of the detection methods mentioned in the text (RV, illumination and timing). For most of these systems the inclination is not known and we report the minimum mass. Horizontal lines show 1 Jupiter mass, 13 Jupiter masses (dividing the exoplanet and brown dwarf regimes) and 75 Jupiter masses (dividing the substellar and stellar regimes). The big dots are the two candidates presented in this paper.-5mm
dataset/figures/1301.2048_phasefolding-0444-f1.eps	[ "wobble of the stararound the common barycenter. Another effect resulting in asinusoidal O--C component is the beating of close unresolvedfrequencies. All these possible components are thoroughlyinvestigated in 2011PhDT........85L. In order to finally obtain the O--C diagrams shown inFigs.~hs0444f1 and hs0702f1, we i) subtracted theparabolic evolutionary component, ii) neglected thecontribution due to proper motion since it is estimated tobe two to three orders of magnitude weaker than theevolutionary component, iii) subtracted beating signals afterconfirming their presence wi", "diagrams for V1636\\,Ori based on the independent frequencies $f_1$ (top) and $f_2$ (bottom). Evolutionary and beating signals are already subtracted. The data are folded with an orbital period as given in the plots. Data points are duplicated on the phase-axis for plotting purposes. *-5mm hs0444f1V1636\\,Ori (HS0444+0458)New results on evolutionary time scaleFrom the parabolic O--C component, we derive a $P_1$ of $(9.3000.0023) 10^-12$ d/d for $f_1$ (631.73495 1/d) and $P_2$of $(3.010 0.0010) 10^-12$ d/d for $f_2$ (509.97773 1/d). The proper motion contrib", "searchAfter subtracting the evolutionary component,we find sinusoidal signatures in the O--C diagram of both frequencies$f_1$ and $f_2$. The most plausible explanation for thissinusoidal behavior is an orbital origin, hence the presence of a companioncandidate around V1636\\,Ori. Figure~hs0444f1 shows the O--C diagrams for$f_1$ and $f_2$, phase-folded with an orbital period close to 72 days. Within the error bars, the same signature consistent in amplitude, phase and period isindependently also seen in the O--C diagram for $f_2$. From theO--C amplitude and period we can d" ]	hs0444f1	Phase-folded O--C diagrams for V1636\,Ori based on the independent frequencies f_1(top) and f_2(bottom). Evolutionary and beating signals are already subtracted. The data are folded with an orbital period as given in the plots. Data points are duplicated on the phase-axis for plotting purposes.-5mm
dataset/figures/1301.2048_phasefolding-0702-f1.eps	[ "stararound the common barycenter. Another effect resulting in asinusoidal O--C component is the beating of close unresolvedfrequencies. All these possible components are thoroughlyinvestigated in 2011PhDT........85L. In order to finally obtain the O--C diagrams shown inFigs.~hs0444f1 and hs0702f1, we i) subtracted theparabolic evolutionary component, ii) neglected thecontribution due to proper motion since it is estimated tobe two to three orders of magnitude weaker than theevolutionary component, iii) subtracted beating signals afterconfirming their presence with an independe", "--C diagrams for DW\\,Lyn based on the independent frequencies $f_1$ (top) and $f_2$ (bottom). Evolutionary and beating signals are already subtracted. The data are folded with an orbital period as given in the plots. Data points are duplicated on the phase-axis for plotting purposes. *-5mm hs0702f1DW\\,Lyn (HS0702+6043)New results on evolutionary time scaleFor DW\\,Lyn we derive a $P_1$ of $(2.871 0.0025) 10^-13$d/d for $f_1$ (237.94106 1/d) and $P_2$ of $(5.5780.006) 10^-12$ d/d for $f_2$ (225.15882 1/d). The proper motioncontribution to the parabolic comp", "on companion searchAfter subtraction of the evolutionary component we find sinusoidal signaturesin the O--C diagram of both frequencies $f_1$ and $f_2$. Themost plausible explanation for this sinusoidal behavior is again an orbitalorigin and a companion candidate around DW\\,Lyn. Figure~hs0702f1shows the O--C diagrams for $f_1$ and $f_2$. Within the error bars, the same signature consistent in amplitude, phase and period is also seen in the O--C diagram for the independent frequency $f_2$. Weighting over the amplitudes and periods in the O--C diagrams of $f_1$ and $f_2$ re" ]	hs0702f1	Phase-folded O--C diagrams for DW\,Lyn based on the independent frequencies f_1(top) and f_2(bottom). Evolutionary and beating signals are already subtracted. The data are folded with an orbital period as given in the plots. Data points are duplicated on the phase-axis for plotting purposes.-5mm
dataset/figures/1301.2048_inclinations-paper.eps	[ "on mass and orbitalseparation. Assuming a canonical sdB mass of $0.47 M_$ and weightingover the independent frequencies $f_1$ and $f_2$, we find aminimum mass $m i$ of $31.41 7.25$ Jupiter masses for thiscandidate, V1636\\,Ori\\,b, which would place it to the brown dwarf regime(see Fig.~inclinations for the effect of the unknown inclination on the truemass). The orbital separation is derived to be $0.269 0.001$ AU. theight=0.44,angle=90phasefolding-0702-f1.epsheight=0.44,angle=90phasefolding-0702-f2.epsPhase-folded O--C diagrams for DW\\,Lyn based on the independen", "f_2$. Weighting over the amplitudes and periods in the O--C diagrams of $f_1$ and $f_2$ results in a minimum companionmass of $5.58 1.44$ Jupiter masses for this candidate and an orbitalseparation of $1.148 0.050$ AU. Hence, DW\\,Lyn\\,b would most likely bein the exoplanet mass regime (see Fig.~inclinations for the effect ofthe unknown inclination on the true mass). height=0.45,angle=90inclinations-paper.epsTrue companion masses as a function of the unknown inclinations forV1636\\,Ori\\,b (HS\\,0444+0458\\,b) and DW\\,Lyn\\,b (HS\\,0702+6043\\,b). Horizontal dashed lines separate the", "minimum companionmass of $5.58 1.44$ Jupiter masses for this candidate and an orbitalseparation of $1.148 0.050$ AU. Hence, DW\\,Lyn\\,b would most likely bein the exoplanet mass regime (see Fig.~inclinations for the effect ofthe unknown inclination on the true mass). height=0.45,angle=90inclinations-paper.epsTrue companion masses as a function of the unknown inclinations forV1636\\,Ori\\,b (HS\\,0444+0458\\,b) and DW\\,Lyn\\,b (HS\\,0702+6043\\,b). Horizontal dashed lines separate the stellar, brown dwarf and exoplanet regimes, respectively. The cases of zero inclination (face on) and", "an orbitalseparation of $1.148 0.050$ AU. Hence, DW\\,Lyn\\,b would most likely bein the exoplanet mass regime (see Fig.~inclinations for the effect ofthe unknown inclination on the true mass). height=0.45,angle=90inclinations-paper.epsTrue companion masses as a function of the unknown inclinations forV1636\\,Ori\\,b (HS\\,0444+0458\\,b) and DW\\,Lyn\\,b (HS\\,0702+6043\\,b). Horizontal dashed lines separate the stellar, brown dwarf and exoplanet regimes, respectively. The cases of zero inclination (face on) and $90$ degrees inclination (edge on) are indicated in the figure. Assuming a", "HS\\,0444+0458\\,b) and DW\\,Lyn\\,b (HS\\,0702+6043\\,b). Horizontal dashed lines separate the stellar, brown dwarf and exoplanet regimes, respectively. The cases of zero inclination (face on) and $90$ degrees inclination (edge on) are indicated in the figure. Assuming a random distribution of orbital inclinations, the arrows at the top show the probabilities $ P (i < ) = 1 - $ thatthe orbital inclination $i$ is lower than a certain value $$, e.\\ g.\\ aninclination lower than $60$ degrees has a probability of $50$\\candidate V1636\\,Ori\\,b would be stellar for inclinations belo", "ution of orbital inclinations, the arrows at the top show the probabilities $ P (i < ) = 1 - $ thatthe orbital inclination $i$ is lower than a certain value $$, e.\\ g.\\ aninclination lower than $60$ degrees has a probability of $50$\\candidate V1636\\,Ori\\,b would be stellar for inclinations below $23.12$degrees. The possibility for this being the case is $8.03$\\exoplanet candidate DW\\,Lyn\\,b would be a brown dwarf for inclinationsbelow $25.42$ degrees (possibility $9.68$\\degrees (possibility $0.24$\\", ".\\ g.\\ aninclination lower than $60$ degrees has a probability of $50$\\candidate V1636\\,Ori\\,b would be stellar for inclinations below $23.12$degrees. The possibility for this being the case is $8.03$\\exoplanet candidate DW\\,Lyn\\,b would be a brown dwarf for inclinationsbelow $25.42$ degrees (possibility $9.68$\\degrees (possibility $0.24$\\SummaryWe present first results for the two EXOTIME targetsV1636\\,Ori and DW\\,Lyn, assuming that the paraboliccomponent in the O--C diagram is due", ". The brown dwarfcandidate V1636\\,Ori\\,b would be stellar for inclinations below $23.12$degrees. The possibility for this being the case is $8.03$\\exoplanet candidate DW\\,Lyn\\,b would be a brown dwarf for inclinationsbelow $25.42$ degrees (possibility $9.68$\\degrees (possibility $0.24$\\SummaryWe present first results for the two EXOTIME targetsV1636\\,Ori and DW\\,Lyn, assuming that the paraboliccomponent in the O--C diagram is due to evolution and that the sinusoidal residuals are the signature of su", "r for inclinations below $23.12$degrees. The possibility for this being the case is $8.03$\\exoplanet candidate DW\\,Lyn\\,b would be a brown dwarf for inclinationsbelow $25.42$ degrees (possibility $9.68$\\degrees (possibility $0.24$\\SummaryWe present first results for the two EXOTIME targetsV1636\\,Ori and DW\\,Lyn, assuming that the paraboliccomponent in the O--C diagram is due to evolution and that the sinusoidal residuals are the signature of sub-stellar companion candidates. The secular period chan" ]	inclinations	True companion masses as a function of the unknown inclinations for V1636\,Ori\,b (HS\,0444+0458\,b) and DW\,Lyn\,b (HS\,0702+6043\,b). Horizontal dashed lines separate the stellar, brown dwarf and exoplanet regimes, respectively. The cases of zero inclination (face on) and 90 degrees inclination (edge on) are indicated in the figure. Assuming a random distribution of orbital inclinations, the arrows at the top show the probabilities P (i < ) = 1 - that the orbital inclination i is lower than a certain value , e.60 degrees has a probability of 50\%. The brown dwarf candidate V1636\,Ori\,b would be stellar for inclinations below 23.12 degrees. The possibility for this being the case is 8.03\%. Accordingly, the exoplanet candidate DW\,Lyn\,b would be a brown dwarf for inclinations below 25.42 degrees (possibility 9.68\%) and a star for inclinations below 4 degrees (possibility 0.24\%).
dataset/figures/1612.08949_figure1.png	[ "simple case with just two agents, $N=2$, and the three possiblecombinations: two mimetics, one mimetic and one contrarian, and twocontrarians. We choose parameters such that for both agents $d$ isslightly higher than $u_i$, for example $d=0.01$ and $u_1=u_2=0$. Theresults are exhibited on Fig.~fig:twoagents (black filledsquares correspond to PD and red open circles to MC dynamics). In thecase of two mimetic agents, both of them will adopt immediately and nofurther changes are observed, the system arrives at a fixedpoint. With one mimetic and one contrarian, both agents adopt in thef", "of $n$ is $n=1$; (b) one mimetic and one contrarian, $n$ quickly converges to $n=0.5$; (c) two contrarians, the system exhibits oscillations. Black squares correspond to PD and open red circles to MC dynamics. In all cases, $d=0.01$ and $u_1=u_2=0$. fig:twoagents Let us now consider the case with an intermediate number of agents, $N=100$; henceforth we use the approximation given by Eq.(4). In Fig.~100agents, it can be verified that when the fraction of contrarians is large, $f=0.9$, the system exhibits oscillations in the parallel dy" ]	fig:twoagents	Case of two agents: (a) Two mimetics, the final value of n is n=1; (b) one mimetic and one contrarian, n quickly converges to n=0.5; (c) two contrarians, the system exhibits oscillations. Black squares correspond to PD and open red circles to MC dynamics. In all cases, d=0.01 and u_1=u_2=0.
dataset/figures/1612.08949_figure2.png	[ "illations. Black squares correspond to PD and open red circles to MC dynamics. In all cases, $d=0.01$ and $u_1=u_2=0$. fig:twoagents Let us now consider the case with an intermediate number of agents, $N=100$; henceforth we use the approximation given by Eq.(4). In Fig.~100agents, it can be verified that when the fraction of contrarians is large, $f=0.9$, the system exhibits oscillations in the parallel dynamics case, while there are no oscillations with Monte Carlo dynamics. For a lower fraction of contrarians, $f=0.5$, oscillations are of smaller amplitude a", "contrarians $f$: (a) $f=0.2$, no oscillations; (b) $f=0.5$, small amplitude oscillations; and (c) $f=0.9$, large amplitude sustained oscillations. Black squares correspond to PD and open red circles to MC dynamics. In all cases, $d=0.4$ and $u_0 = 0.5$. 100agents\tFor an even larger number of agents, $N=10^7$, oscillations alwaysdisappear in the long term. Even for a high proportion of contrarians,$f = 0.9$, and with parallel dynamics, oscillations decay after ashort transient, as can be seen in Fig.~muchos. For a lowerfraction of contra", "trarians ($f=0.9$), but a low value of advertising ($d=-0.2$). Results for different system sizes: (a) $N=2$, (b) $N=100$, and (c) $N=10^7$. Black squares correspond to PD and open red circles to MC dynamics. The qualitative behavior is the same as in Fig.~100agents and muchos with the same value of $f$, but a bigger value of $d$. lowdAnalytic ResultsanalyticalIn this section we present analytic mean field results and comparethem with numerical simulations of the preceding section. As theanalytic calculations impl" ]	100agents	Fraction of adopters as a function of time for N=100 agents and different values of the fraction of contrarians f: (a) f=0.2, no oscillations; (b) f=0.5, small amplitude oscillations; and (c) f=0.9, large amplitude sustained oscillations. Black squares correspond to PD and open red circles to MC dynamics. In all cases, d=0.4 and u_0 = 0.5.
dataset/figures/1612.08949_figure3.png	[ ", $d=0.4$ and $u_0 = 0.5$. 100agents\tFor an even larger number of agents, $N=10^7$, oscillations alwaysdisappear in the long term. Even for a high proportion of contrarians,$f = 0.9$, and with parallel dynamics, oscillations decay after ashort transient, as can be seen in Fig.~muchos. For a lowerfraction of contrarians, oscillations are very short lived; for$f=0.5$, for instance, no more than three oscillations are seen inFig.~muchosb. The previous results, all put together, suggestthat for uniform distribution of resistance to adoption ---which is araw simplifica", "a high proportion of contrarians,$f = 0.9$, and with parallel dynamics, oscillations decay after ashort transient, as can be seen in Fig.~muchos. For a lowerfraction of contrarians, oscillations are very short lived; for$f=0.5$, for instance, no more than three oscillations are seen inFig.~muchosb. The previous results, all put together, suggestthat for uniform distribution of resistance to adoption ---which is araw simplification of the society representation---, oscillations arepossible for a large number of contrarians, but are a finite size,transient effect. We have investiga", "arians $f$: (a) $f=0.2$, no oscillations; (b) $f=0.5$, very short lived oscillations; and (c) $f=0.9$, transient oscillations. Black squares correspond to PD and open red circles to MC dynamics. The other parameters in all cases are $d=0.4$ and $u_0 = 0.5$. muchosIt is also interesting to investigate the effect of theadvertising. The values considered, $d=0.4$ may be too high. It can beargued that a too high value of the incentive to adopt could have arole in the appearance, or not, of oscillations. And it has. In orderto check this we try a lo", "low value of advertising ($d=-0.2$). Results for different system sizes: (a) $N=2$, (b) $N=100$, and (c) $N=10^7$. Black squares correspond to PD and open red circles to MC dynamics. The qualitative behavior is the same as in Fig.~100agents and muchos with the same value of $f$, but a bigger value of $d$. lowdAnalytic ResultsanalyticalIn this section we present analytic mean field results and comparethem with numerical simulations of the preceding section. As theanalytic calculations implicitly assume $N $ we wil", "and the number ofadopters will fall to $n=0.5$ in the second step. After that, thenumber of adopters increases again, and then decreases to finallyconverge to an intermediary value of $n=0.6$. These decayingoscillations converging to $n=0.6$ are also observed in the numericalresults, on Fig. muchos(b)htbp\t width=0.45figure5.pdf\tExtreme pay-offs as a function of the number of adoppters,$n$, for the uniform distribution with $d=0.4$, $u_0 = 0.5$. $$ lines are extreme pay-offs, blue lines for mimetics and red lines for contrarians. In general they", "lower bound isalways $0$. The fixed point can be evaluated using Eqs.~eq:fixed point. Considering $f=0.5$ in those equations, it is easy to verifythat the equilibrium is in the region $0.1 n 0.9$ and theresult is $n 0.63$, that coincides very well with theasymptotic limit showed in Fig.~muchosb. For $f=0.9$ theasymptotic value is $n 0.48$ that also coincides with thenumerical result (Fig.~muchosc). The figure also explains theoscillations before attaining the fixed point, as described above. In the case with $d=-0.2$, the boundaries are: eq:MaxMinPayoffs3 _max", "5$ in those equations, it is easy to verifythat the equilibrium is in the region $0.1 n 0.9$ and theresult is $n 0.63$, that coincides very well with theasymptotic limit showed in Fig.~muchosb. For $f=0.9$ theasymptotic value is $n 0.48$ that also coincides with thenumerical result (Fig.~muchosc). The figure also explains theoscillations before attaining the fixed point, as described above. In the case with $d=-0.2$, the boundaries are: eq:MaxMinPayoffs3 _max^M(n) &=& 0.3+ n \\\\ _min^M(n) &=& -0.7+ n \\\\ _max^C(n) &=& 0.3- n \\\\ _min^C(n) &=& -0.7-" ]	muchos	Fraction of adopters as a function of time for N=10^7 agents and different values of the fraction of contrarians f: (a) f=0.2, no oscillations; (b) f=0.5, very short lived oscillations; and (c) f=0.9, transient oscillations. Black squares correspond to PD and open red circles to MC dynamics. The other parameters in all cases are d=0.4 and u_0 = 0.5.
dataset/figures/1612.08949_figure4.png	[ "implies that $30\\the agents have an idiosyncrasy below $d$, i.e. $30\\early adopters. As we are interested in possible oscillations wefocus on a high concentration of contrarians, $f=0.9$, and threesystem sizes, $N=2$, $N=100$, and $N=10^7$. The results are shownin Fig.~lowd where a clear feature can be seen: the asymptoticvalues for the average fraction of adopters are much lower ($n 0.15$) than in the case of $d=0.4$. This is expected because theadvertising is what promotes the adoption in the first place. But onthe other hand the oscillatory behavior is ver", "sizes: (a) $N=2$, (b) $N=100$, and (c) $N=10^7$. Black squares correspond to PD and open red circles to MC dynamics. The qualitative behavior is the same as in Fig.~100agents and muchos with the same value of $f$, but a bigger value of $d$. lowdAnalytic ResultsanalyticalIn this section we present analytic mean field results and comparethem with numerical simulations of the preceding section. As theanalytic calculations implicitly assume $N $ we willcompare them with the numerical results for the big size system, i.e.,$N", "$, restricted to $n_t> 0.3$ there are no contrarians adopting and the number of adoptersshould be $n= (1-f) n_t$ that is always lower than $n_t$, incontradiction with the hypothesis. So, $n$ must be lower than $0.3$and the solution is $n 0.16$ again in agreement with thesimulations (See Fig.~lowdc). Finally, and as we said, sustained oscillations can be obtained for aset of parameters such that $0<n_4 d-u_0<n_3 d+u_0<1$,provided that both, $u_0$ and $d$ be small enough. We show inFig.~fig:extremes-b the extreme pay-offs obtained analyticallyfor $d=0.6$ and $u_0 = 0.25$. The inter" ]	lowd	Fraction of adopters as a function of time for a large fraction of contrarians (f=0.9), but a low value of advertising (d=-0.2). Results for different system sizes: (a) N=2, (b) N=100, and (c) N=10^7. Black squares correspond to PD and open red circles to MC dynamics. The qualitative behavior is the same as in Fig.~100agents and muchos with the same value of f, but a bigger value of d.
dataset/figures/1612.08949_figure5.png	[ "ar, we have chosen$u_0=0.5$. If a narrower distribution of the idiosyncratic resistanceto adopt is considered, stable oscillations may appear for relativelyhigh values of the advertising. In the next section we show, as anexample, that such is the case for $u_0 = 0.25$ and $ P(u)=2$(see Fig.fig:extremes-b). Moreover, the effect of the width ofthe distribution on the existence of oscillations will be discussed indetail in section logistic, as the logistic distribution issimpler to be treated. htbp\t width=0.45figure4.pdf\tFraction of adopters as a function of time for a", "the preceding section. As theanalytic calculations implicitly assume $N $ we willcompare them with the numerical results for the big size system, i.e.,$N=10^7$. Due to the compact support of $ P$, the possible (normalized)pay-offs as a function of $n$ (see Eq.~eq:payoffsModel1 andFig.~fig:extremes) are bounded by eq:MaxMinPayoffs _max^M(n) &= d+u_0+ n \\\\ _min^M(n) &= d-u_0+ n \\\\ _max^C(n) &= d+u_0- n \\\\ _min^C(n) &= d-u_0- n and the fixed point equations of the dynamics, $n(t+1)=n(t)=n$ are:eq:fixed pointn =& n^M+n^C; eq:fixed point_n", "Cthat must be solved for $n$. We call $n^M$ the number of adopters whoare mimetic and $n^C$ those who are contrarian. There are different regimes that have to be analyzed separately,depending on the signs of the extreme pay-offs at $n=0$ and at$n=1$. To illustrate this point we show on Fig. fig:extremes theextreme pay-offs as a function of the number of adopters, $n$, for$d=0.4$ and $u_0=0.5$. Blue lines are extreme pay-offs for mimeticsand red lines for contrarians. The area with positive pay-offcorrespond to the number of mimetics (blue ones) and contrarians (redones) but one s", "adoppters,$n$, for the uniform distribution with $d=0.4$, $u_0 = 0.5$. $$ lines are extreme pay-offs, blue lines for mimetics and red lines for contrarians. In general they are given by Eq.~eq:MaxMinPayoffs, in this case by Eq.~eq:MaxMinPayoffs2. fig:extremesWe consider now the points where the extreme pay-offs change sign bysolving Eqs.~eq:fixed point for the pay-off equal to zero: eq:intersections n_1 &=& -d-u_0 \\\\ n_2 &=& -d+u_0 \\\\ n_3 &=& d+u_0 = -n_1 \\\\ n_4 &=& d-u_0 = -n_2 Two of these points, $n_", "where the extreme pay-offs change sign bysolving Eqs.~eq:fixed point for the pay-off equal to zero: eq:intersections n_1 &=& -d-u_0 \\\\ n_2 &=& -d+u_0 \\\\ n_3 &=& d+u_0 = -n_1 \\\\ n_4 &=& d-u_0 = -n_2 Two of these points, $n_2$ and $n_3$, are also indicated onFig. fig:extremes; $_max^M(n)$ is always positive and$_min^C(n)$ always negative, so $n_1$ and $n_4$ are both negativeand are not solutions. In the general case we can state that $u_0 >0$, $n_2 > n_1$ and $n_3 > n_4$, but depending on the relative valuesof $d$ and $u_0$, $n_3$ may be larger or s", "and $d=-0.2$, both with $u_0 = 0.5$. In the firstcase ($d=0.4$) one has the following boundaries: eq:MaxMinPayoffs2 _max^M(n) &=& 0.9+ n \\\\ _min^M(n) &=& -0.1+ n \\\\ _max^C(n) &=& 0.9- n \\\\ _min^C(n) &=& -0.1- n Those boundaries are the ones plotted on Fig.~fig:extremes. Theboundary $_max^M(n)$ is always positive, $_min^M(n)$ ispositive for $n>0.1$, $_max^C(n)$ is positive if $n<0.9$ and$_min^C(n)$ is always negative, so in the correspondingcontrarian integral (eq.~eq:fixed point_C) the lower bound isalways $0$. The fixed point can be e", "lower than $0.3$and the solution is $n 0.16$ again in agreement with thesimulations (See Fig.~lowdc). Finally, and as we said, sustained oscillations can be obtained for aset of parameters such that $0<n_4 d-u_0<n_3 d+u_0<1$,provided that both, $u_0$ and $d$ be small enough. We show inFig.~fig:extremes-b the extreme pay-offs obtained analyticallyfor $d=0.6$ and $u_0 = 0.25$. The interpretation of this figure is thesame as the one done for Fig.~fig:extremes. Moreover, the insetof Fig.~fig:extremes-b shows the numerical result for the samevalues of parameters and $f=0.7$. It ca", "obtained for aset of parameters such that $0<n_4 d-u_0<n_3 d+u_0<1$,provided that both, $u_0$ and $d$ be small enough. We show inFig.~fig:extremes-b the extreme pay-offs obtained analyticallyfor $d=0.6$ and $u_0 = 0.25$. The interpretation of this figure is thesame as the one done for Fig.~fig:extremes. Moreover, the insetof Fig.~fig:extremes-b shows the numerical result for the samevalues of parameters and $f=0.7$. It can be observed that the fractionof adopters as a function of time for parallel update dynamics presentoscillations, in accordance with the analytical result. h", "$0<n_4 d-u_0<n_3 d+u_0<1$,provided that both, $u_0$ and $d$ be small enough. We show inFig.~fig:extremes-b the extreme pay-offs obtained analyticallyfor $d=0.6$ and $u_0 = 0.25$. The interpretation of this figure is thesame as the one done for Fig.~fig:extremes. Moreover, the insetof Fig.~fig:extremes-b shows the numerical result for the samevalues of parameters and $f=0.7$. It can be observed that the fractionof adopters as a function of time for parallel update dynamics presentoscillations, in accordance with the analytical result. htbp\t width=0.45figure5b.pdf", "for mimetics and red lines for contrarians. In general they are given by Eq.~eq:MaxMinPayoffs. Inset: Numerical results of the fraction of adopters as a function of time in the parallel update dynamics for $N=10^7$ ($d=0.6$, $u_0 = 0.25$, and $f=0.7$). fig:extremes-bLogistic distributionlogisticWhile the uniform distribution is simpler than other distributions,the discontinuity at the borders generates some complicationsparticularly for the analytic calculations. Also, one may imagine thatthe distribution of idiosyncrasies in a real" ]	fig:extremes	Extreme pay-offs as a function of the number of adoppters,n, for the uniform distribution with d=0.4, u_0 = 0.5. lines are extreme pay-offs, blue lines for mimetics and red lines for contrarians. In general they are given by Eq.~eq:MaxMinPayoffs, in this case by Eq.~eq:MaxMinPayoffs2.
dataset/figures/1612.08949_figure5b.png	[ "ar, we have chosen$u_0=0.5$. If a narrower distribution of the idiosyncratic resistanceto adopt is considered, stable oscillations may appear for relativelyhigh values of the advertising. In the next section we show, as anexample, that such is the case for $u_0 = 0.25$ and $ P(u)=2$(see Fig.fig:extremes-b). Moreover, the effect of the width ofthe distribution on the existence of oscillations will be discussed indetail in section logistic, as the logistic distribution issimpler to be treated. htbp\t width=0.45figure4.pdf\tFraction of adopters as a function of time for a", "lower than $0.3$and the solution is $n 0.16$ again in agreement with thesimulations (See Fig.~lowdc). Finally, and as we said, sustained oscillations can be obtained for aset of parameters such that $0<n_4 d-u_0<n_3 d+u_0<1$,provided that both, $u_0$ and $d$ be small enough. We show inFig.~fig:extremes-b the extreme pay-offs obtained analyticallyfor $d=0.6$ and $u_0 = 0.25$. The interpretation of this figure is thesame as the one done for Fig.~fig:extremes. Moreover, the insetof Fig.~fig:extremes-b shows the numerical result for the samevalues of parameters and $f=0.7$. It ca", "$0<n_4 d-u_0<n_3 d+u_0<1$,provided that both, $u_0$ and $d$ be small enough. We show inFig.~fig:extremes-b the extreme pay-offs obtained analyticallyfor $d=0.6$ and $u_0 = 0.25$. The interpretation of this figure is thesame as the one done for Fig.~fig:extremes. Moreover, the insetof Fig.~fig:extremes-b shows the numerical result for the samevalues of parameters and $f=0.7$. It can be observed that the fractionof adopters as a function of time for parallel update dynamics presentoscillations, in accordance with the analytical result. htbp\t width=0.45figure5b.pdf", "for mimetics and red lines for contrarians. In general they are given by Eq.~eq:MaxMinPayoffs. Inset: Numerical results of the fraction of adopters as a function of time in the parallel update dynamics for $N=10^7$ ($d=0.6$, $u_0 = 0.25$, and $f=0.7$). fig:extremes-bLogistic distributionlogisticWhile the uniform distribution is simpler than other distributions,the discontinuity at the borders generates some complicationsparticularly for the analytic calculations. Also, one may imagine thatthe distribution of idiosyncrasies in a real" ]	fig:extremes-b	Extreme pay-offs as a function of the number of adopters, n, for the uniform distribution with d=0.6, u_0 = 0.25. lines are extreme pay-offs, blue lines for mimetics and red lines for contrarians. In general they are given by Eq.~eq:MaxMinPayoffs. Inset: Numerical results of the fraction of adopters as a function of time in the parallel update dynamics for N=10^7(d=0.6, u_0 = 0.25, and f=0.7).
dataset/figures/1612.08949_figure6-new.png	[ "is with its variance given by$ = 2 \\, \\, 3.$Following the practice of the previous section, we present first thenumerical results. Numerical ResultsWe have performed different simulations with the logistic distributiongiven by Eq.~eq:logis. The results are presented inFigs.~umbral, logd04, logd03, and logres. Whenthe simulation is performed in parallel (PD), permanent oscillationsmay appear. This is the case for intermediate values of theadvertising, $d$, and relatively high values of the fraction ofcontrarians, $f$. This can be verified in Fig.~umbral whe", "inFigs.~umbral, logd04, logd03, and logres. Whenthe simulation is performed in parallel (PD), permanent oscillationsmay appear. This is the case for intermediate values of theadvertising, $d$, and relatively high values of the fraction ofcontrarians, $f$. This can be verified in Fig.~umbral where wehave represented a threshold value of the fraction of contrarians$f_c$, above which oscillations appear, as a function of theadvertising $d$. Notice that there are no oscillations for $d<0$ orfor high values of $d$. Oscillations are present in a region of valuesof $d$ around $d=", "ause contrarians adopt when the number of adopters is low, butabandon the innovation when the number of adopters is high. Howeversome mimetics may follow the contrarian's behavior. The amplitude ofthe oscillations decreases when decreasing $f$ or when $d$ is smalleror bigger than $1$ (See Fig. umbral). The region where stableoscillations occur is larger the narrower the width of thedistribution of idiosyncrasies, $$. We have represented in Figs.~logd04 and logd03 the timeevolution of the number of adopters exhibiting the oscillations, whenthey happen, or the convergence to a fixe", "just positive values of $d$ as there are no oscillations for negative values. The curves go through a minimum that is lower the narrower the distribution. Notice that the oscillations disappear when the advertising is slightly higher than $d=1$ \tumbralhtbp\t width=0.45figure7.pdf\tTemporal behavior of the fraction of adopters for the logistic distribution with $ = 0.25$, $d=0.4$, and different values of the fraction of contrarians $f$: (a) $f=0.2$, (b) $f=0.5$, and (c) $f=0.9$. Results are for a", "tribution is bell shaped, as it is thecase of the logistic distribution presented in section logistic,we obtain similar results. That is, stable long term oscillations mayappear for intermediate values of the advertising, $d $, or a largefraction of contrarians, $f$, as it is evident in Fig.~umbral. While a high number of contrarians may be unreal considering a noveltechnology, that could be the case regarding brand choices, forexample ( iPhone vs. Samsung). In any case,Fig.~umbral shows that oscillations may appear with a relativelylow fraction of contrarians, provided the", "te values of the advertising, $d $, or a largefraction of contrarians, $f$, as it is evident in Fig.~umbral. While a high number of contrarians may be unreal considering a noveltechnology, that could be the case regarding brand choices, forexample ( iPhone vs. Samsung). In any case,Fig.~umbral shows that oscillations may appear with a relativelylow fraction of contrarians, provided the advertising is strong: seefor example that for a narrow distribution of idiosyncrasies($=0.05$) and for $d 0.95$ the threshold is of the orderof $f 0.15$. Also, the coexistence of contrarians w" ]	umbral	Thresholds value of the fraction of contrarians above which oscillations appear. The curves correspond to different values of the width of the logistic distribution , as indicated. We have represented just positive values of d as there are no oscillations for negative values. The curves go through a minimum that is lower the narrower the distribution. Notice that the oscillations disappear when the advertising is slightly higher than d=1
dataset/figures/1612.08949_figure7.png	[ "h its variance given by$ = 2 \\, \\, 3.$Following the practice of the previous section, we present first thenumerical results. Numerical ResultsWe have performed different simulations with the logistic distributiongiven by Eq.~eq:logis. The results are presented inFigs.~umbral, logd04, logd03, and logres. Whenthe simulation is performed in parallel (PD), permanent oscillationsmay appear. This is the case for intermediate values of theadvertising, $d$, and relatively high values of the fraction ofcontrarians, $f$. This can be verified in Fig.~umbral where wehave", "contrarian's behavior. The amplitude ofthe oscillations decreases when decreasing $f$ or when $d$ is smalleror bigger than $1$ (See Fig. umbral). The region where stableoscillations occur is larger the narrower the width of thedistribution of idiosyncrasies, $$. We have represented in Figs.~logd04 and logd03 the timeevolution of the number of adopters exhibiting the oscillations, whenthey happen, or the convergence to a fixed point when there are nooscillations. When performing Monte Carlo simulations there are nooscillations in none of the cases. Figure logres summarizes the", "to PD simulations. In the PD case it is possible to see the oscillations in the number of adopters for a high concentration of contrarians. We have considered much longer times than those represented in the figure and the oscillations are stable. logd04htbp\t width=0.45figure8.pdf\tTemporal behavior for the logistic distribution with $ = 0.25$, $f=0.9$ and two different values of the parameter $d$ (the normalized effective marketing): (a) $d=-0.2$ and (b) $d=0.1$. Oscillations in the number of", "while the other two represent the extremes of the oscillations. These extreme values are approximately $0.12$ and $0.9$ and correspond to the extreme value of the oscillations in the PD simulations, see Fig. logd04(c). logana02The comparison between numerical and analytical solutions is discussedin detail in the caption of Figs. logana01 andlogana02. We find a very good agreement of both solutions, then,there is no need of further discussion of this point. We willconcentrate in the next s" ]	logd04	Temporal behavior of the fraction of adopters for the logistic distribution with = 0.25, d=0.4, and different values of the fraction of contrarians f: (a) f=0.2, (b) f=0.5, and (c) f=0.9. Results are for a large number of agents, N=10^7. Open red circles correspond to the MC simulations and black squares to PD simulations. In the PD case it is possible to see the oscillations in the number of adopters for a high concentration of contrarians. We have considered much longer times than those represented in the figure and the oscillations are stable.
dataset/figures/1612.08949_figure8.png	[ "ance given by$ = 2 \\, \\, 3.$Following the practice of the previous section, we present first thenumerical results. Numerical ResultsWe have performed different simulations with the logistic distributiongiven by Eq.~eq:logis. The results are presented inFigs.~umbral, logd04, logd03, and logres. Whenthe simulation is performed in parallel (PD), permanent oscillationsmay appear. This is the case for intermediate values of theadvertising, $d$, and relatively high values of the fraction ofcontrarians, $f$. This can be verified in Fig.~umbral where wehave represent", "behavior. The amplitude ofthe oscillations decreases when decreasing $f$ or when $d$ is smalleror bigger than $1$ (See Fig. umbral). The region where stableoscillations occur is larger the narrower the width of thedistribution of idiosyncrasies, $$. We have represented in Figs.~logd04 and logd03 the timeevolution of the number of adopters exhibiting the oscillations, whenthey happen, or the convergence to a fixed point when there are nooscillations. When performing Monte Carlo simulations there are nooscillations in none of the cases. Figure logres summarizes thenumerical res", ".pdf\tTemporal behavior for the logistic distribution with $ = 0.25$, $f=0.9$ and two different values of the parameter $d$ (the normalized effective marketing): (a) $d=-0.2$ and (b) $d=0.1$. Oscillations in the number of adopters are obtained if $d > 0$. logd03htbp\t width=0.45figure9-new.pdf\tThis figure summarizes the numerical results for the logistic distribution of idiosyncrasies with $ = 0.25$. All four panels exhibit the fraction of adopters as a function of the fraction of contrarians for four" ]	logd03	Temporal behavior for the logistic distribution with = 0.25, f=0.9 and two different values of the parameter d(the normalized effective marketing): (a) d=-0.2 and (b) d=0.1. Oscillations in the number of adopters are obtained if d > 0.
dataset/figures/1612.08949_figure9-new.png	[ "$ = 2 \\, \\, 3.$Following the practice of the previous section, we present first thenumerical results. Numerical ResultsWe have performed different simulations with the logistic distributiongiven by Eq.~eq:logis. The results are presented inFigs.~umbral, logd04, logd03, and logres. Whenthe simulation is performed in parallel (PD), permanent oscillationsmay appear. This is the case for intermediate values of theadvertising, $d$, and relatively high values of the fraction ofcontrarians, $f$. This can be verified in Fig.~umbral where wehave represented a threshold", "represented in Figs.~logd04 and logd03 the timeevolution of the number of adopters exhibiting the oscillations, whenthey happen, or the convergence to a fixed point when there are nooscillations. When performing Monte Carlo simulations there are nooscillations in none of the cases. Figure logres summarizes thenumerical results for the logistic distribution. Red curves (dashed)correspond to the final number of adopters (fixed points) whenperforming MC simulations, while black curves correspond to ParallelDynamics (PD). In the later case, oscillations may be observed above acriti", "lue of $f$ when the parallel dynamics exhibits period two oscillations. When increasing $d$ the region of oscillations increases up to $d=0.7$ and then decreases for $d=1.0$. When $d < 0$ there are no oscillations and both dynamics produce the same results. logresAnalytic resultsThe dynamics of adoption, given by equation (eq:dynamics), iseq:dynamicsLogisticn(t+1) = (1-f) F(d+ n(t)) + f F(d- n(t))where $ F(u)$ is the cumulative distribution F(u) = _-^u P(x) dx = 11+e^-2 u. The fixed points may be obtained by", "2$ the derivatives at the intersections are always $ \|y_1'\| <1$, thus no oscillations are expected. (b) When $d=0.1$ three possible stable intersections appear in each case, and the values roughly correspond to the numerical results plotted on Fig.~logres(a). (c) When $d=0.4$ and $f=0.2$ the stable solution correspond to $n 0.8$ that coincides with the numerical solution (See Fig.~logres(b)). For $f=0.5$, $n 0.5$ that also coincides with both PD and MC simulations. Finally, for $f=0.9$ the solution", "intersections appear in each case, and the values roughly correspond to the numerical results plotted on Fig.~logres(a). (c) When $d=0.4$ and $f=0.2$ the stable solution correspond to $n 0.8$ that coincides with the numerical solution (See Fig.~logres(b)). For $f=0.5$, $n 0.5$ that also coincides with both PD and MC simulations. Finally, for $f=0.9$ the solution is unstable ($ \|y_1'\| >1$). However the fixed point corresponds to the value obtained with MC simulations (see Fig.~logres), w", "(See Fig.~logres(b)). For $f=0.5$, $n 0.5$ that also coincides with both PD and MC simulations. Finally, for $f=0.9$ the solution is unstable ($ \|y_1'\| >1$). However the fixed point corresponds to the value obtained with MC simulations (see Fig.~logres), while PD simulations indicated the existence of oscillations. logana01\thtbp\t\t width=0.4figure11.pdf\t\tFixed points of $y_1(y_1(n))$ with $y_2(n)$ (gray dot-dashed line). We have plot just the case with $d=0.4$. It" ]	logres	This figure summarizes the numerical results for the logistic distribution of idiosyncrasies with = 0.25. All four panels exhibit the fraction of adopters as a function of the fraction of contrarians for four different values of d: (a) d=0.1, (b) d=0.4, (c) d=0.7, and (d) d=1.0. As expected, the number of adopters decreases when the number of contrarians increases. The red curves (dashed) correspond to Monte Carlo simulations and the black ones to a parallel dynamics. An oscillatory behavior is obtained only for parallel dynamics and the black lines correspond to the average value of the oscillations, while the shadowed areas indicates the amplitude of the oscillations. Both dynamics exhibit identical results for low and intermediate values of f, but there exists a critical value of f when the parallel dynamics exhibits period two oscillations. When increasing d the region of oscillations increases up to d=0.7 and then decreases for d=1.0. When d < 0 there are no oscillations and both dynamics produce the same results.
dataset/figures/1612.08949_figure11.png	[ "ond to the fixed points and arestable solutions provided that $ y_1' d y_1d n < 1$. However, solutions with $\| y_1'\| \|d y_1d n\| >1$ areunstable, and we are then obliged to consider a second iteration,i.e., $y_1(y_1(n))$. The solutions for this second iteration arerepresented on Fig. logana02: if more than one intersection ispresent, the upper and lower intersections correspond to the extremevalue of the oscillations. htbp\t width=1.0figure10.pdf\tFixed points of $y_1(n)$. The fixed points correspond to the intersections of $y_1(n)$ and $y_2(n)$ (indicated by", "er two represent the extremes of the oscillations. These extreme values are approximately $0.12$ and $0.9$ and correspond to the extreme value of the oscillations in the PD simulations, see Fig. logd04(c). logana02The comparison between numerical and analytical solutions is discussedin detail in the caption of Figs. logana01 andlogana02. We find a very good agreement of both solutions, then,there is no need of further discussion of this point. We willconcentrate in the next section in the", "and $0.9$ and correspond to the extreme value of the oscillations in the PD simulations, see Fig. logd04(c). logana02The comparison between numerical and analytical solutions is discussedin detail in the caption of Figs. logana01 andlogana02. We find a very good agreement of both solutions, then,there is no need of further discussion of this point. We willconcentrate in the next section in the discussion of the results andcomparison with a previous model~GoncalvesLagunaIglesias12." ]	logana02	Fixed points of y_1(y_1(n)) with y_2(n)(gray dot-dashed line). We have plot just the case with d=0.4. It is possible to observe that for f=0.2 and f=0.5 there is just one intersection, that corresponds to the stable solutions previously obtained. For f=0.9 there are three intersections. The middle one corresponds to the fixed point of y_1(n) while the other two represent the extremes of the oscillations. These extreme values are approximately 0.12 and 0.9 and correspond to the extreme value of the oscillations in the PD simulations, see Fig. logd04(c).
dataset/figures/1612.08949_figure12.png	[ "Iglesias12. Here we include thepossibility of coming back from previous decisions, thus, individualswill abandon innovation if the pay-off is negative. No doubts ordelays are allowed in this version of the model. The results of thepresent and the previous~GoncalvesLagunaIglesias12 models arecompared and discussed in the following, that is, when adoption can bereverted or not. When considering a large number of agents we can take the limit $N $. Introducing the fraction of adopters (eq:n)in equations (eq:payoffsModel1), and assuming that theidiosyncratic normalized resistance to", "ons $ P(u)$, the uniform distribution and the logisticone. Uniform distributionsec:UDIn this section, we present first results of simulations and then wediscuss analytic results for a uniform distribution, i.e. $ P(u)=(2 \\, u_0)^-1$ in $-u_0,u_0$ and $ P(u)=0$elsewhere. We will compare the results of this model with the onespresented in GoncalvesLagunaIglesias12, thus we adopt the samevalue of the parameters of that paper: i.e. we consider $u_0=0.5$ sothat $ P(u)=1$. We also restrict the comparison to the resultsin ref. GoncalvesLagunaIglesias12 where $J=1$, so w", "agent is selected at random and its status is updateddepending on its pay-off, then the number of adopters is immediatelyadjusted. This process is repeated $N$ times, which corresponds to oneMC step. The reason for considering these two dynamics is that thefirst one (PD) is better adapted to be compared with analyticalresults, while MC simulations probably provides a better descriptionof the changes in real societies. The difference between the twodynamics is that in the MC method a sequential update is performed,which means that the number of adopters changes in a continuous waydurin", "PD and open red circles to MC dynamics. The qualitative behavior is the same as in Fig.~100agents and muchos with the same value of $f$, but a bigger value of $d$. lowdAnalytic ResultsanalyticalIn this section we present analytic mean field results and comparethem with numerical simulations of the preceding section. As theanalytic calculations implicitly assume $N $ we willcompare them with the numerical results for the big size system, i.e.,$N=10^7$. Due to the compact support of $ P$, the possible (normalized)pay-offs as a function of", "chos with the same value of $f$, but a bigger value of $d$. lowdAnalytic ResultsanalyticalIn this section we present analytic mean field results and comparethem with numerical simulations of the preceding section. As theanalytic calculations implicitly assume $N $ we willcompare them with the numerical results for the big size system, i.e.,$N=10^7$. Due to the compact support of $ P$, the possible (normalized)pay-offs as a function of $n$ (see Eq.~eq:payoffsModel1 andFig.~fig:extremes) are bounded by eq:MaxMinPayoffs _max^M(n) &= d+u_0+ n", "and for $d 0.95$ the threshold is of the orderof $f 0.15$. Also, the coexistence of contrarians with thepossibility of changing decisions makes the final total number ofadopters lower than in the case with noregrets~GoncalvesLagunaIglesias12. To check this point we haverepresented in Fig.~compare the present results for the uniformdistribution of $u_i$ together with those ofRef.~GoncalvesLagunaIglesias12. It is possible to see that theshape is similar in both cases, but when the decision is``reversible'' the final adoption is lower than when not. To producethis comparison we", "($d=0.4$, squares, and $d=-0.2$, circles). Filled symbols correspond to no repentants and open ones with repentants (present contribution). Pairs of curves display similar behavior with always lower values of adoption for the case with repentants. compareThe presence of repentants and contrarians have the effect of reducingthe final number of adopters. Also, oscillations may appear when thedistribution of resistances to adopt is smaller than $1$, i.e. smaller than the social interaction, $J$. Also, such cycles are onlypossible if bo" ]	compare	Comparison between the results of ref.~GoncalvesLagunaIglesias12(without repentants) and the present ones with repentants: final number of adopters for two values of d(d=0.4, squares, and d=-0.2, circles). Filled symbols correspond to no repentants and open ones with repentants (present contribution). Pairs of curves display similar behavior with always lower values of adoption for the case with repentants.
dataset/figures/2303.05972_images_dbn.png	[ "_t=0^T-1 p(X^t+1 \| X^t). eq:markov_1!t\twidth=0.6images/dbn.pdf\tExample of the structure of a first-order Markovian DBN with two time slices $t_0$ and $t_1$. To calculate the future values in $t_1$, we would only need to know the current values of our variables in $t_0$. fig:dbn_figAn example of the structure of a DBN with Markovian order 1 is shown in Fig. (fig:dbn_fig). One advantage that DBN models present is that they do not need to be trained with time series of constant length. Due to the Markovian order assumption in Equation (eq:markov_1), we only ne", "ple of the structure of a first-order Markovian DBN with two time slices $t_0$ and $t_1$. To calculate the future values in $t_1$, we would only need to know the current values of our variables in $t_0$. fig:dbn_figAn example of the structure of a DBN with Markovian order 1 is shown in Fig. (fig:dbn_fig). One advantage that DBN models present is that they do not need to be trained with time series of constant length. Due to the Markovian order assumption in Equation (eq:markov_1), we only need to recover several batches of two consecutive instants from the original dataset to learn t" ]	fig:dbn_fig	Example of the structure of a first-order Markovian DBN with two time slices t_0 and t_1. To calculate the future values in t_1, we would only need to know the current values of our variables in t_0.
dataset/figures/2303.05972_images_hybrid_ex.png	[ "expected severity of the symptoms in that patient. With this method, we can see if a patient is expected to end up suffering from critical COVID-19 and when approximately will this situation occur. To illustrate this whole process, a schematic representation of this framework can be seen in Fig. (fig:hybrid_fig). !t\twidth=images/hybrid_ex.pdf\tSchematic representation of the classifier-DBN framework. After obtaining a state vector $S_0$ from a patient, we can use it to forecast the next $t$ state vectors with the DBN model and check if they are critical with our static classifier.", ":hybrid_fig). !t\twidth=images/hybrid_ex.pdf\tSchematic representation of the classifier-DBN framework. After obtaining a state vector $S_0$ from a patient, we can use it to forecast the next $t$ state vectors with the DBN model and check if they are critical with our static classifier. fig:hybrid_figOur proposed framework supports any kind of classifier that is able to produce a discrete prediction given a continuous state vector $S^t$. We used a modular implementation where the classifier used can be a support vector machine, an XGBoost, a neural network and a Bayesian clas" ]	fig:hybrid_fig	Schematic representation of the classifier-DBN framework. After obtaining a state vector S_0 from a patient, we can use it to forecast the next t state vectors with the DBN model and check if they are critical with our static classifier.
dataset/figures/2303.05972_images_nn_arch.png	[ "layer used a single neuron with a sigmoid activation function for binary classification. A result greater than 0.5 is equated to predicting a critical status for a patient, and a result lesser or equal to 0.5 predicts a non-critical scenario. A representation of this structure can be seen in Fig. (fig:nn_arch). !t\twidth=images/nn_arch.pdf\tStructure of the neural network model used in the experiments. fig:nn_archExperimental resultssec:resultsFor our experiments, we used a dataset consisting of anonymous data recovered from 4 different Spanish hospitals from the Fundació", "equated to predicting a critical status for a patient, and a result lesser or equal to 0.5 predicts a non-critical scenario. A representation of this structure can be seen in Fig. (fig:nn_arch). !t\twidth=images/nn_arch.pdf\tStructure of the neural network model used in the experiments. fig:nn_archExperimental resultssec:resultsFor our experiments, we used a dataset consisting of anonymous data recovered from 4 different Spanish hospitals from the Fundación Jiménez Díaz in Madrid. After preprocessing it, we used this data to fit our proposed model and evaluate its capabil" ]	fig:nn_arch	Structure of the neural network model used in the experiments.
dataset/figures/2303.05972_images_inst_hist.png	[ "owever, it will be used to train the classifier models. From the remaining patients with more than a single instance, the majority of them have either two or three rows of recorded values. To illustrate this, we show a histogram with the distribution of the number of instances per patient in Fig. (fig:hist). !t\twidth=images/inst_hist.pdf\tHistogram with the number of instances per patient greater than 1 in the dataset. Inside the last bracket we have grouped all the patients with 10 or more instances. A higher number of instances indicates a longer stay in the hospital and as such a", "r of instances per patient greater than 1 in the dataset. Inside the last bracket we have grouped all the patients with 10 or more instances. A higher number of instances indicates a longer stay in the hospital and as such a more severe case of COVID-19, which is far less common than a mild case. fig:histRegarding the 532 variables in our dataset, most of them correspond to specific values in uncommon tests and analysis, and they have over 70\\" ]	fig:hist	Histogram with the number of instances per patient greater than 1 in the dataset. Inside the last bracket we have grouped all the patients with 10 or more instances. A higher number of instances indicates a longer stay in the hospital and as such a more severe case of COVID-19, which is far less common than a mild case.
dataset/figures/2303.05972_images_nn_time.png	[ "o be performed once. !t\twidth=images/nn_time.pdf\tClassification results of the neural network model as we feed it state vectors further ahead in time with the DBN model. The classification performance of the neural network improves monotonically by combining it with the DBN forecastings. fig:subplotsGiven that the model with the NN obtains the best average results, we show in Fig. (fig:subplots) the details of its performance depending on the time horizon. The first instant at 0 hours is equivalent to performing classification with the NN model directly to the state vector obt", "k model as we feed it state vectors further ahead in time with the DBN model. The classification performance of the neural network improves monotonically by combining it with the DBN forecastings. fig:subplotsGiven that the model with the NN obtains the best average results, we show in Fig. (fig:subplots) the details of its performance depending on the time horizon. The first instant at 0 hours is equivalent to performing classification with the NN model directly to the state vector obtained from the patient. From there, we perform forecasting up to 40 hours with the DBN model of this" ]	fig:subplots	Classification results of the neural network model as we feed it state vectors further ahead in time with the DBN model. The classification performance of the neural network improves monotonically by combining it with the DBN forecastings.