The shape of things to come

.title[
# The shape of things to come
]
.subtitle[
## Exploring the mathematical shape of plants
]
.author[
### <strong>Erik Amézquita</strong> <br> — <br> Computational Mathematics, Science, and Engineering <br> Michigan State University <br> —
]
.date[
### 2023-04-11
]

---

background-image: url("../../img/endlessforms.png")
background-size: 150px
background-position: 89% 7%

# Plant morphology

<div class="row">
  <div class="column" style="max-width:50%">
    <iframe width="375" height="210" src="https://www.youtube-nocookie.com/embed/oM9kAq0PBvw?controls=0" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
    <iframe width="375" height="210" src="https://www.youtube-nocookie.com/embed/V39K58evWlU?controls=0" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
  </div>
  <div class="column" style="max-width:50%">
    <iframe width="375" height="210" src="https://www.youtube-nocookie.com/embed/efF5PSvFQ2A?controls=0" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
    <iframe width="375" height="210" src="https://www.youtube-nocookie.com/embed/qkOjHHuoUhA?controls=0" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
  </div>
</div>
<p style="font-size: 24px; text-align: right; font-family: 'Yanone Kaffeesatz'">Check out more 3D X-ray CT scans at <a href="https://www.youtube.com/@endlessforms6756">youtube.com/@endlessforms6756</a></p>

---

background-image: url("../../img/cmse_logo.svg")
background-size: 150px
background-position: 1% 50%

# My research: Crossing and merging bridges

<div class="row">
  <div class="column" style="width:15%">
  <p style="font-size:5px">&mdash;</p>
  </div>
  <div class="column" style="max-width:28%">
    <a href="https://plantsandpython.github.io/PlantsAndPython/00_Opening_page.html" target="_blank"><img style="padding: 0 0 0 0;" src="../../tutorials/figs/plants_and_python_group_photo.jpg"></a>
  </div>
  <div class="column" style="max-width:50%">
    <a href="https://doi.org/10.1073/pnas.2217564120" target="_blank"><img style="padding: 0 0 0 0;" src="../../journal_diversity/figs/frequencies_globe_inv.jpg"></a>
  </div>
</div>

<div class="list" style="font-size: 10px; text-align: left;">
    <ul>
      <li>Marks <em>et al.</em> (2023) A critical analysis of plant science literature reveals ongoing inequities. DOI: <a href="https://doi.org/10.1073/pnas.2217564120" target="_blank">10.1101/2022.10.15.512190</a></li>
      <li><strong>A</strong> <em>et al.</em> (2022) The shape of aroma: measuring and modeling citrus oil gland distribution. DOI: <a href="https://doi.org/10.1002/ppp3.10333" target="_blank">10.1002/ppp3.10333</a></li>
      <li><strong>A</strong> <em>et al.</em> (2022) Genomics data analysis via spectral shape and topology. DOI: <a href="https://doi.org/10.48550/arXiv.2211.00938" target="_blank">10.48550/arXiv.2211.00938</a></li>
      <li>VanBuren<em>et al.</em> (2022) Teaching tools in plant biology. Plants and Python, coding from scratch in the plant sciences. DOI: <a href="https://doi.org/10.1093/plcell/koac187" target="_blank">10.1093/plcell/koac187</a>.</li>
      <li><strong>A</strong> <em>et al.</em> (2021) Measuring hidden phenotype: Quantifying the shape of barley seeds using the Euler Characteristic Transform. DOI: <a href="https://doi.org/10.1093/insilicoplants/diab033" target="_blank">10.1093/insilicoplants/diab033</a></li>
      <li><strong>A</strong> <em>et al.</em> (2020) The shape of things to come: Topological data analysis and biology, from molecules to organisms. DOI: <a href="https://doi.org/10.1002/dvdy.175" target="_blank">10.1002/dvdy.175</a></li>
    </ul>
</div>

---

# The shape of things to come

<div class="row" style="font-family: 'Yanone Kaffeesatz'; font-size:22px;">
  <div class="column" style="max-width:33%">
    <p style="line-height:0;text-align: center; font-size:28px">The shape of adaptability</p>
    <img style="padding: 0 70px;" src="../figs/S017_L3_1.gif"></img>
    <img style="padding: 0 55px;" src="../figs/ecc_X.gif"></img>
    <p style="text-align: center;">Topological Data Analysis</p>
    <p style="text-align: center;">Euler Characteristic Transform</p>
  </div>
  <div class="column" style="max-width:33%">
    <p style="line-height:0;font-size:28px;text-align: center;">The shape of development</p>
    <img style="padding: 0 60px;" src="../../citrus/figs/SR01_L01_black_exocarp.gif"></img>
    <img style="padding: 0 27px;" src="../../citrus/figs/SW03_CRC1241-B_12B-4-3_L00_lambproj_v.jpg"></img>
    <p style="text-align: center;">Ellipsoidal modeling</p>
    <p style="text-align: center;">Directional statistics</p>
  </div>
  <div class="column" style="max-width:33%">
    <p style="line-height:0;font-size:28px;text-align: center;">The shape of domestication</p>
    <img style="padding: 0 35px;" src="../../walnuts/figs/2014SBa_R5_T81_meat_2.gif"></img>
    <img style="padding: 0 10px;" src="../../walnuts/figs/kernel_volume_vs_nut_volume.png"></img>
    <p style="text-align: center;">Allometry of multiple tissues</p>
    <p style="text-align: center;">Convexity indices</p>
  </div>
</div>

---

# 1. Quantifying the barley morphology

## Brewing with the Euler Characteristic Transform

---

<div class="row">
  <div class="column" style="max-width:44%">
    <a href="https://kizilvest.ru/20150827-v-kizilskom-rajone-nachalas-uborochnaya-strada/" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_kizilskoye.jpg"></a>
    <a href="https://ipad.fas.usda.gov/highlights/2008/11/eth_25nov2008/" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_ethiopia.gif"></a>
    <a href="https://www.doi.org/10.1007/978-1-4419-0465-2_2168" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_historical_expansion.jpg"></a>
  </div>
  <div class="column" style="max-width:44%">
    <a href="https://www.resilience.org/stories/2020-03-09/the-last-crop-before-the-desert/" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_morocco.jpg"></a>
    <a href="https://www.tibettravel.org/tibetan-culture/highland-barley.html" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_seed_tibet.jpg"></a>
    <a href="https://www.nationalgeographic.co.uk/travel/2020/05/photo-story-from-barley-fields-to-whisky-barrels-in-rural-scotland" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_seed_scotland_cropped.jpg"></a>
  </div>
  <div class="column" style="max-width:8%; font-size: 15px;">
    <p style="text-align: center; font-size: 30px; line-height: 1em;"> <strong> Barley across the world </strong></p>
    <p>Kiliskoye (Chelyabinsk, Russia)</p>
    <p>Marchouch (Rabat, Morocco)</p>
    <p>Aksum (Tigray, Ethiopia)</p>
    <p>Salar (Tsetang, Tibet)</p>
    <p>Expansion of the barley. </p>
    <p>Turriff (Aberdeenshire, Scotland)</p>
  </div>
</div>

---

## Evolution in real time &rarr; X-rays &rarr; Image Processing

<div class="row">
  <div class="column" style="max-width:41%; color: Navy; font-size: 15px;">
    <img style="padding: 2px 0 2px 0;" src="../figs/barley_world.jpg">
    <p style="text-align: center;">28 accessions around the world</p>
  </div>
  <div class="column" style="max-width:50%; color: Navy; font-size: 15px;">
    <img style="padding: 2px 0 2px 0;" src="../figs/composite_cross_collection_06.svg">
    <p style="text-align: center;">58 generations in California</p>
  </div>
</div>

<div class="row">
  <div class="column" style="max-width:51%; color: Navy; font-size: 15px;">
    <img style="padding: 2px 0 2px 0;" src="../figs/x3000_setup.jpg">
    <p style="text-align: center;"> Proprietary X-Ray CT scan reconstruction </p>
  </div>
  <div class="column" style="max-width:17.5%; color: Navy; font-size: 15px;">
    <img src="../figs/S019_L0_1.gif">
    <p style="text-align: center;"> 975 spikes </p>
  </div>
  <div class="column" style="max-width:20.5%; color: Navy; font-size: 15px;">
    <img src="../figs/S017_L0_seed_10_0.gif">
    <p style="text-align: center;"> 38,000 seeds </p>
  </div>
</div>

---

background-image: url("../figs/S017_L0_seed_10_0.gif")
background-size: 85px
background-position: 90% 2%

# Traditional shape descriptors

---

# Topology: The Euler characteristic

`$$\begin{align} \chi &= \#(\text{Vertices}) - \#(\text{Edges}) + \#(\text{Faces}) \\ &= \#(\text{Connected Components}) - \#(\text{Loops}) + \#(\text{Voids}). \end{align}$$`

---

background-image: url("../figs/ecc_ver2.gif")
background-size: 750px
background-position: 50% 90%

## Euler Characteristic Curve (ECC)

- Consider a cubical complex `$X\subset\mathbb{R}^d$`
- And a unit-length direction `$\nu\in S^{d-1}$`

- And the subcomplex containing all cubical cells below height `$h$` in the direction `$\nu$`
`$$X(\nu)_h =\{\Delta \in X\::\:\langle x,\nu\rangle\leq h\text{ for all }x\in\Delta\}$$`

- The Euler Characteristic Curve (ECC) of direction `$\nu$` is defined as the sequence `$$\{\chi(X(\nu)_h)\}_{h\in\mathbb{R}}$$`

---

background-image: url("../figs/ect_ver2.gif")
background-size: 800px
background-position: 50% 88%

## Euler Characteristic Transform (ECT)

- Repeat and concatenate for all possible directions.

$$
`\begin{split}
ECT(X):\; & S^{d-1} \to \mathbb{Z}^{\mathbb{R}}\\
&\nu\mapsto\{\chi(X(\nu)_h)\}_{h\in\mathbb{R}}.
\end{split}`
$$

- [**Theorem** (Turner, Mukherjee, Boyer 2014) & (Curry, Mukherjee, Turner, 2018)](http://arxiv.org/abs/1805.09782):  The ECT is injective with a finite bound of necessary directions.

---

background-image: url("../figs/turner_etal_2014.png")
background-size: 280px
background-position: 99% 1%

# More on the ECT

- Easy to compute: a quick alternating sum.

- *Different* simplicial complexes correspond to *different* ECTs.

- [**Theorem _(ibid)_**](https://arxiv.org/abs/1310.1030): The ECT effectively summarizes all possible information related to shape.

There is elusive math research on computationally efficient reconstruction algorithms:
- [Turner, Mukherjee, Curry (2021)](https://arxiv.org/abs/1805.09782): Finite number of directions
- [Betthauser (2018)](https://people.clas.ufl.edu/peterbubenik/files/Betthauser_Thesis.pdf): 2D reconstruction
- [Fasy, Micka, Millman, Schenfisch, Williams (2022)](https://arxiv.org/abs/1912.12759): 3D reconstruction
- [Crawford, Monod, Chen, Mukherjee, Rabadan (2020)](https://doi.org/10.1080/01621459.2019.1671198): Smooth ECT
- [Jiang, Kurtek, Needham (2020)](https://openaccess.thecvf.com/content_CVPRW_2020/papers/w50/Jiang_The_Weighted_Euler_Curve_Transform_for_Shape_and_Image_Analysis_CVPRW_2020_paper.pdf): Weighted ECT

---

background-image: url("../figs/ect_ver2.gif")
background-size: 600px
background-position: 50% 98%

## Topological shape descriptors for barley seeds

.pull-left[
<img src="../figs/pole_directions_p7_m12_crop.jpg" width="250" style="display: block; margin: auto;" />
]

- 16 slices per direction

- Every seed is associated a `$158\times16=2528$`-dim vector

- Reduced to 12 dimensions with UMAP
]

---

# Supervised Learning

![](../../demat/figs/supervised_learning.png)

---

background-image: url("../figs/barley_world.jpg")
background-size: 225px
background-position: 98% 2%

# Quantify the shape of barley

**Goal:** Classify the **28** barley accessions solely by grain morphology.

### What does topology actually measure?

.pull-left[
<img src="../figs/discerning_directions.png" width="225" style="display: block; margin: auto;" />
]

---

# Predicting with Semi-Supervised Learning

![](../../demat/figs/semisupervised_learning.png)

---

# Prediction into semi-supervised territory

- Train an SVM with 100% of the founders `$(F_0)$`

- Classify the progeny `$(F_{18}\text{ and }F_{58})$` to detect genotype enrichment

---

background-image: url("../figs/comparison_lines_combined_topounscaled_d158_T16_horz.png")
background-size: 900px
background-position: 50% 70%

## Observe shape distribution across lines

---

background-image: url("../figs/amezquita_etal_2021.png")
background-size: 300px
background-position: 98% 2%

# Summary

.left-column[
<img src="../figs/S017_L3_1.gif" width="150" style="display: block; margin: auto;" /><img src="../figs/ecc_X.gif" width="150" style="display: block; margin: auto;" />
]

.right-column[
- **TDA** captures **nuanced** morphological information that is not obvious to the naked eye.

- We get the best results by **combining** both traditional and topological morphological descriptors.

- We can tell **similar** population genetic dynamics by using combined **morphological** descriptors.

- Seed phenotyping can be **cheaper** than genotyping.

- This is one of the **first** applications of the ECT to real-world data.

- First application of the ECT to **plant biology** specifically.
]

---

# 2. If life gives you lemons...

## Modeling citrus oil gland distribution

### Comparing limes to oranges with directional statistics

---

## Think of citrus as lego blocks

![](../../citrus/figs/citrus_family_tree_1.jpg)
<p style="font-size: 10px; text-align: right; color: Grey;"> Credits: <a href="https://doi.org/10.1038/nature25447">Wu <em>et al.</em> (2018)</a></p>

---

## X-rays &rarr; Image Processing &rarr; Oil glands

<div class="row">
  <div class="column" style="max-width:37%; color: Navy; font-size: 15px;">
    <img style="padding: 2px 0 2px 0;" src="../../citrus/crc_pics/crc_diversity.jpg">
    <p style="text-align: center;">UCR Collaboration</p>
  </div>
  <div class="column" style="max-width:37%; color: Navy; font-size: 15px;">
    <img style="padding: 2px 0 2px 0;" src="../../citrus/crc_pics/citrus_xrayct_scanning.jpeg">
    <p style="text-align: center;">3D X-Ray CT scan</p>
  </div>
  <div class="column" style="max-width:25%; color: Navy; font-size: 15px;">
    <img src="../../citrus/figs/lemon_development.jpg">
    <p style="text-align: center;">Fruit development</p>
  </div>
</div>

<div class="row" style="color: black; font-size: 20px; font-family: 'Yanone Kaffeesatz'; margin: 0 auto;">
  <div class="column" style="max-width:20%;">
    <img src="../../citrus/figs/SR01_L01_black_endocarp.gif">
    <p style="text-align: center;"> Endocarp </p>
  </div>
  <div class="column" style="max-width:20%;">
    <img src="../../citrus/figs/SR01_L01_black_rind.gif">
    <p style="text-align: center; padding:5px 0;"> Rind </p>
  </div>
  <div class="column" style="max-width:20%;">
    <img src="../../citrus/figs/SR01_L01_black_exocarp.gif">
    <p style="text-align: center;"> Exocarp </p>
  </div>
  <div class="column" style="max-width:20%;">
    <img src="../../citrus/figs/SR01_L01_black_oil_glands.gif">
    <p style="text-align: center;"> Oil glands</p>
  </div>
  <div class="column" style="max-width:20%;padding: 10px 0 0 20px;">
    <p>
      <li>53 different citrus species</li><br>
      <li>All fundamental lego blocks and several relatives and hybrids of interest</li><br>
      <li>166 individual fruits</li>
    </p>
  </div>
</div>

---

background-image: url("../../citrus/figs/lambert_equal_area_N.gif")
background-size: 150px
background-position: 98% 1%

## Citrus modeling: Sour and sweet orange

---

# Citrus projections

![](../../citrus/figs/citrus_comparison_panel_alt.jpg)

---

background-image: url("../../citrus/ellipsoids/GarciaPortugues_etal_2020a.png")
background-size: 200px
background-position: 99% 1%

# Uniform and rotationally symmetric spherical distributions

![](../../citrus/figs/rotasym_comparison_panel_alt.jpg)

- A battery of tests reveal that citrus oil glands are neither uniformly nor rotationally symmetrically distributed.

---

background-image: url("../../citrus/ellipsoids/GarciaPortugues_2013.png")
background-size: 150px
background-position: 95% 3%

# Spherical Kernel Density Estimators

![](../../citrus/figs/WR19_CRC3842_18B-18-5_L00_emi_kde_N.jpg)

- Oil glands of a papeda
- Red arrows indicate the most significant gradient values for the density function
- Concentration parameter `$k$` is chosen to be optimal

---

background-image: url("../../citrus/figs/ppp3.png")
background-size: 225px
background-position: 95% 3%

# Summary

]

.right-column[
- It is possible to **compare** ~~apples~~ limes to oranges, despite diversity in shapes and sizes.

- We can define the non-parametrical **distribution** of oil glands for most of the citrus.

- **First** time citrus shape has been examined using X-ray CT scans.

- AFAIK, this is also the **first** time directional statistics have been **applied** to plant biology.
]

---

# 3. All about cracks, kernels, and domestication

## In a nutshell

---

# The wal(nu)tzing nutcracker!

<div class="row" style="font-family: 'Yanone Kaffeesatz'; margin: 0 auto; font-size:22px">
  <div class="column" style="max-width:25%;">
    <img src="../../walnuts/figs/IMGA04011.jpg">
    <p style="text-align: center;">148 accessions</p>
  </div>
  <div class="column" style="max-width:42%;">
    <img src="../../barley/figs/x3000_setup.jpg">
    <p style="text-align: center;">1301 walnuts scanned</p>
  </div>
  <div class="column" style="max-width:33%;">
    <img src="../../walnuts/figs/pat_walnut_crack_detail4.jpg">
    <p style="text-align: center;">Qualitative data for crackability</p>
  </div>
</div>

<div class="row" style="font-size: 22px; font-family: 'Yanone Kaffeesatz'; margin: 0 auto;">
  <div class="column" style="max-width:20%;">
    <img src="../../walnuts/figs/2014SBa_R5_T81_shell_1.gif">
    <p style="text-align: center; margin: 0.5ex;">Shell</p>
  </div>
  <div class="column" style="max-width:20%;">
    <img src="../../walnuts/figs/2014SBa_R1_T3_001_air.gif">
    <p style="text-align: center;margin: 0.5ex; ">Air</p>
  </div>
  <div class="column" style="max-width:20%;">
    <img src="../../walnuts/figs/2014SBa_R1_T3_001_vein.gif">
    <p style="text-align: center;margin: 0.5ex; ">Packing tissue</p>
  </div>
  <div class="column" style="max-width:20%;">
    <img src="../../walnuts/figs/2014SBa_R5_T81_meat_2.gif">
    <p style="text-align: center;margin: 0.5ex;">Kernel</p>
  </div>
  <div class="column" style="max-width:20%; padding: 0 0 0 5px">
    <p style="margin:5px 0 0 0; text-align:left">
      &#9656;&ensp;Individuals separated manually<br>
      &#9656;&ensp;Tissues separated with watershed segmentation<br>
      &#9656;&ensp;38 traditional shape and size descriptors
    </p>
  </div>
</div>

---

# The power of allometry: `$\;y = e^bV_N^m$`

For most living organisms, different tissues grow at different rates with respect to each other.

Growth does **not** scale linearly but following a power law.

<div class="row" style="color: black; font-size: 20px; font-family: 'Yanone Kaffeesatz'; margin: 0 auto;">
  <div class="column" style="max-width:33%;">
    <img src="../../walnuts/figs/nut_convex_volume_vs_nut_volume.png">
    <p style="padding: 0 2ex 0 0;">Walnut changes dramatically after its diameter is larger than 1.6cm</p>
  </div>
  <div class="column" style="max-width:33%;">
    <img src="../../walnuts/figs/air_volume_vs_nut_volume.png">
    <p style="margin: 3px 0 0 0; padding: 0 2ex 0 0;">If nut volume increases by 2x, then air volume increases by 2.3x</p>
    <p style="padding: 0 2ex 0 0;">Walnut diameter is below 16cm</p>
  </div>
  <div class="column" style="max-width:33%;">
    <img src="../../walnuts/figs/kernel_volume_vs_nut_volume.png">
    <p style="margin: 1.1ex 0 0 0; padding: 0 2ex 0 0;">If nut volume increases by 2x, then kernel volume only increases by 1.8x</p>
  </div>
</div>

There are biophysical constraints at play in walnut development

---

## Correlation with traits of interest

![](../../walnuts/figs/combination_hbar_correlation.svg)

- Less air filling ratio
- Smaller volume
- Smoother shells
- Kernel overall shape is more convex 
- But it also has numerous deep but thin grooves.
]

- Less total shell volume and shell ratio
- More air filling ratio
- Smoother shells
]

---

<h3 style="line-height:0">Descriptors that explain the most crackability variance</h3>

---

## Can you spot the Earliest Himalayan accession?

This one accession is the most heterozygous wild type of the bunch

---

## The Earliest Himalayan accession breaks the pattern

- The kernel of Earliest has deeper, wider cavities
- Does it refer to the cavity located at the proximal end?

---

background-image: url("https://toasterovenlove.com/wp-content/uploads/Stirred-nuts-on-pan.jpg")
background-size: 180px
background-position: 98% 2%

# Summary

]

- There are serious **biophysical** constraints that govern the kernel filling ratio.

- Larger walnuts tend to have **less** kernel and **more** air relative to their size.

- Walnuts with thinner shells also have **more** air.

- **Less** packing tissue in general corresponds to better **crackability**.

- The shape of **domestication** is quite **nuanced**: it is a hard nut to crack.

- AFAIK, this is the first time that **allometry** has been studied for walnut fruit.

- AFAIK, first time packing tissue volume and **convexity** indices have been measured.
]

---

# 4. Future directions

## Barley scratching the surface

---

# Grains, oranges, and nuts oh my!

]

.right-column[
- Identify specific **molecular markers** corresponding to topological traits of **barley seeds**.
- Develop a high-throughput **seed phenotyping** pipeline for seed morphology.

- Compute a pairwise distance matrix for citrus oil gland **distributions**.
- Use **persistent homology** as an alternative to quantify the distribution of such oil glands.

- Measure the size and volume of the central **cavity** of the walnut kernel.
- Use the ECT or a similar approach to quantify **nuances** present in the kernel.
]

---

background-image: url("https://gradschool.missouri.edu/wp-content/uploads/2019/02/MU_UnitSig_GraduateSchool_rgb_std_horiz.png")
background-size: 330px
background-position: 98% 2%

## Future research at Mizzou

The shape of dodder movement

]

![](https://pub.mdpi-res.com/remotesensing/remotesensing-11-02075/article_deploy/html/images/remotesensing-11-02075-ag.png?1569418523)

- David Mendoza Cozatl
- Robert Sharpe
- So-Yon Park
- Andrew Scaboo

]

---

background-image: url("../../tutorials/figs/plantspython22_01.png")
background-size: 225px
background-position: 99% 1%

# Plants & Python _a la_ Mizzou

.pull-left[
![](https://plantsandpython.github.io/PlantsAndPython/_static/plants_python_logo.jpg)
![](../../tutorials/figs/class_foto1.png)
]

- Offered in hybrid format between MSU and UNAM

- **HRT 841**: Foundation in Computational and Plant Science

- **UNAM Temas Selectos**: Bioinformática y Minería de Datos con Python

- Freely available material in jupyter notebook format.

- Material in English and Spanish.
]

---

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## Thank you!

<div class="row" style="margin-top: -25px;">
  <div class="column" style="max-width:17.5%; font-size: 13px;">
    <img style="padding: 0 0 0 0;" src="https://i1.rgstatic.net/ii/profile.image/607374528233472-1521820780707_Q128/Elizabeth-Munch.jpg">
    <p style="text-align: center; color: White">Liz Munch<br>(MSU)</p>
    <img style="padding: 0 0 0 0;" src="https://alga.win.tue.nl/images/staff/tim.jpg">
    <p style="text-align: center; color: White">Tim Ophelders<br>(Utrecht)</p>
    <img style="padding: 0 0 0 0;" src="https://publons.com/media/thumbs/academic/photos/252a7116-ee14-4a5e-b44c-7c62ac11e217.png.200x200_q95_crop_detail_upscale.png">
    <p style="text-align: center; color: White">Jacob Landis<br>(Cornell)</p>
  </div>
  <div class="column" style="max-width:17.5%; font-size: 13px;">
    <img style="padding: 0 0 0 0;" src="https://www.canr.msu.edu/contentAsset/image/9ae9777d-157c-46e6-9f12-d062ad35671e/fileAsset/filter/Jpeg,Resize,Crop/jpeg_q/80/resize_w/400/crop_x/0/crop_y/45/crop_w/400/crop_h/400">
    <p style="text-align: center; color: White">Dan Chitwood<br>(MSU)</p>
    <img style="padding: 0 0 0 0;" src="https://i1.rgstatic.net/ii/profile.image/926632407748609-1597937790454_Q128/Michelle-Quigley.jpg">
    <p style="text-align: center; color: White">Michelle Quigley<br>(MSU)</p>
    <img style="padding: 0 0 0 0;" src="https://www.plantsciences.ucdavis.edu/sites/g/files/dgvnsk1736/files/styles/sf_profile/public/images/person/pjbrown_1.jpg?h=9707347b&itok=gDYXMHJj">
    <p style="text-align: center; color: White">Pat Brown<br>(UC Davis)</p>
  </div>
  <div class="column" style="max-width:13%; font-size: 13px;">
  <img style="padding: 0 0 0 0;" src="https://plantbiology.ucr.edu/sites/g/files/rcwecm1001/files/styles/scale_225/public/Koenig.jpg?itok=P92Ow61p">
  <p style="text-align: center; color: White">Dan Koenig<br>(UC Riverside)</p>
  <img style="padding: 0 0 0 0;" src="https://iigb.ucr.edu/sites/g/files/rcwecm5716/files/styles/scale_225/public/Seymour.jpg?itok=pnUK_orh">
  <p style="text-align: center; color: White">Danelle Seymour<br>(UC Riverside)</p>
  </div>
  <div class="column" style="width:10%; font-size: 24px;">
  </div>
  <div class="column" style="max-width:40%; font-size: 24px; line-height:1.25">
  <p style="text-align: center; color: White"><strong>Email</strong></p>
  <p style="text-align: center; color: Yellow">amezqui3@msu.edu</p>
  <p style="text-align: center; color: White"><strong>Slides</strong></p>
  <p style="text-align: center; color: Yellow">bit.ly/mu_22</p>
  <p style="text-align: center; color: White"><strong>References</strong></p>
  <p style="text-align: center; color: White; font-size: 12px; text-align:left">
    <strong>E.A.</strong> <em>et al.</em> (2022) The shape of aroma: measuring and modeling citrus oil gland distribution. <a href="https://doi.org/10.1002/ppp3.10333" target="_blank">DOI: 10.1002/ppp3.10333</a>
  </p>
  <p style="text-align: center; color: White; font-size: 12px; text-align:left">
    <strong>E.A.</strong> <em>et al.</em> (2021) Measuring hidden phenotype: Quantifying the shape of barley seeds using the Euler Characteristic Transform. <a href="https://doi.org/10.1093/insilicoplants/diab033" target="_blank">DOI: 10.1093/insilicoplants/diab033</a>
  </p>
  <p style="text-align: center; color: White; font-size: 12px; text-align:left">
    VanBuren, R. <em>et al.</em> (2022) Plants & Python: A series of lessons in coding, plant biology, computation, and bioinformatics. <a href="https://doi.org/10.1093/plcell/koac187" target="_blank">DOI: 10.1093/plcell/koac187</a>
  </p>
    <p style="text-align: center; color: White; font-size:15px; line-height:1.1">Slides made in <a href="https://bookdown.org/yihui/rmarkdown/xaringan.html" target="_blank">xaringan</a>.</p>
  </div>
</div>

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# Questions?

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