adaptation_specialization_material/code/comparative_analysis.py

from cProfile import label
import numpy as np
import pandas as pd
from scipy.stats import entropy
import ot
from sklearn.linear_model import LinearRegression

from matplotlib import pyplot as plt
import matplotlib
matplotlib.use("pgf")
matplotlib.rcParams.update(
    {
        "pgf.texsystem": "xelatex",
        "font.family": "serif",
        "font.serif": "Times New Roman",
        "text.usetex": True,
        "pgf.rcfonts": False,
    }
)
plt.rcParams["text.latex.preamble"].join([
        r"\usepackage{amsmath}",              
        r"\setmainfont{amssymb}",
])

from textwrap import wrap

import argparse
from os.path import join as opj, exists
import pickle

from cmdstanpy import CmdStanModel

parser = argparse.ArgumentParser()
parser.add_argument("--input")
parser.add_argument("--suffix", default=None)
parser.add_argument("--metric", default="change", choices=["change", "disruption", "diversification", "diversification_stirling", "entered", "exited"])
parser.add_argument("--diversity", default="entropy", choices=["entropy", "stirling"])
parser.add_argument("--power", choices=["magnitude", "brokerage"], default="magnitude")
parser.add_argument("--model", default="", choices=["", "bare"])
parser.add_argument("--compact", action="store_true", default=False)
args = parser.parse_args()

def institution_stability():
    if exists(opj(args.input, "institutional_stability.csv")):
        return pd.read_csv(opj(args.input, "institutional_stability.csv"), index_col="bai")
    
    affiliations = pd.read_parquet("../semantics/inspire-harvest/database/affiliations.parquet")
    affiliations["article_id"] = affiliations.article_id.astype(int)

    articles = pd.read_parquet("../semantics/inspire-harvest/database/articles.parquet")[["article_id", "date_created"]]

    articles = articles[articles["date_created"].str.len() >= 4]
    articles["year"] = articles["date_created"].str[:4].astype(int) - 2000

    articles["article_id"] = articles.article_id.astype(int)
    articles = articles[articles["year"] <= 2019 - 2000]
    articles = articles[articles["year"] >= 0]

    affiliations["article_id"] = affiliations.article_id.astype(int)
    affiliations = affiliations.merge(articles, how="inner", left_on="article_id", right_on="article_id")
    affiliations = affiliations[affiliations["bai"].isin(df["bai"])]

    authors_last = affiliations.groupby("bai").agg(last_article=("year", "max"))

    hosts = affiliations.sort_values(["bai", "institution_id", "year"]).groupby(["bai", "institution_id"]).agg(
        first=("year", "min"),
        last=("year", "max")
    )
    hosts["duration"] = hosts["last"]-hosts["first"]
    stability = hosts.groupby("bai").agg(stability=("duration", "max"), last=("last", "max"), first=("first", "min"))
    stability = stability.merge(authors_last, left_index=True, right_index=True)
    stability["stable"] = stability["stability"]>=(stability["last"]-stability["first"]-1)
    stability.to_csv(opj(args.input, "institutional_stability.csv"))
    return stability

suffix = f"_{args.suffix}" if args.suffix is not None else ""

topics = pd.read_csv(opj(args.input, "topics.csv"))
junk = topics["label"].str.contains("Junk")
topics = topics[~junk]["label"].tolist()

fig, ax = plt.subplots()

n_topics = len(pd.read_csv(opj(args.input, "topics.csv")))
df = pd.read_csv(opj(args.input, "aggregate.csv"))

resources = pd.read_parquet(opj(args.input, "pooled_resources.parquet"))
df = df.merge(resources, left_on="bai", right_on="bai")

NR = np.stack(df[[f"start_{k+1}" for k in range(n_topics)]].values).astype(int)
NC = np.stack(df[[f"end_{k+1}" for k in range(n_topics)]].values).astype(int)
expertise = np.stack(df[[f"expertise_{k+1}" for k in range(n_topics)]].values)
S = np.stack(df["pooled_resources"])

brokerage = pd.read_csv("output/authors_brokerage.csv")
df = df.merge(brokerage, left_on="bai", right_on="bai")

NR = NR[:,~junk]
NC = NC[:,~junk]
expertise = expertise[:,~junk]
S = S[:,~junk]

x = NR/NR.sum(axis=1)[:,np.newaxis]
y = NC/NC.sum(axis=1)[:,np.newaxis]
S_distrib = S/S.sum(axis=1)[:,np.newaxis]


# R = np.array([
#     [((expertise[:,i]>expertise[:,i].mean())&(expertise[:,j]>expertise[:,j].mean())).mean()/((expertise[:,i]>expertise[:,i].mean())|(expertise[:,j]>expertise[:,j].mean())).mean() for j in range(len(topics))]
#     for i in range(len(topics))
# ])

R = np.array([
    [((expertise[:,i]>expertise[:,i].mean())&(expertise[:,j]>expertise[:,j].mean())).mean()/(expertise[:,i]>expertise[:,i].mean()).mean() for j in range(len(topics))]
    for i in range(len(topics))
])

change = np.abs(y-x).sum(axis=1)/2
diversification = (np.exp(entropy(y, axis=1))-np.exp(entropy(x, axis=1)))/x.shape[1]
x_matrix = np.einsum("ki,kj->kij", x, x)
y_matrix = np.einsum("ki,kj->kij", y, y)
x_stirling = 1-np.einsum("ij,kij->k", R, x_matrix)
y_stirling = 1-np.einsum("ij,kij->k", R, y_matrix)

disruption = np.zeros(len(change))
for a in range(len(change)):
    disruption[a] = ot.emd2(x[a,:].copy(order='C'), y[a,:].copy(order='C'), 1-R, processes=4)

alpha = 1
exited = ((x>alpha*x.mean(axis=0))&(y<alpha*y.mean(axis=0))).sum(axis=1)
entered = ((x<alpha*x.mean(axis=0))&(y>alpha*y.mean(axis=0))).sum(axis=1)

fig, ax = plt.subplots(figsize=[6.4, 3.2])
ax.hist(change, bins=np.linspace(0,1,50), histtype="step")
ax.set_xlabel(f"Change score $c_a = \\frac{{1}}{{2}}\\sum_k |y_{{ak}}-x_{{ak}}|$")
ax.set_ylabel("\\# of scientists")
fig.savefig(opj(args.input, "change_score.eps"), bbox_inches="tight")

print("change 50%% interval: ", np.quantile(change,q=0.25), np.quantile(change,q=1-0.25))

fig, ax = plt.subplots(figsize=[6.4, 3.2])
ax.hist(diversification, bins=np.linspace(-0.5,0.5,50), histtype="step")
ax.set_xlabel(f"Diversification score $\\Delta_a$")
ax.set_ylabel("\\# of scientists")
fig.savefig(opj(args.input, "diversification_score.eps"), bbox_inches="tight")

fig, ax = plt.subplots()
ax.hist(disruption, bins=np.linspace(0,1,50), histtype="step")
ax.set_xlabel(f"Disruption score $d_a$")
ax.set_ylabel("\\# of scientists")
fig.savefig(opj(args.input, "disruption_score.eps"), bbox_inches="tight")

df["change_score"] = change
df["disruption_score"] = disruption
df["diversification_score"] = diversification
df["diversification_stirling_score"] = y_stirling-x_stirling
df["entered_score"] = (entered>0).astype(int)
df["exited_score"] = (exited>0).astype(int)

df["origin"] = np.argmax(x, axis=1)
df["target"] = np.argmax(y, axis=1)

df["origin_value"] = x.max(axis=1)
df["target_value"] = y.max(axis=1)

df["origin_final_value"] = np.array(y[a,df.loc[a, "origin"]] for a in range(x.shape[0]))
df["target_initial_value"] = np.array(x[a,df.loc[a, "target"]] for a in range(x.shape[0]))

df["origin_label"] = df["origin"].apply(lambda k: topics[k])
df["target_label"] = df["target"].apply(lambda k: topics[k])

df["origin_label"] = df.apply(lambda row: row["origin_label"] + (f" ({row['origin_value']:.2f})" if row["origin"]==row["target"] else f" ({row['origin_value']:.2f}$\\to${row['origin_final_value']:.2f})"), axis=1)
df["target_label"] = df.apply(lambda row: row["target_label"] + (f" ({row['target_value']:.2f})" if row["origin"]==row["target"] else f" ({row['target_initial_value']:.2f}$\\to${row['target_value']:.2f})"), axis=1)

df["social_entropy"] = np.exp(entropy(S,axis=1))
df["intellectual_entropy"] = np.exp(entropy(expertise,axis=1))

expertise_matrix = np.einsum("ki,kj->kij", expertise, expertise)
social_expertise_matrix = np.einsum("ki,kj->kij", S_distrib, S_distrib)
df["intellectual_stirling"] = 1-np.einsum("ij,kij->k", R, expertise_matrix)
df["social_stirling"] = 1-np.einsum("ij,kij->k", R, social_expertise_matrix)


stability = institution_stability()
df = df.merge(stability, left_on="bai", right_index=True)

age = pd.read_csv(opj(args.input, "outcomes.csv"))[["bai", "age"]].drop_duplicates()
df = df.merge(age, left_on="bai", right_on="bai")

df["primary_research_area"] = x.argmax(axis=1)

df["social_diversity"] = df[f"social_{args.diversity}"].fillna(0)
df["intellectual_diversity"] = df[f"intellectual_{args.diversity}"].fillna(0)

df["res_social_diversity"] = df["social_diversity"]-LinearRegression().fit(df[["intellectual_diversity"]], df["social_diversity"]).predict(df[["intellectual_diversity"]])

data = {
    "N": len(df),
    "K": x.shape[1],
    "m": df[f"{args.metric}_score"],
    # "soc_cap": np.log(1+S.sum(axis=1)),
    "soc_cap": S.sum(axis=1) if args.power == "magnitude" else df["brokerage"].values,
    "soc_div": df["social_diversity"],
    "int_div": df["intellectual_diversity"],
    "res_soc_div": df["res_social_diversity"],
    "x": x,
    "initial_div": np.exp(entropy(x, axis=1)),
    "primary_research_area": df["primary_research_area"],
    "stable": df["stable"].astype(float).values,
    "age": df["age"].values
}

fig, ax = plt.subplots(figsize=[6.4, 3.2])
ax.hist(change[df["primary_research_area"] != 4], bins=np.linspace(0,1,25), histtype="step", label=f"Others ($\\mu={change[df['primary_research_area'] != 4].mean():.2f}$)", density=True)
ax.hist(change[df["primary_research_area"] == 4], bins=np.linspace(0,1,25), histtype="step", label=f"Collider physics ($\\mu={change[df['primary_research_area'] == 4].mean():.2f}$)", density=True)
ax.set_xlabel(f"Change score $c_a = \\frac{{1}}{{2}}\\sum_k |y_{{ak}}-x_{{ak}}|$")
ax.set_ylabel("\\# of scientists")
ax.legend(loc='upper right', bbox_to_anchor=(1, 1.2))
fig.savefig(opj(args.input, "change_score_collider_physics.eps"), bbox_inches="tight")

fig, ax = plt.subplots(figsize=[6.4, 3.2])
ax.hist(disruption[df["primary_research_area"] != 4], bins=np.linspace(0,1,25), histtype="step", label=f"Others ($\\mu={disruption[df['primary_research_area'] != 4].mean():.2f}$)", density=True)
ax.hist(disruption[df["primary_research_area"] == 4], bins=np.linspace(0,1,25), histtype="step", label=f"Collider physics ($\\mu={disruption[df['primary_research_area'] == 4].mean():.2f}$)", density=True)
ax.set_xlabel(f"Disruption score $d_a$")
ax.set_ylabel("\\# of scientists")
ax.legend(loc='upper right', bbox_to_anchor=(1, 1.2))
fig.savefig(opj(args.input, "disruption_score_collider_physics.eps"), bbox_inches="tight")

if not exists(opj(args.input, f"samples_{args.metric}_{args.diversity}_{args.power}.npz")):
    model = CmdStanModel(
        stan_file=f"code/{args.metric}.stan" if args.model=="" else f"code/{args.metric}_{args.model}_{args.power}.stan",
    )

    fit = model.sample(
        data=data,
        chains=4,
        iter_sampling=10000,
        iter_warmup=1000,
        show_console=True
    )

    vars = fit.stan_variables()
    samples = {}
    for (k, v) in vars.items():
        samples[k] = v

    np.savez_compressed(opj(args.input, f"samples_{args.metric}_{args.diversity}_{args.power}.npz"), **samples)


samples = np.load(opj(args.input, f"samples_{args.metric}_{args.diversity}_{args.power}.npz"))

labels = [
    "Intellectual capital (diversity)",
    "Social capital (diversity)",
    "Social capital (power)",
    "Stable affiliation",
]
labels = [f"\\textbf{{{label}}}" for label in labels]

labels += topics

names = [
    "beta_int_div", "beta_soc_div", "beta_soc_cap", "beta_stable"
]

if args.metric not in ["entered", "exited"]:
    mu = np.array([samples[name].mean() for name in names] + [(samples["beta_x"][:,i]*samples["tau"]).mean() for i in range(x.shape[1])])
    low = np.array([np.quantile(samples[name], q=0.05/2) for name in names] + [np.quantile(samples["beta_x"][:,i]*samples["tau"], q=0.05/2) for i in range(x.shape[1])])
    up = np.array([np.quantile(samples[name], q=1-0.05/2) for name in names] + [np.quantile(samples["beta_x"][:,i]*samples["tau"], q=1-0.05/2) for i in range(x.shape[1])])
    sig = up*low>0

    prob = np.array([(samples[name]*np.sign(samples[name].mean())<0).mean() for name in names] + [((samples["beta_x"][:,i]*np.sign(samples["beta_x"][:,i].mean()))<0).mean() for i in range(x.shape[1])])

    keep = sig | (np.arange(len(sig))<len(names))
    mu = mu[keep]
    low = low[keep]
    up = up[keep]
    prob = prob[keep]

    sign = ["<" if _mu>0 else ">" for i, _mu in enumerate(mu)]
    labels = [label for i, label in enumerate(labels) if keep[i]]
    n_vars = len(labels)


    # effect of capital and controls
    fig, ax = plt.subplots(figsize=[6.4, 0.4*(1+n_vars)])

    ax.scatter(mu, np.arange(len(labels))[::-1])
    ax.errorbar(mu, np.arange(len(labels))[::-1], xerr=(mu-low,up-mu), ls="none", capsize=4, elinewidth=1)
    ax.set_yticks(np.arange(len(labels))[::-1], labels)
    for i, p in enumerate(prob):
        if p>1e-4 and np.abs(p-0.5)>0.4:
            ax.text(
                -0.02 if mu[i]>0 else 0.02,
                np.arange(len(labels))[::-1][i],
                f"\\scriptsize $\\mu(\\beta)={mu[i]:.2g}, P(\\beta{sign[i]}0)={p:.2g}$",
                ha="right" if mu[i]>0 else "left",
                va="center"
            )
        elif p<0.05/2 or p>1-0.05/2:
            ax.text(
                -0.02 if mu[i]>0 else 0.02,
                np.arange(len(labels))[::-1][i],
                f"\\scriptsize $\\mu(\\beta)={mu[i]:.2g}$",
                ha="right" if mu[i]>0 else "left",
                va="center"
            )

    ax.set_xlabel(f"Effect on {args.metric}")
    ax.axvline(0, color="black")
    fig.savefig(opj(args.input, f"{args.metric}_score_effects_{args.diversity}_{args.power}.eps"), bbox_inches="tight")

    # average change score per research area
    ratio = args.metric != "diversification"
    labels = topics
    if ratio:
        mu = np.array([(samples["mu_x"][:,i]/samples["mu_pop"]).mean() for i in range(x.shape[1])])
        low = np.array([np.quantile(samples["mu_x"][:,i]/samples["mu_pop"], q=0.05/2) for i in range(x.shape[1])])
        up = np.array([np.quantile(samples["mu_x"][:,i]/samples["mu_pop"], q=1-0.05/2) for i in range(x.shape[1])])
        sig = (up-1)*(low-1)>0
    else:
        mu = np.array([(samples["mu_x"][:,i]-samples["mu_pop"]).mean() for i in range(x.shape[1])])
        low = np.array([np.quantile(samples["mu_x"][:,i]-samples["mu_pop"], q=0.05/2) for i in range(x.shape[1])])
        up = np.array([np.quantile(samples["mu_x"][:,i]-samples["mu_pop"], q=1-0.05/2) for i in range(x.shape[1])])
        sig = (up)*(low)>0

    keep = sig
    mu = mu[keep]
    low = low[keep]
    up = up[keep]
    labels = [label for i, label in enumerate(labels) if keep[i]]

    fig, ax = plt.subplots(figsize=[6.4, 3.2])
    ax.scatter(mu, np.arange(len(labels))[::-1])
    ax.errorbar(mu, np.arange(len(labels))[::-1], xerr=(mu-low,up-mu), ls="none", capsize=4, elinewidth=1)
    ax.set_yticks(np.arange(len(labels))[::-1], labels)

    fig, ax = plt.subplots(figsize=[6.4, 3.2])

    df["m_ratio"] = df[f"{args.metric}_score"]/df[f"{args.metric}_score"].mean()
    research_areas = df.groupby("primary_research_area").agg(
        mu=("m_ratio", "mean"),
        low=("m_ratio", lambda x: np.quantile(x, q=0.05/2)),
        up=("m_ratio", lambda x: np.quantile(x, q=1-0.05/2)),
        label=("origin_label", lambda x: x.iloc[0])
    ).reset_index()

    ax.scatter(research_areas["mu"], research_areas.index)
    ax.errorbar(research_areas["mu"], research_areas.index, xerr=(research_areas["mu"]-research_areas["low"],research_areas["up"]-research_areas["low"]), ls="none", capsize=4, elinewidth=1)
    ax.set_yticks(research_areas.index, research_areas["label"])

    ax.set_xlabel(f"Ratio to average {args.metric} score" if ratio else f"Difference with average {args.metric} score")
    ax.axvline(1 if ratio else 0, color="black")
    fig.savefig(opj(args.input, f"{args.metric}_research_area.eps"), bbox_inches="tight")
else:

    labels = [
        "Intellectual capital (diversity)",
        "Social capital (diversity)",
        "Social capital (power)",
        "Stable affiliation",
    ]

    if not args.compact:
        labels = [f"\\textbf{{{label}}}" for label in labels]

    labels += topics

    samples = [
        np.load(opj(args.input, f"samples_entered_{args.diversity}_{args.power}.npz")),
        np.load(opj(args.input, f"samples_exited_{args.diversity}_{args.power}.npz"))
    ]

    mu = [None, None]
    low = [None, None]
    up = [None, None]
    sig = [None, None]
    prob = [None, None]
    for i in range(2):
        mu[i] = np.array([samples[i][name].mean() for name in names] + [(samples[i]["beta_x"][:,j]*samples[i]["tau"]).mean() for j in range(x.shape[1])])
        low[i] = np.array([np.quantile(samples[i][name], q=0.05/2) for name in names] + [np.quantile(samples[i]["beta_x"][:,j]*samples[i]["tau"], q=0.05/2) for j in range(x.shape[1])])
        up[i] = np.array([np.quantile(samples[i][name], q=1-0.05/2) for name in names] + [np.quantile(samples[i]["beta_x"][:,j]*samples[i]["tau"], q=1-0.05/2) for j in range(x.shape[1])])
        sig[i] = up[i]*low[i]>0
        prob[i] = np.array([(samples[i][name]*np.sign(samples[i][name].mean())<0).mean() for name in names] + [((samples[i]["beta_x"][:,j]*np.sign(samples[i]["beta_x"][:,j].mean()))<0).mean() for j in range(x.shape[1])])

    if args.compact:
        keep = (np.arange(len(sig[0]))<len(names))
    else:
        keep = sig[0] | sig[1] | (np.arange(len(sig[0]))<len(names))

    for i in range(2):
        mu[i] = mu[i][keep]
        low[i] = low[i][keep]
        up[i] = up[i][keep]
        prob[i] = prob[i][keep]

    sign = [["<" if _mu>0 else ">" for j, _mu in enumerate(mu[i])] for i in range(2)]
    labels = [label for i, label in enumerate(labels) if keep[i]]
    n_vars = len(labels)

    if args.compact:
        labels = [
            '\n'.join(map(lambda x: f"\\textbf{{{x}}}", wrap(label, width=15))) if i < 4
            else
            '\n'.join(wrap(label, width=15))
            for i, label in enumerate(labels)
        ]
        print(labels)


    # effect of capital and controls
    fig, ax = plt.subplots(figsize=[4.8 if args.compact else 6.4, 0.52*(1+n_vars)])
    colors = ['#377eb8', '#ff7f00']
    legend = ["entered new research area", "exited research area"]

    if args.compact:
        ax.set_xlim(-0.9, 1.25)

    for j in range(2):
        dy = -0.125 if j else +0.125
        ax.scatter(mu[j], np.arange(len(labels))[::-1]+dy, color=colors[j])
        ax.errorbar(mu[j], np.arange(len(labels))[::-1]+dy, xerr=(mu[j]-low[j],up[j]-mu[j]), ls="none", capsize=4, elinewidth=1, color=colors[j], label=legend[j])
        for i, p in enumerate(prob[j]):
            significant = p<0.05/2
            if p>1e-4 and np.abs(p-0.5)>0.4 and significant:
                ax.text(
                    -0.02 if mu[j][i]>0 else 0.02,
                    np.arange(len(labels))[::-1][i]+dy,
                    f"\\scriptsize $\\mu(\\beta)={mu[j][i]:.2g},P(\\beta{sign[j][i]}0)={p:.2g}$",
                    ha="right" if mu[j][i]>0 else "left",
                    va="center"
                )
            elif p>1e-4 and np.abs(p-0.5)>0.4 and (not significant):
                ax.text(
                    -0.02 if mu[j][i]>0 else 0.02,
                    np.arange(len(labels))[::-1][i]+dy,
                    f"\\scriptsize $P(\\beta{sign[j][i]}0)={p:.2g}$",
                    ha="right" if mu[j][i]>0 else "left",
                    va="center"
                )
            elif significant:
                ax.text(
                    -0.02 if mu[j][i]>0 else 0.02,
                    np.arange(len(labels))[::-1][i]+dy,
                    f"\\scriptsize $\\mu(\\beta)={mu[j][i]:.2g}$",
                    ha="right" if mu[j][i]>0 else "left",
                    va="center"
                )

    ax.set_yticks(np.arange(len(labels))[::-1], labels)
    ax.set_xlabel(f"Effect size (log odds ratio)")
    ax.axvline(0, color="black")
    if args.compact:
        ax.legend(loc='upper right', bbox_to_anchor=(1, 1.3))
    else:
        ax.legend(loc='upper right', bbox_to_anchor=(1, 1.2))
    fig.savefig(opj(args.input, f"{args.metric}_score_effects_{args.diversity}_{args.power}{'_compact' if args.compact else ''}.eps"), bbox_inches="tight")    

table = df[["bai", "stable", f"{args.metric}_score", "intellectual_entropy", "social_entropy", "origin_label", "target_label"]].sort_values(f"{args.metric}_score", ascending=False)
table.to_csv(opj(args.input, f"{args.metric}_scores.csv"))

table["bai"] = table["bai"].str.replace(".1", "")
table["bai"] = table["bai"].str.replace(r"^([A-Z])\.", r"\1.~")
table["bai"] = table["bai"].str.replace(r"\.\~([A-Z])\.", r".~\1.~")
table["bai"] = table["bai"].str.replace(r"([a-zA-Z]{2,})\.", r"\1 ")
table["bai"] = table.apply(lambda r: r["bai"] if not r["stable"] else f"{r['bai']} ($\\ast$)", axis=1)

table["target_label"] += "EOL"

latex = table.head(20).to_latex(
    columns=["bai", f"{args.metric}_score", "intellectual_entropy", "social_entropy", "origin_label", "target_label"],
    header=["Physicist", "$c_a$", "$D(\\bm{I_a})$", "$D(\\bm{S_a})$", "Previous main area", "Current main area"],
    index=False,    
    multirow=True,
    multicolumn=True,
    column_format='p{0.15\\textwidth}|c|c|c|b{0.25\\textwidth}|b{0.25\\textwidth}',
    escape=False,
    float_format=lambda x: f"{x:.2f}",
    caption="Physicists with the highest change scores $c_a$. $D(\\bm{I_a})$ and $D(\\bm{S_a})$ measure the diversity of intellectual and social capital. Numbers in parentheses indicate the share of attention dedicated to each research area during each time-period. Asterisks ($\\ast$) indicate physicists with a permanent position.",
    label=f"table:top_{args.metric}",
    position="H"
)

latex = latex.replace('EOL \\\\\n', '\\\\ \\hline\n')

with open(opj(args.input, f"top_{args.metric}.tex"), "w+") as fp:
    fp.write(latex)


latex = table.sort_values(f"{args.metric}_score", ascending=True).head(20).to_latex(
    columns=["bai", f"{args.metric}_score", "intellectual_entropy", "social_entropy", "origin_label", "target_label"],
    header=["Physicist", "$c_a$", "$D(\\bm{I_a})$", "$D(\\bm{S_a})$", "Previous main area", "Current main area"],
    index=False,    
    multirow=True,
    multicolumn=True,
    column_format='p{0.15\\textwidth}|c|c|c|b{0.25\\textwidth}|b{0.25\\textwidth}',
    escape=False,
    float_format=lambda x: f"{x:.2f}",
    caption="Physicists with the lowest change scores $c_a$. $D(\\bm{I_a})$ and $D(\\bm{S_a})$ measure the diversity of intellectual and social capital. Numbers in parentheses indicate the share of attention dedicated to each research area. Asterisks ($\\ast$) indicate physicists with a permanent position.",
    label=f"table:low_{args.metric}",
    position="H"
)

latex = latex.replace('EOL \\\\\n', '\\\\ \\hline\n')

with open(opj(args.input, f"low_{args.metric}.tex"), "w+") as fp:
    fp.write(latex)