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Fixes numpy#82 latest review inputs
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config.yaml

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url: /learn
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- title: Array computing
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url: /arraycomputing
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- title: Case Studies
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url: /case-studies/blackhole-image
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- title: Community
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url: /community
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- title: About Us

content/en/case-studies/blackhole-image.md

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{{< figure src="/images/content_images/cs/blackhole.jpg" caption="**Black Hole M87**" alt="bhimg" attr="(**Image Credits:** Event Horizon Telescope Collaboration)" attrlink="https://www.jpl.nasa.gov/images/universe/20190410/blackhole20190410.jpg" >}}
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{{< figure src="/images/content_images/cs/blackhole.jpg" caption="**Black Hole M87**" alt="black hole image" attr="(**Image Credits:** Event Horizon Telescope Collaboration)" attrlink="https://www.jpl.nasa.gov/images/universe/20190410/blackhole20190410.jpg" >}}
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<blockquote cite="https://www.youtube.com/watch?v=BIvezCVcsYs">
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<p>Imaging the M87 Black Hole is like trying to see something that is by definition impossible to see.</p>
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The sequence of correlation and engineering releases represents a year-long effort of identifying and mitigating data issues, and developing new software and procedures that could reliably choose the most likely image based on actual measurements.
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{{< figure src="/images/content_images/cs/dataprocessbh.png" class="fig-center" caption="**EHT Data Processing Pipeline**" alt="dpipe" align="middle" attr="(Diagram Credits: The Astrophysical Journal, Event Horizon Telescope Collaboration)" attrlink="https://iopscience.iop.org/article/10.3847/2041-8213/ab0c57" >}}
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{{< figure src="/images/content_images/cs/dataprocessbh.png" class="fig-center" caption="**EHT Data Processing Pipeline**" alt="data pipeline" align="middle" attr="(Diagram Credits: The Astrophysical Journal, Event Horizon Telescope Collaboration)" attrlink="https://iopscience.iop.org/article/10.3847/2041-8213/ab0c57" >}}
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## NumPy’s Role in Black Hole Imaging
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There are several aspects to black hole imaging besides data collection, noise elimination, data cleanup, reduction and correlation. Imaging is crucial as it can help to predict not only the black hole mass but also rule out whether a black hole could be a wormhole, a theoretical bridge between distant points in spacetime. But it is also incredibly hard to measure given the astronomical distances involved. As Katie Bouman mentions in her [TED talk](https://www.youtube.com/watch?v=BIvezCVcsYs), ‘It is like taking a picture of an orange on the surface of the moon.’
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{{< figure src="/images/content_images/cs/bh_numpy_role.png" class="fig-center" alt="numpyr" caption="**The role of NumPy in Black Hole imaging**" >}}
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{{< figure src="/images/content_images/cs/bh_numpy_role.png" class="fig-center" alt="role of numpy" caption="**The role of NumPy in Black Hole imaging**" >}}
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Once the key challenges posed by EHT, data collection and reduction are taken care of, the next big challenge in data processing is related to imaging. The imaging algorithms form the core of this task as through imaging, scientists could calculate the shadow of the black hole which forms the crux of several other calculations related to event horizon and nearby objects. One of the key algorithms used in imaging was developed by Katie Bouman – Continuous High-resolution Image Reconstruction using Patch priors, or ‘CHIRP’. It can parse the cumulative telescope data gathered by the Event Horizon Telescope project.For imaging tasks, researchers banked on Python to run the datasets on these algorithms, arraying and plotting data for meaningful insights.
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Besides NumPy, there were other packages such as [SciPy](https://www.scipy.org), [Pandas](https://pandas.io) and [Matplotlib](https://matplotlib.org) that helped in imaging and [data processing for imaging the black hole](https://iopscience.iop.org/article/10.3847/2041-8213/ab0c57). The standard astronomical file formats and time/coordinate transformations were handled by [Astropy](https://www.astropy.org) while Matplotlib was used in visualizing data throughout the analysis pipeline, including the generation of the final image of the black hole.
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Andrew Chael and the ehtim project team came up with [eht-imaging](https://github.com/achael/eht-imaging) Python modules for simulating and manipulating VLBI data and producing images with regularized maximum likelihood methods. NumPy is at the core of array data processing used in this software package named ehtim as indicated by the partial software dependency chart below.
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{{< figure src="/images/content_images/cs/ehtim_numpy.png" class="fig-center" alt="ehtimnumpy" caption="**Software dependency chart of ehtim package highlighting NumPy**" >}}
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{{< figure src="/images/content_images/cs/ehtim_numpy.png" class="fig-center" alt="ehtim dependency map highlighting numpy" caption="**Software dependency chart of ehtim package highlighting NumPy**" >}}
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The challenge posed during reconstruction of an image using VLBI measurements is that there can be an infinite number of possible images that explain the data. The ehtim software addresses this challenge by implementing algorithms that help find a set of most likely reasonable images that respects prior scientific assumptions while still satisfying the observed data.
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NumPy enabled researchers to manipulate large numerical datasets through its efficient data structures of vectors and matrices leading to imaging and plotting of the first ever image of a black hole. Imaging of M87 black hole is a major scientific feat that was almost presumed impossible a century ago. In a way, black hole image has helped in a stunning confirmation of Einstein’s general theory of relativity. This is not only a breakthrough in technology, but an example of international scale collaboration that uses connections between the world's best radio observatories, over 200 scientists worked with observations collected over 10 days and analyzed for over a year. They used innovative algorithms and data processing techniques improving upon existing astronomical models to help unfold some of the mysteries of the universe.
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{{< figure src="/images/content_images/cs/numpy_bh_benefits.png" class="fig-center" alt="benefits" caption="**Key NumPy Capabilities utilized**" >}}
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{{< figure src="/images/content_images/cs/numpy_bh_benefits.png" class="fig-center" alt="numpy benefits" caption="**Key NumPy Capabilities utilized**" >}}

content/en/case-studies/gw-discov.md

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{{< figure src="/images/content_images/cs/gw_sxs_image.png" caption="**Gravitational Waves**" alt="gwimg" attr="(**Image Credits: The Simulating eXtreme Spacetimes (SXS) Project at LIGO** )" attrlink="https://youtu.be/Zt8Z_uzG71o" >}}
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{{< figure src="/images/content_images/cs/gw_sxs_image.png" caption="**Gravitational Waves**" alt="binary coalesce black hole generating gravitational waves" attr="(**Image Credits: The Simulating eXtreme Spacetimes (SXS) Project at LIGO** )" attrlink="https://youtu.be/Zt8Z_uzG71o" >}}
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<blockquote cite="https://www.youtube.com/watch?v=BIvezCVcsYs">
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<p>The scientific Python ecosystem is critical infrastructure for the research done at LIGO.</p>
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* **Visualization**
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Once the obstacles related to understanding Einstein’s equations well enough to solve them using supercomputers are taken care of, the next big challenge was making data comprehensible to the human brain. Simulation modeling as well as signal detection requires effective visualization techniques. Visualization also plays a role in lending more credibility to numerical relativity in the eyes of pure science aficionados.
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Once the obstacles related to understanding Einstein’s equations well enough to solve them using supercomputers are taken care of, the next big challenge was making data comprehensible to the human brain. Simulation modeling as well as signal detection requires effective visualization techniques. Visualization also plays a role in lending more credibility to numerical relativity in the eyes of pure science aficionados, who did not give enough importance to numerical relativity until imaging and simulations made it easier to comprehend results for a larger audience. Speed of complex computations and rendering, re-rendering images and simulations using latest experimental inputs and insights can be a time consuming activity that challenges researchers in this domain.
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{{< figure src="/images/content_images/cs/gw_strain_amplitude.png" class="fig-center" alt="gwstrain" caption="**Estimated gravitational-wave strain amplitude from GW150914**" attr="(**Graph Credits:** Observation of Gravitational Waves from a Binary Black Hole Merger, ResearchGate Publication)" attrlink="https://www.researchgate.net/publication/293886905_Observation_of_Gravitational_Waves_from_a_Binary_Black_Hole_Merger" >}}
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{{< figure src="/images/content_images/cs/gw_strain_amplitude.png" class="fig-center" alt="gravitational waves strain amplitude" caption="**Estimated gravitational-wave strain amplitude from GW150914**" attr="(**Graph Credits:** Observation of Gravitational Waves from a Binary Black Hole Merger, ResearchGate Publication)" attrlink="https://www.researchgate.net/publication/293886905_Observation_of_Gravitational_Waves_from_a_Binary_Black_Hole_Merger" >}}
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## NumPy’s Role in the detection of Gravitational Waves
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GW detection has enabled researchers to discover entirely unexpected phenomena while providing new insight into many of the most profound astrophysical phenomena known. Number crunching and data visualization is a crucial step that helps scientists gain insights into data gathered from the scientific observations and understand the results. The computations are complex and cannot be comprehended by humans unless it is visualized using computer simulations that are fed with the real observed data and analysis. NumPy along with other Python packages such as matplotlib, pandas and scikit-learn is [enabling researchers](https://www.gw-openscience.org/events/GW150914/) to answer complex questions and discover new horizons in our understanding of the universe.
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{{< figure src="/images/content_images/cs/numpy_gw_benefits.png" class="fig-center" alt="gwnpben" caption="**Key NumPy Capabilities utilized**" >}}
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{{< figure src="/images/content_images/cs/numpy_gw_benefits.png" class="fig-center" alt="numpy benefits" caption="**Key NumPy Capabilities utilized**" >}}

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