prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What molecule was the focus of the study?

Read the following text and answer briefly.

Context 1: \section{Introduction}

Spectral line surveys have revealed that high-mass star-forming
regions are rich reservoirs of molecules from simple diatomic species
to complex and larger molecules (e g ,
\citealt{schilke1997b,hatchell1998b,comito2005,bisschop2007}) 
However, there have been rarely studies undertaken to investigate the
chemical evolution during massive star formation from the earliest
evolutionary stages, i e , from High-Mass Starless Cores (HMSCs) and
High-Mass Cores with embedded low- to intermediate-mass protostars
destined to become massive stars, via High-Mass Protostellar Objects
(HMPOs) to the final stars that are able to produce Ultracompact H{\sc
  ii} regions (UCH{\sc ii}s, see \citealt{beuther2006b} for a recent
description of the evolutionary sequence)  The first two evolutionary
stages are found within so-called Infrared Dark Clouds (IRDCs)   While
for low-mass stars the chemical evolution from early molecular
freeze-out to more evolved protostellar cores is well studied (e g ,
\citealt{bergin1997,dutrey1997,pavlyuchenkov2006,joergensen2007}),
it is far from clear whether similar evolutionary patterns are present
during massive star formation 

To better understand the chemical evolution of high-mass star-forming
regions we initiated a program to investigate the chemical properties
from IRDCs to UCH{\sc ii}s from an observational and theoretical
perspective  We start with single-dish line surveys toward a large
sample obtaining their basic characteristics, and then perform
detailed studies of selected sources using interferometers on smaller
scales  These observations are accompanied by theoretical modeling of
the chemical processes   Long-term goals are the chemical
characterization of the evolutionary sequence in massive star
formation, the development of chemical clocks, and the identification
of molecules as astrophysical tools to study the physical processes
during different evolutionary stages  Here, we present an initial
study of the reactive radical ethynyl (C$_2$H) combining single-dish
and interferometer observations with chemical modeling   Although
C$_2$H was previously observed in low-mass cores and Photon Dominated
Regions (e g , \citealt{millar1984,jansen1995}), so far it was not
systematically investigated in the framework of high-mass star
formation 

\section{Observations}
\label{obs}

The 21 massive star-forming regions were observed with the Atacama
Pathfinder Experiment (APEX) in the 875\,$\mu$m window in fall 2006 
We observed 1\,GHz from 338 to 339\,GHz and 1\,GHz in the image
sideband from 349 to 350\,GHz   The spectral resolution was
0 1\,km\,s$^{-1}$, but we smoothed the data to
$\sim$0 9\,km\,s$^{-1}$  The average system temperatures were around
200\,K, each source had on-source integration times between 5 and 16
min  The data were converted to main-beam temperatures with forward
and beam efficiencies of 0 97 and 0 73, respectively
\citep{belloche2006}  The average $1\sigma$ rms was 0 4\,K   The main
spectral features of interest are the C$_2$H lines around 349 4\,GHz
with upper level excitation energies $E_u/k$ of 42\,K (line blends of
C$_2$H$(4_{5,5}-3_{4,4})$ \& C$_2$H$(4_{5,4}-3_{4,3})$ at
349 338\,GHz, and C$_2$H$(4_{4,4}-3_{3,3})$ \&
C$_2$H$(4_{4,3}-3_{3,2})$ at 349 399\,GHz)  The beam size was $\sim
18''$ 

The original Submillimeter Array (SMA) C$_2$H data toward the
HMPO\,18089-1732 were first presented in \citet{beuther2005c}  There
we used the compact and extended configurations resulting in good
images for all spectral lines except of C$_2$H  For this project, we
re-worked on these data only using the compact configuration  Because
the C$_2$H emission is distributed on larger scales (see
\S\ref{results}), we were now able to derive a C$_2$H image  The
integration range was from 32 to 35\,km\,s$^{-1}$, and the achieved
$1\sigma$ rms of the C$_2$H image was 450\,mJy\,beam$^{-1}$   For more
details on these observations see \citet{beuther2005c} 

\section{Results}
\label{results}

The sources were selected to cover all evolutionary stages from IRDCs
via HMPOs to UCH{\sc ii}s  We derived our target list from the samples
of \citet{klein2005,fontani2005,hill2005,beltran2006}   Table
\ref{sample} lists the observed sources, their coordinates, distances,
luminosities and a first order classification into the evolutionary
sub-groups IRDCs, HMPOs and UCH{\sc ii}s based on the previously
available data  Although this classification is only based on a
limited set of data, here we are just interested in general
evolutionary trends  Hence, the division into the three main classes
is sufficient 

Figure \ref{spectra} presents sample spectra toward one source of each
evolutionary group  While we see several CH$_3$OH lines as well as
SO$_2$ and H$_2$CS toward some of the HMPOs and UCH{\sc ii}s but not
toward the IRDCs, the surprising result of this comparison is the
presence of the C$_2$H lines around 349 4\,GHz toward all source types
from young IRDCs via the HMPOs to evolved UCH{\sc ii}s   Table
\ref{sample} lists the peak brightness temperatures, the integrated
intensities and the FWHM line-widths of the C$_2$H line blend at
349 399\,GHz  The separation of the two lines of 1 375\,MHz already
corresponds to a line-width of 1 2\,km\,s$^{-1}$  We have three C$_2$H
non-detections (2 IRDCs and 1 HMPO), however, with no clear trend with
respect to the distances or the luminosities (the latter comparison is
only possible for the HMPOs)  While IRDCs are on average colder than
more evolved sources, and have lower brightness temperatures, the
non-detections are more probable due to the relatively low sensitivity
of the short observations (\S\ref{obs})  Hence, the data indicate
that the C$_2$H lines are detected independent of the evolutionary
stage of the sources in contrast to the situation with other
molecules   When comparing the line-widths between the different
sub-groups, one finds only a marginal difference between the IRDCs and
the HMPOs (the average $\Delta v$ of the two groups are 2 8 and
3 1\,km\,s$^{-1}$)   However, the UCH{\sc ii}s exhibit significantly
broader line-widths with an average value of 5 5\,km\,s$^{-1}$ 

Intrigued by this finding, we wanted to understand the C$_2$H spatial
structure during the different evolutionary stages   Therefore, we
went back to a dataset obtained with the Submillimeter Array toward
the hypercompact H{\sc ii} region IRAS\,18089-1732 with a much higher
spatial resolution of $\sim 1''$ \citep{beuther2005c}   Albeit this
hypercompact H{\sc ii} region belongs to the class of HMPOs, it is
already in a relatively evolved stage and has formed a hot core with a
rich molecular spectrum   \citet{beuther2005c} showed the spectral
detection of the C$_2$H lines toward this source, but they did not
present any spatially resolved images  To recover large-scale
structure, we restricted the data to those from the compact SMA
configuration (\S\ref{obs})  With this refinement, we were able to
produce a spatially resolved C$_2$H map of the line blend at
349 338\,GHz with an angular resolution of $2 9''\times 1 4''$
(corresponding to an average linear resolution of 7700\,AU at the
given distance of 3 6\,kpc)  Figure \ref{18089} presents the
integrated C$_2$H emission with a contour overlay of the 860\,$\mu$m
continuum source outlining the position of the massive protostar  In
contrast to almost all other molecular lines that peak along with the
dust continuum \citep{beuther2005c}, the C$_2$H emission surrounds the
continuum peak in a shell-like fashion 

\section{Discussion and Conclusions}

To understand the observations, we conducted a simple chemical
modeling of massive star-forming regions  A 1D cloud model with a mass
of 1200\,M$_\sun$, an outer radius of 0 36\,pc and a power-law density
profile ($\rho\propto r^p$ with $p=-1 5$) is the initially assumed
configuration  Three cases are studied: (1) a cold isothermal cloud
with $T=10$\,K, (2) $T=50$\,K, and (3) a warm model with a temperature
profile $T\propto r^q$ with $q=-0 4$ and a temperature at the outer
radius of 44\,K  The cloud is illuminated by the interstellar UV
radiation field (IRSF, \citealt{draine1978}) and by cosmic ray
particles (CRP)  The ISRF attenuation by single-sized $0 1\mu$m
silicate grains at a given radius is calculated in a plane-parallel
geometry following \citet{vandishoeck1988}  The CRP ionization rate is
assumed to be $1 3\times 10^{-17}$~s$^{-1}$ \citep{spitzer1968}  The
gas-grain chemical model by \citet{vasyunin2008} with the desorption
energies and surface reactions from \citet{garrod2006} is used 
Gas-phase reaction rates are taken from RATE\,06 \citep{woodall2007},
initial abundances, were adopted from the ``low metal'' set of
\citet{lee1998} 

Figure \ref{model} presents the C$_2$H abundances for the three models
at two different time steps: (a) 100\,yr, and (b) in a more evolved
stage after $5\times10^4$\,yr  The C$_2$H abundance is high toward the
core center right from the beginning of the evolution, similar to
previous models (e g , \citealt{millar1985,herbst1986,turner1999}) 
During the evolution, the C$_2$H abundance stays approximately
constant at the outer core edges, whereas it decreases by more than
three orders of magnitude in the center, except for the cold $T=10$~K
model   The C$_2$H abundance profiles for all three models show
similar behavior 

The chemical evolution of ethynyl is determined by relative removal
rates of carbon and oxygen atoms or ions into molecules like CO, OH,
H$_2$O  Light ionized hydrocarbons CH$^+_{\rm n}$ (n=2  5) are quickly
formed by radiative association of C$^+$ with H$_2$ and hydrogen
addition reactions: C$^+$ $\rightarrow$ CH$_2^+$ $\rightarrow$
CH$_3^+$ $\rightarrow$ CH$_5^+$   The protonated methane reacts with
electrons, CO, C, OH, and more complex species at later stage and
forms methane   The CH$_4$ molecules undergo reactive collisions with
C$^+$, producing C$_2$H$_2^+$ and C$_2$H$_3^+$  An alternative way to
produce C$_2$H$_2^+$ is the dissociative recombination of CH$_5^+$
into CH$_3$ followed by reactions with C$^+$   Finally, C$_2$H$_2^+$
and C$_2$H$_3^+$ dissociatively recombine into CH, C$_2$H, and
C$_2$H$_2$  The major removal for C$_2$H is either the direct
neutral-neutral reaction with O that forms CO, or the same reaction
but with heavier carbon chain ions that are formed from C$_2$H by
subsequent insertion of carbon  At later times, depletion and
gas-phase reactions with more complex species may enter into this
cycle   At the cloud edge the interstellar UV radiation
instantaneously dissociates CO despite its self-shielding,
re-enriching the gas with elemental carbon 

The transformation of C$_2$H into CO and other species proceeds
efficiently in dense regions, in particular in the ``warm'' model
where endothermic reactions result in rich molecular complexity of the
gas (see Fig ~\ref{model})   In contrast, in the ``cold'' 10\,K model
gas-grain interactions and surface reactions become important   As a
result, a large fraction of oxygen is locked in water ice that is hard
to desorb ($E_{\rm des} \sim 5500$~K), while half of the elemental
carbon goes to volatile methane ice ($E_{\rm des} \sim 1300$~K)  Upon
CRP heating of dust grains, this leads to much higher gas-phase
abundance of C$_2$H in the cloud core for the cold model compared to
the warm model  The effect is not that strong for less dense regions
at larger radii from the center 

Since the C$_2$H emission is anti-correlated with the dust continuum
emission in the case of IRAS\,18089-1732 (Fig \,\ref{18089}), we do
not have the H$_2$ column densities to quantitatively compare the
abundance profiles of IRAS\,18089-1732 with our model  However, data
and model allow a qualitative comparison of the spatial structures 
Estimating an exact evolutionary time for IRAS\,18089-1732 is hardly
possible, but based on the strong molecular line emission, its high
central gas temperatures and the observed outflow-disk system
\citep{beuther2004a,beuther2004b,beuther2005c}, an approximate age of
$5\times10^4$\,yr appears reasonable   Although dynamical and chemical
times are not necessarily exactly the same, in high-mass star
formation they should not differ to much: Following the models by
\citet{mckee2003} or \citet{krumholz2006b}, the luminosity rises
strongly right from the onset of collapse which can be considered as a
starting point for the chemical evolution  At the same time disks and
outflows evolve, which should hence have similar time-scales   The
diameter of the shell-like C$_2$H structure in IRAS\,18089-1732 is
$\sim 5''$ (Fig \,\ref{18089}), or $\sim$9000\,AU in radius at the
given distance of 3 6\,kpc   This value is well matched by the modeled
region with decreased C$_2$H abundance (Fig \,\ref{model})   Although
in principle optical depths and/or excitation effects could mimic the
C$_2$H morphology, we consider this as unlikely because the other
observed molecules with many different transitions all peak toward the
central submm continuum emission in IRAS\,18089-1732
\citep{beuther2005c}  Since C$_2$H is the only exception in that rich
dataset, chemical effects appear the more plausible explanation 

The fact that we see C$_2$H at the earliest and the later evolutionary
stages can be explained by the reactive nature of C$_2$H: it is
produced quickly early on and gets replenished at the core edges by
the UV photodissociation of CO  The inner ``chemical'' hole observed
toward IRAS\,18089-1732 can be explained by C$_2$H being consumed in
the chemical network forming CO and more complex molecules like larger
carbon-hydrogen complexes and/or depletion 

The data show that C$_2$H is not suited to investigate the central gas
cores in more evolved sources, however, our analysis indicates that
C$_2$H may be a suitable tracer of the earliest stages of (massive)
star formation, like N$_2$H$^+$ or NH$_3$ (e g ,
\citealt{bergin2002,tafalla2004,beuther2005a,pillai2006})  While a
spatial analysis of the line emission will give insights into the
kinematics of the gas and also the evolutionary stage from chemical
models, multiple C$_2$H lines will even allow a temperature
characterization  With its lowest $J=1-0$ transitions around 87\,GHz,
C$_2$H has easily accessible spectral lines in several bands between
the 3\,mm and 850\,$\mu$m   Furthermore, even the 349\,GHz lines
presented here have still relatively low upper level excitation
energies ($E_u/k\sim42$\,K), hence allowing to study cold cores even
at sub-millimeter wavelengths   This prediction can further be proved
via high spectral and spatial resolution observations of different
C$_2$H lines toward young IRDCs 

\acknowledgments{H B  acknowledges financial support
  by the Emmy-Noether-Programm of the Deutsche Forschungsgemeinschaft
  (DFG, grant BE2578)  }



Context 2: KSTP (1500 AM; SKOR North) is a commercial AM radio station licensed to Saint Paul, Minnesota  It is the flagship AM radio station of Hubbard Broadcasting, which also owns several other television and radio stations across the United States   KSTP has a sports radio format and is the ESPN Radio Network affiliate for Minneapolis-St  Paul   The radio studios are  on University Avenue in Minneapolis, shared with sister stations KSTP-FM, KSTP-TV, KTMY, and KSTC-TV  On weekdays, KSTP airs local sports shows from 9 a m  to 9 p m  and carries ESPN programming weekday mornings, late nights and weekends  Some KSTP shows are simulcast on other sports radio stations in the region 

KSTP runs the maximum power for AM stations, 50,000 watts   It shares clear-channel, Class A status on 1500 AM with WFED in Washington, D C   KSTP broadcasts a directional signal at night, using a three-tower array, with its transmitter on U S  Route 61 at Beam Avenue in Maplewood   Programming is also heard on 250 watt FM translator K235BP at 94 9 MHz in Bemidji 

History

WAMD and KFOY
KSTP's start in 1928 was the product of a merger between two pioneering Twin Cities stations: WAMD ("Where All Minneapolis Dances") in Minneapolis, first licensed on February 16, 1925 to Stanley E  Hubbard, and KFOY in St  Paul, first licensed on March 12, 1924 to the Beacon Radio Service in St  Paul 

Following a few test transmissions, WAMD made its formal debut broadcast on February 22, 1925  (In later interviews Stanley Hubbard traced WAMD's start to April 1924 ) It was located at the Marigold Dance Garden, and featured nightly "Midnight Frolics" broadcasts by the ballroom's orchestra  It is claimed that WAMD was the first radio station to be completely supported by running paid advertisements  Effective June 15, 1927, WAMD was assigned to 1330 kHz 

On November 11, 1927 WAMD's transmitter site at Oxboro Heath on Lyndale Avenue South burned down, two weeks after the station had been sold to the National Battery Company  An initial arrangement was made to carry WAMD's programs over WRHM (now WWTC), transmitting on WAMD's 1330 kHz frequency  Beginning on November 24, 1927 the WAMD broadcasts, still on 1330 kHz, were shifted to KFOY's facility in St  Paul  (At this time KFOY was assigned to 1050 kHz)  The next day it was announced that National Battery had purchased KFOY, and as of December 1, 1927 both KFOY and WAMD were reassigned to 1350 kHz  WAMD continued making regular broadcasts until the end of March 1928, while KFOY, although it continued to be licensed for a few more months on a time-sharing basis with WAMD, ceased operations at this point 

National Battery Company
In mid-December 1927, the National Battery Company announced it had received permission from the Federal Radio Commission (FRC) to build a new station, with the call letters KSTP, operating from a transmitter site to be constructed three miles south of Wescott  The next month it was reported that the new station, still under construction, had been assigned to 1360 kHz  KSTP made its debut broadcast on March 29, 1928  Although technically it was a separate station from WAMD and KFOY, both of which were formally deleted on April 30, 1928, overall KSTP was treated as the direct successor to a consolidated WAMD and KFOY 

Hubbard became the merged station's general manager, acquiring controlling interest in 1941  A month after the merger, KSTP became an affiliate for the NBC Red Network   It remained with NBC for 46 years  On November 11, 1928, under the provisions of the FRC's General Order 40, KSTP was assigned to a "high-powered regional" frequency of 1460 kHz  The only other station assigned to this frequency was WTFF in Mount Vernon Hills, Virginia (later WJSV, now WFED, Washington, D C )  On February 7, 1933, the FRC authorized KSTP to increase its daytime power to 25 KW  In 1938 and 1939 KSTP also operated a high-fidelity AM "experimental audio broadcasting station" Apex station, W9XUP, originally on 25,950 kHz and later on 26,150 kHz  In 1941, as part of the implementation of the North American Regional Broadcasting Agreement, KSTP was assigned to its current "clear channel" frequency of 1500 kHz, with the provision that it and WJSV, as "Class I-B" stations, had to maintain directional antennas at night in order to mutually protect each other from interference  An FM station, KSTP-FM, was founded in 1946 but shut down in 1952 

Hubbard reportedly acquired an RCA TV camera in 1939, and started experimenting with television broadcasts   But World War II put a hold on the development of television   In 1948, with the war over, KSTP-TV became the first television station in Minnesota   With KSTP 1500 already associated with NBC Radio, KSTP-TV became an NBC Television Network affiliate   From 1946 to 1952, KSTP also had an FM counterpart
Context 3: Paper Info

Title: Age and market capitalization drive large price variations of cryptocurrencies
Publish Date: 23 Feb 2023
Author List: 

Figure

Figure 3  Illustration of different effects of age and market capitalization on power-law exponents of cryptocurrencies (a) Posterior probability distributions of the linear coefficients associated with the effects of age [p(A)] and (b) the effects of market capitalization [p(C)] on power-law exponents related to large positive returns Panels (c) and (d) show the analogous distributions for the association with power-law exponents related to large negative returns In all panels, the different curves show the distributions for each of the top 20 cryptoassets by market capitalization Cryptocurrencies significantly affected by age or market capitalization are highlighted in boldface, and the numbers between brackets show their positions in the market capitalization rank 
Figure S5 There is more probability mass in the positive tail than in the negative tail of price returns (a) Probability distributions of the lower cut-offs (r min ) obtained by applying the Clauset-Shalizi-Newman method to positive (blue) and negative (red) returns The vertical dashed lines indicate the median values of r min for positive and negative returns (b) Probability distributions of 90th percentiles (r 90 ) estimated from the power-law models adjusted to positive (blue) and negative (red) returns The vertical dashed lines indicate the median values of r 90 for positive and negative returns (c) Probability distributions of the fraction of weeks that r 90 estimated from positive returns (r + 90 ) is larger than r 90 estimated from negative returns (r − 90 ) This fraction is calculated only for weeks in which the power-law hypothesis is not rejected for both tails The percentage of cryptoassets for which r + 90 > r − 90 is shown in the panels The first column of panels depicts the results when considering data from all cryptocurrencies, while the second and third columns present the results for the top 2000 and top 200 cryptocurrencies by market capitalization, respectively 
Figure S7 Robustness of the results of Fig  2(b)-(d) against considering only cryptocurrencies with fraction of rejection f r < 0 1 Panels (a) and (b) show the same distributions of Fig  S4 but after filtering out all time series of cryptocurrencies with fraction of rejections f r ≥ 0 1 As in the case related to sampling issues, we observe that these distributions barely change when considering only cryptocurrencies with f r < 0 1 Indeed, the distributions in this figure are not significantly distinguishable from their counterparts in Fig  S4 (two-sample Kolmogorov-Smirnov test, p > 0 05) 

abstract

Cryptocurrencies are considered the latest innovation in finance with considerable impact across social, technological, and economic dimensions  This new class of financial assets has also motivated a myriad of scientific investigations focused on understanding their statistical properties, such as the distribution of price returns 
However, research so far has only considered Bitcoin or at most a few cryptocurrencies, whilst ignoring that price returns might depend on cryptocurrency age or be influenced by market capitalization  Here, we therefore present a comprehensive investigation of large price variations for more than seven thousand digital currencies and explore whether price returns change with the coming-of-age and growth of the cryptocurrency market 
We find that tail distributions of price returns follow power-law functions over the entire history of the considered cryptocurrency portfolio, with typical exponents implying the absence of characteristic scales for price variations in about half of them  Moreover, these tail distributions are asymmetric as positive returns more often display smaller exponents, indicating that large positive price variations are more likely than negative ones 
Our results further reveal that changes in the tail exponents are very often simultaneously related to cryptocurrency age and market capitalization or only to age, with only a minority of cryptoassets being affected just by market capitalization or neither of the two quantities  Lastly, we find that the trends in power-law exponents usually point to mixed directions, and that large price variations are likely to become less frequent only in about 28% of the cryptocurrencies as they age and grow in market capitalization 
Since the creation of Bitcoin in 2008 , various different cryptoassets have been developed and are now considered to be at the cutting edge of innovation in finance   These digital financial assets are vastly diverse in design characteristics and intended purposes, ranging from peer-to-peer networks with underlying cash-like digital currencies (e g 
Bitcoin) to general-purpose blockchains transacting in commodity-like digital assets (e g  Ethereum), and even to cryptoassets that intend to replicate the price of conventional assets such as the US dollar or gold (e g  Tether and Tether Gold)   With more than nine thousand cryptoassets as of 2022 , the total market value of cryptocurrencies has grown massively to a staggering $2 trillion peak in 2021  
Despite long-standing debates over the intrinsic value and legality of cryptoassets , or perhaps even precisely due to such controversies, it is undeniable that cryptocurrencies are increasingly attracting the attention of academics, investors, and central banks, around the world   Moreover, these digital assets have been at the forefront of sizable financial gains and losses in recent years , they have been recognized as the main drivers of the brand-new phenomena of cryptoart and NFTs , but also as facilitators of illegal activities, such as money laundering and dark trade  
Financial research dedicated Our results are based on daily price time series of 7111 cryptocurrencies that comprise a significant part of all currently available cryptoassets (see Methods for details)  From these price series, we have estimated their logarithmic returns 2/16 Log-return, r )  The black horizontal arrow represents a given position of the expanding time window (at t = 2004 days) used to sample the return series over the entire history of Bitcoin 
This time window expands in weekly steps (seven time series observations), and for each position, we separate the positive (blue) from the negative (red) price returns  The gray line illustrates observations that will be included in future positions of the expanding time window (t > 2004)  (b) Survival functions or the complementary cumulative distributions of positive (blue) and negative (red) price returns within the expanding time window for t = 2004 days and above the lower bound of the power-law regime estimated from the Clauset-Shalizi-Newman method  
The dashed lines show the adjusted power-law functions, p(r) ∼ r −α , with α = 4 5 for positive returns and α = 3 0 for negative returns  (c) Time series of the power-law exponents α t for the positive (blue) and negative (red) return distributions obtained by expanding the time window from the hundredth observation (t = 100) to the latest available price return of Bitcoin 
The circular markers represent the values for the window position at t = 2004 days and the dashed lines indicate the median of the power-law exponents ( α+ = 4 50 for positive returns and α− = 2 99 for negative returns)  (d) Time series of the p-values related to the power-law hypothesis of positive (blue) and negative (red) price returns for every position of the expanding time window 
The dashed line indicates the threshold (p = 0 1) above which the power-law hypothesis cannot be rejected  For Bitcoin, the power-law hypothesis is never rejected for positive returns (fraction of rejection f r = 0) and rejected in only 4% of the expanding time window positions (fraction of rejection f r = 0 04) 
where x t represents the price of a given cryptocurrency at day t  All return time series in our analysis have at least 200 observations (see Supplementary Figure for the length distribution)  Figure (a) illustrates Bitcoin's series of daily returns  To investigate whether and how returns have changed over the aging and growing processes of all cryptocurrencies, we sample all time series of log-returns using a time window that expands in weekly steps (seven time series observations), starting from the hundredth observation to the latest return observation 
In each step, we separate the positive from the negative return values and estimate their power-law behavior using the Clauset-Shalizi-Newman method   Figure (a) further illustrates this procedure, where the vertical dashed line represents a given position of the time window (t = 2004 days), the blue and red lines indicate positive and negative returns, respectively, and the gray lines show the return observations that will be included in the expanding time window in future steps 
Moreover, Fig  (b) shows the corresponding survival functions (or complementary cumulative distributions) for the positive (blue) and negative (red) returns of Bitcoin within the time window highlighted in Fig  (a)  These survival functions correspond to return values above the lower bound of the power-law regime (r min ) and dashed lines in Fig  (b) show the power-law functions adjusted to data, that is,
with α = 4 5 for the positive returns and α = 3 0 for the negative returns in this particular position of the time window (t = 2004 days)  We have further verified the goodness of the power-law fits using the approach proposed by Clauset et al  (see also Preis et al  )  As detailed in the Methods section, this approach consists in generating several synthetic samples under the power-law hypothesis, adjusting these simulated samples, and estimating the fraction of times the Kolmogorov-Smirnov distance between the adjusted power-law and the synthetic samples is larger than the value calculated from the empirical data 
This fraction defines a p-value and allows us to reject or not the power-law hypothesis of the return distributions under a given confidence level  Following Refs  we consider the more conservative 90% confidence level (instead of the more lenient and commonly used 95% confidence level), rejecting the power-law hypothesis when p-value ≤ 0 1 
For the particular examples in Fig  (b), the p-values are respectively 1 00 and 0 17 for the positive and negative returns, and thus we cannot reject the power-law hypotheses  After sampling the entire price return series, we obtain time series for the power-law exponents (α t ) associated with positive and negative returns as well as the corresponding p-values time series for each step t of the expanding time window 
These time series allow us to reconstruct the aging process of the return distributions over the entire history of each cryptoasset and probe possible time-dependent patterns  Figures ) and 1(d) show the power-law exponents and p-values time series for the case of Bitcoin  The power-law hypothesis is never rejected for positive returns and rarely rejected for negative returns (about 4% of times) 
Moreover, the power-law exponents exhibit large fluctuations at the beginning of the time series and become more stable as Bitcoin matures as a financial asset (a similar tendency as reported by Begušić et al  )  The time evolution of these exponents further shows that the asymmetry between positive and negative returns observed in Fig  ) is not an incidental feature of a particular moment in Bitcoin's history 
Indeed, the power-law exponent for positive returns is almost always larger than the exponent for negative returns, implying that large negative price returns have been more likely to occur than their positive counterparts over nearly the entire history of Bitcoin covered by our data  However, while the difference between positive and negative exponents has approached a constant value, both exponents exhibit an increasing trend, indicating that large price variations are becoming less frequent with the coming-of-age of Bitcoin 
The previous analysis motivates us to ask whether the entire cryptocurrency market behaves similarly to Bitcoin and what other common patterns digital currencies tend to follow  To start answering this question, we have considered the p-values series of all cryptocurrencies to verify if the power-law hypothesis holds in general 
Figure (a) shows the percentage of cryptoassets rejecting the power-law hypothesis in at most a given fraction of the weekly positions of the expanding time window ( f r )  Remarkably, the hypothesis that large price movements (positive or negative) follow a power-law distribution is never rejected over the entire history of about 70% of all digital currencies in our dataset 
This analysis also shows that only ≈2% of cryptocurrencies reject the power-law hypothesis in more than half of the positions of the expanding time window ( f r ≥ 0 5)  For instance, considering a 10% threshold as a criterion ( f r ≤ 0 1), we find that about 85% of cryptocurrencies have return distributions adequately modeled by power laws 
Increasing this threshold to a more lenient 20% threshold ( f r ≤ 0 2), we find large price movements to be power-law distributed for about 91% of cryptocurrencies  These results thus provide strong evidence that cryptoassets, fairly generally, present large price movements quite well described by power-law distributions 
Moreover, this conclusion is robust when starting the expanding window with a greater   Large price movements are power-law distributed over the entire history of most cryptocurrencies with median values typically smaller than those found for traditional assets  (a) Percentage of cryptoassets rejecting the power-law hypothesis for large positive (blue) or negative (red) price returns in at most a given fraction of the weekly positions of the expanding time window ( f r ) used to sample the return series 
Remarkably, 68% of all 7111 digital currencies are compatible with the power-law hypothesis over their entire history, and about 91% of them reject the power-law hypothesis in less than 20% of the positions of the expanding time window ( f r ≤ 0 2)  (b) Probability distributions obtained via kernel density estimation of the median values of the power-law exponents along the history of each digital currency 
The blue curve shows the distribution of the median exponents related to positive returns ( α+ ) and the red curve does the same for negative returns ( α− )  The medians of α+ and α− are indicated by vertical dashed lines  Panels (c) and (d) show the distributions of these median exponents when considering the top 2000 and the top 200 cryptocurrencies by market capitalization, respectively 
We observe that the distributions of α+ and α− tend to shift toward larger values when considering the largest cryptoassets  number of return observations (between 100 and 300 days) and filtering out cryptoassets with missing observations (Supplementary Figures )  Still, it is worth noticing the existence of a few cryptoassets (9 of them) with relatively small market capitalization (ranking below the top 1000) for which the power-law hypothesis is always rejected (Supplementary Table ) 
Having verified that large price movements in the cryptocurrency market are generally well-described by powerlaw distributions, we now focus on the power-law exponents that typically characterize each cryptoasset  To do so, we select all exponent estimates over the entire history of each digital asset for which the power-law hypothesis is not rejected and calculate their median values for both the positive ( α+ ) and negative ( α− ) returns 
The dashed lines in Fig  ) show these median values for Bitcoin where α+ = 4 50 and α− = 2 99  It is worth noticing that the variance of large price movements σ 2 is finite only for α > 3, as the integral σ 2 ∼ ∞ r min r 2 p(r)dr diverges outside this interval  Thus, while the typical variance of large positive returns is finite for Bitcoin, negative returns are at the limit of not having a typical scale and are thus susceptible to much larger variations 
Figure shows the probability distribution for the median power-law exponents of all cryptoassets grouped by large positive and negative returns  We note that the distribution of typical power-law exponents associated with large positive returns is shifted to smaller values when compared with the distribution of exponents related to large negative returns 
The medians of these typical exponents are respectively 2 78 and 3 11 for positive and negative returns  This result suggests that the asymmetry in large price movements we have observed for Bitcoin is an overall feature of the cryptocurrency market  By calculating the difference between the typical exponents related to positive and negative large returns (∆α = α+ − α− ) for each digital currency, we find that about 2/3 of cryptocurrencies have α+ < α− (see Supplementary Figure for the probability distribution of ∆α) 
Thus, unlike Bitcoin, most cryptocurrencies have been more susceptible to large positive price variations than negative ones  While this asymmetry in the return distributions indicates that extremely large price variations tend to be positive, it does not necessarily imply positive price variations are more common for any threshold in the return values 
This happens because the fraction of events in each tail is also related to the lower bound of the power-law regime (r min )  However, we have found the distribution of r min to be similar among the positive and negative returns [Supplementary Figure ]  The distribution of high percentile scores (such as the 90th percentile) is also shifted to larger values for positive returns [Supplementary Figure ] 
Moreover, this asymmetry in high percentile scores related to positive and negative returns is systematic along the evolution of the power-law exponents [Supplementary Figure ]  These results thus indicate that there is indeed more probability mass in the positive tails than in the negative ones, a feature that likely reflects the current expansion of the cryptocurrency market as a whole 
The distributions in Fig  ) also show that large price variations do not have a finite variance for a significant part of cryptoassets, that is, α+ ≤ 3 for 62% of cryptocurrencies and α− ≤ 3 for 44% of cryptocurrencies  A significant part of the cryptocurrency market is thus prone to price variations with no typical scale 
Intriguingly, we further note the existence of a minority group of cryptoassets with α+ ≤ 2 (7%) or α− ≤ 2 (3%)  These cryptocurrencies, whose representative members are Counos X (CCXX, rank 216) with α − = 1 96 and α + = 1 84 and Chainbing (CBG, rank 236) with α + = 1 87, are even more susceptible to extreme price variations as one cannot even define the average value µ for large price returns, as the integral µ ∼ ∞ r min rp(r)dr diverges for α ≤ 2  We have also replicated the previous analysis when considering cryptocurrencies in the top 2000 and top 200 rankings of market capitalization (as of July 2022) 
Figures ) and 2(d) show the probability distribution for the median power-law exponents of these two groups  We observe that these distributions are more localized (particularly for the top 200) than the equivalent distributions for all cryptocurrencies  The fraction of cryptocurrencies with no typical scale for large price returns ( α+ ≤ 3 and α− ≤ 3) is significantly lower in these two groups compared to all cryptocurrencies 
In the top 2000 cryptocurrencies, 51% have α+ ≤ 3 and 26% have α− ≤ 3  These fractions are even smaller among the top 200 cryptocurrencies, with only 44% and 15% not presenting a typical scale for large positive and negative price returns, respectively  We further observe a decrease in the fraction of cryptoassets for which the average value for large price returns is not even finite, as only 2% and 1% of top 2000 cryptoassets have α+ ≤ 2 and α− ≤ 2  This reduction is more impressive among the top 200 cryptocurrencies as only the cryptoasset Fei USD (FEI, rank 78) has α+ = 1 97 and none is characterized by α− ≤ 2  The medians of α+ and α− also increase from 2 78 and 3 11 for all cryptocurrencies to 2



ground_truth: The focus of the study was on the reactive radical ethynyl (C$_2$H).

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: When did KSTP switch to a sports radio format?

Read the following text and answer briefly.

Context 2:   KSTP-FM 102 1 was only on the air four years   There were few radios equipped to receive FM signals in that era, and management decided to discontinue FM broadcasts 

MOR and Top 40
As network programming moved from radio to television, KSTP programmed a full service Middle of the Road (MOR) radio format, in the shadow of its chief competitor, CBS Radio affiliate 830 WCCO  In 1965, a new FM station, reviving the KSTP-FM call sign, was put on the air, largely simulcasting the AM station   But by the late 1960s, KSTP-FM began a separate format of beautiful music   KSTP was the radio home of the Minnesota Vikings football team from 1970 to 1975  

In 1973, KSTP broke away from its longtime adult MOR sound and became one of four area stations at the time to program a Top 40 format  "15 KSTP, The Music Station" competed with Top 40 AM rivals WDGY, KDWB and later, WYOO  The competition would eventually shake itself out, with outrageous rocker WYOO dropping out after being sold in 1976, and then the staid WDGY switching to country music the following year   As for uptempo hits station 15 KSTP, it went from a tight Top 40 format to leaning adult rock in 1978, to leaning adult contemporary in 1979, to evolving into adult contemporary/talk by 1980   In 1982, it officially shifted to talk   Most Top 40 rock music, by this time, had moved to the FM band 

Past Personalities

Notable hosts who have been on KSTP include John Hines, Jesse Ventura, Larry Carolla, Tom Barnard, Big Al Davis, Don Vogel, John MacDougall, Griff, Mike Edwards, Geoff Charles, Joe Soucheray, James Lileks, Leigh Kamman, Barbara Carlson, Peter Thiele, Tom Mischke, Jason Lewis, Chuck Knapp, Machine Gun Kelly, Charle Bush, Mark O'Connell and Paul Brand  These broadcasters were supported by producers such as Bruce Huff, Rob Pendleton, Alison Brown, Jean Bjorgen, David Elvin (who Vogel dubbed the "Steven Spielberg of Talk Radio"), Mitch Berg and others 

The station has, for the most part, emphasized local hosts over the years   But in 1988, KSTP was one of Rush Limbaugh's first affiliates when his conservative talk show was rolled out for national syndication   (Clear Channel-owned KTLK-FM took over rights to Limbaugh's show in January 2006)  Other syndicated hosts previously heard on KSTP include Sean Hannity, Bruce Williams, Larry King, and Owen Spann 

Sports Radio
KSTP switched to Sports Radio on February 15, 2010   As the station had to wait for ESPN's contract with rival KFAN and its sister station KFXN to expire, it did not become an ESPN Radio affiliate until April 12, the same day that the Minnesota Twins were scheduled to play the first game in their new ball park, Target Field, against the Boston Red Sox   As a result Coast to Coast AM and Live on Sunday Night, it's Bill Cunningham were retained during this period   One ESPN Radio network program, The Herd with Colin Cowherd, was picked up by KSTP immediately following the format change 

In 2018, the station was approved for an FM translator on 94 1 FM, broadcasting from a transmitter atop the IDS Center in downtown Minneapolis  The two-watt signal threw most of its power to the west, preventing interference to low powered FM stations on the same channel including WFNU-LP in St  Paul  With only two watts of power, however, the signal was limited to the immediate downtown area surrounding the IDS Center   It later acquired a 250 watt translator, K235BP at 94 9 MHz   The original translator was discontinued 

On January 15, 2019, KSTP rebranded as "SKOR North" (a reference to the Vikings team song/chant, "Skol, Vikings"), with local programming between 12 noon and 7 pm  About a year later, in May of 2020, KSTP suspended most of its local programming and laid off nearly all of its local staff  Station management cited the economic toll of the coronavirus for the changes  Sports broadcasting continues, primarily composed of ESPN radio network broadcasts 

Sports Teams

KSTP-AM served as the radio flagship for the Minnesota Vikings football team from 1970 to 1975 

On August 1, 2006, the station announced that it would be the new flagship station for the Minnesota Twins baseball team, effective with the start of the 2007 season  The Twins had been on rival WCCO since arriving in Minnesota in 1961   KSTP served as the flagship for the Twins until the end of the 2012 season, when games moved to 96 3 KTWN-FM (now KMWA)   The Twins have since returned to WCCO 830 

The switch to a fairly weak FM station caused dissent among some listeners, particularly in communities that had trouble picking up KSTP 1500   Although KSTP is the state's second most powerful AM station, it must operate directionally at night, delivering a reduced signal to parts of the market  WCCO, by comparison, offers a signal with a wider coverage area during the day than KSTP does, with WCCO's non-directional 50,000 watt signal  In response, the Twins have expanded the number of affiliates 

On March 9, 2011, KSTP announced it would be the new flagship for the University of Minnesota Golden Gophers men's and women's basketball and men's ice hockey, ending a 68-year run on WCCO  The rights have since moved to KFXN-FM, which already aired Gopher football 

On March 2, 2017, KSTP announced it would be the first radio broadcaster for Minnesota United FC   The move brings live soccer action to 1500 AM 

Previous logos

References

External links
KSTP website

FCC History Cards for KSTP (covering 1928-1980)
Radiotapes com Historic Minneapolis/St  Paul airchecks dating back to 1924 including KSTP and other Twin Cities radio stations 
Rick Burnett's TwinCitiesRadioAirchecks com has additional airchecks of KSTP and other Twin Cities radio stations from the '60s and '70s, including Chuck Knapp's 2nd show on KSTP 

Hubbard Broadcasting
ESPN Radio stations
Peabody Award winners
Radio stations in Minneapolis–Saint Paul
Radio stations established in 1925
1925 establishments in Minnesota
Minnesota Kicks
Sports radio stations in the United States
Clear-channel radio stations



ground_truth: KSTP switched to a sports radio format on February 15, 2010.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What type of distribution do the tail distributions of price returns follow?

Read the following text and answer briefly.

Context 3: 98 and 3 35 for the top 2000 and to 3 08 and 3 58 for the top 200 cryptocurrencies 
Conversely, the asymmetry between positive and negative large price returns does not differ much among the three groups, with the condition α+ < α− holding only for a slightly larger fraction of top 2000 (69 1%) and top 200 (70 6%) cryptoassets compared to all cryptocurrencies (66 4%)  Moreover, all these patterns are robust when filtering out time series with sampling issues or when considering only cryptoassets that stay compatible with the power-law hypothesis in more than 90% of the positions of the expanding time window (Supplementary Figures ) 
We also investigate whether the patterns related to the median of the power-law exponents differ among groups of cryptocurrencies with different designs and purposes  To do so, we group digital assets using the 50 most common tags in our dataset (e g  "bnb-chain", "defi", and "collectibles-nfts") and estimate the probability distributions of the median exponents α+ and α− (Supplementary Figures ) 
These results show that design and purpose affect the dynamics of large price variations in the cryptocurrency market as the medians of typical exponents range from 2 4 to 3 7 among the groups  The lowest values occur for cryptocurrencies tagged as "doggone-doggerel" (medians of α+ and α− are 2 38 and 2 83), "memes" (2 41 and 2 87), and "stablecoin" (2 65 and 2 79) 
Digital currencies belonging to the first two tags overlap a lot and have Dogecoin (DOGE, rank 9) and Shiba Inu (SHIB, rank 13) as the most important representatives  Cryptoassets with these tags usually have humorous characteristics (such as an Internet meme) and several have been considered as a form of pump-and-dump scheme , a type of financial fraud in which false statements artificially inflate asset prices so the scheme operators sell their overvalued cryptoassets 
Conversely, cryptoassets tagged as "stablecoin" represent a class of cryptocurrencies designed to have a fixed exchange rate to a reference asset (such as a national currency or precious metal)   While the price of stablecoins tends to stay around the target values, their price series are also marked by sharp variations, which in turn are responsible for their typically small power-law exponents 
This type of cryptoasset has been shown to be prone to failures , such as the recent examples of TerraUSD (UST) and Tron's USDD (USDD) that lost their pegs to the US Dollar producing large variations in their price series  The asymmetry between positive and negative large returns also emerges when grouping the cryptocurrencies using their tags 
All 50 tags have distributions of α+ shifted to smaller values when compared with the distributions of α− , with differences between their medians ranging from −0 74 ("okex-blockdream-ventures-portfolio") to −0 14 ("stablecoin")  Indeed, only four ('stablecoin", "scrypt", "fantom-ecosystem" and "alameda-research-portfolio") out of the fifty groupings have both distributions indistinguishable under a two-sample Kolmogorov-Smirnov test (p-value > 0 05) 
Focusing now on the evolution of the power-law exponents quantified by the time series α t for positive and negative returns, we ask whether these exponents present particular time trends  For Bitcoin [Fig  )], α t seems to increase with time for both positive and negative returns  At the same time, the results of Fig  also suggest that market capitalization affects these power-law exponents 
To verify these possibilities, we assume the power-law exponents (α t ) to be linearly associated with the cryptocurrency's age (y t , measured in years) and the logarithm of market capitalization (log c t )  As detailed in the Methods section, we frame this problem using a hierarchical Bayesian model 
This approach assumes that the linear coefficients associated with the effects of age (A) and market capitalization (C) of each digital currency are drawn from distributions with means µ A and µ C and standard deviations σ A and σ C , which are in turn distributed according to global distributions representing the overall impact of these quantities on the cryptocurrency market 
The Bayesian inference process consists of estimating the posterior probability distributions of the linear coefficients for each cryptocurrency as well as the posterior distributions of µ A , µ C , σ A , and σ C , allowing us to simultaneously probe asset-specific tendencies and overall market characteristics 
Moreover, we restrict this analysis to the 2140 digital currencies having more than 50 observations of market capitalization concomitantly to the time series of the power-law exponents in order to have enough data points for detecting possible trends  When considering the overall market characteristics, we find that the 94% highest density intervals for µ A ([-0 01, 0 06] for positive and [-0 02, 0 03] for negative returns) and µ C ([-0 02, 0 03] for positive and [-0 001, 0 04] for negative returns) include the zero (see Supplementary Figure for their distributions) 
Thus, there is no evidence of a unique overall pattern for the association between the power-law exponents and age or market capitalization followed by a significant part of the cryptocurrency market  Indeed, the 94% highest density intervals for σ A ([0 87, 0 93] for positive and [0 63, 0 70] for negative returns) and σ C ([0 57, 0 61] for positive and [0 49, 0 52] for negative returns) indicate that the cryptocurrency market is highly heterogeneous regarding the evolution of power-law exponents associated with large price variations (see Supplementary Figure for the distributions of σ A and σ C )  Figure illustrates these heterogeneous behaviors by plotting the posterior probability distributions for the linear coefficients associated with the effects of age (A) and market capitalization (C) for the top 20 digital assets, where cryptocurrencies which are significantly affected (that is, the 94% highest density intervals for A or C do not include the zero) by these quantities are highlighted in boldface 
Even this small selection of digital  currencies already presents a myriad of patterns  First, we observe that the power-law exponents of a few top 20 cryptocurrencies are neither correlated with age nor market capitalization  That is the case of Shiba Inu (SHIB, rank 13) and Dai (DAI, rank 11) for both positive and negative returns, UNUS SED LEO (LEO, rank 18) and Polkadot (DOT, rank 12) for the positive returns, and USDCoin (USDC, rank 4) and Solana (SOL, rank 9) for negative returns 
There are also cryptocurrencies with exponents positively or negatively correlated only with market capitalization  Examples include Tether (USDT, rank 3) and Dogecoin (DOGE, rank 10), for which the power-law exponents associated with positive returns increase with market capitalization, and Binance USD (BUSD, rank 6), for which power-law exponents associated with positive and negative returns decrease with market capitalization 
We also observe cryptocurrencies for which age and market capitalization simultaneously affect the power-law exponents  Polygon (MATIC, rank 14) is an example where the power-law exponents associated with positive returns tend to increase with age and decrease with market capitalization  Finally, there are also cryptocurrencies with power-law exponents only associated with age 
That is the case of Bitcoin (BTC, rank 1), Ethereum (ETH, rank 2), and Cardano (ADA, rank 8), for which the power-law exponents related to positive and negative returns increase with age, but also the case of Uniswap (UNI, rank 19), for which the exponents decrease with age  Figure systematically extends the observations made for the top 20 cryptoassets to all 2140 digital currencies for which we have modeled the changes in the power-law exponents as a function of age and market capitalization 
First, we note that only 10% of cryptocurrencies have power-law exponents not significantly affected by age and market capitalization  The vast majority (90%) displays some relationship with these quantities  However, these associations are as varied as the ones we have observed for the top 20 cryptoassets 
About 52% of cryptocurrencies have power-law exponents simultaneously affected by age and market capitalization  In this group, these quantities simultaneously impact the exponents related to positive and negative returns of 34% of cryptoassets, whereas the remainder is affected only in the positive tail (9%) or only in the negative tail (9%) 
Moving back in the hierarchy, we find that the power-law exponents of 32% of cryptocurrencies are affected only by age while a much minor fraction (6%) is affected only by market capitalization  Within the group only affected by age, we observe that the effects are slightly more frequent only on the exponents related to negative returns (12%), compared to cases where effects are restricted only to positive returns (10%) or simultaneously affect both tails (10%) 
Finally, within the minor group only affected by market capitalization, we note that associations more frequently involve only exponents related to negative returns (3%) compared to the other two cases (2% only positive returns and 1% for both positive and negative returns)  Beyond the previous discussion about whether positive or negative returns are simultaneously or individually affected by age and market capitalization, we have also categorized the direction of the trend imposed by these two quantities on the power-law exponents 
Blue rectangles in Fig  represent the fraction of relationships for which increasing age or market capitalization (or both) is associated with a raise in the power-law exponents  About 28% of all cryptocurrencies exhibit this pattern in which large price variations are expected to occur less frequently as they grow and age 
Conversely, the red rectangles in Fig  depict the fraction of relationships for which increasing age or market capitalization (or both) is associated with a reduction in the power-law exponents  This case comprises about 25% of all cryptocurrencies for which large price variations are likely to become more frequent as they grow in market capitalization and age 
Still, the majority of associations represented by green rectangles refer to the case where the effects of age and market capitalization point in different directions (e g  exponents increasing with age while decreasing with market capitalization)  About 36% of cryptocurrencies fit this condition which in turn contributes to consolidating the cumbersome hierarchical structure of patterns displayed by cryptocurrencies regarding the dynamics of large price variations 
This complex picture is not much different when considering only cryptocurrencies in the top 200 market capitalization rank (Supplementary Figure )  However, we do observe an increased prevalence of patterns characterized by exponents that rise with age and market capitalization (37%), suggesting that large price variations are becoming less frequent among the top 200 cryptocurrencies than in the overall market 
)  Each of the previous three levels is further classified regarding whether both positive and negative returns are simultaneously affected or whether the effect involves only positive or only negative returns  Finally, the former levels are classified regarding whether the power-law exponents increase, decrease or have a mixed trend with the predictive variables 
Overall, 36% of the associations are classified as mixed trends (green rectangles), 28% are increasing trends (blue rectangles), and 26% are decreasing trends (red rectangles)  We have studied the distributions of large price variations of a significant part of the digital assets that currently comprise the entirety of the cryptocurrency market 
Unlike previous work, we have estimated these distributions for entire historical price records of each digital currency, and we have identified the patterns under which the return distributions change as cryptoassets age and grow in market capitalization  Similarly to conventional financial assets , our findings show that the return distributions of the vast majority of cryptoassets have tails that are described well by power-law functions along their entire history 
The typical power-law exponents of cryptocurrencies (α ∼ 3) are, however, significantly smaller than those reported for conventional assets (α ∼ 4)   This feature corroborates the widespread belief that cryptoassets are indeed considerably more risky for investments than stocks or other more traditional financial assets 
Indeed, we have found that about half of the cryptocurrencies in our analysis do not have a characteristic scale for price variations, and are thus prone to much higher price variations than those typically observed in stock markets  On the upside, we have also identified an asymmetry in the power-law exponents for positive and negative returns in about 2/3 of all considered cryptocurrencies, such that these exponents are smaller for positive than they are for negative returns 
This means that sizable positive price variations have generally been more likely to occur than equally sizable negative price variations, which in turn may also reflect the recent overall expansion of the cryptocurrency market  Using a hierarchical Bayesian linear model, we have also simultaneously investigated the overall market characteristics and asset-specific tendencies regarding the effects of age and market capitalization on the power-law exponents 
We have found that the cryptocurrency market is highly heterogeneous regarding the trends exhibited by each cryptocurrency; however, only a small fraction of cryptocurrencies (10%) have power-law exponents neither correlated with age nor market capitalization  These associations have been mostly ignored by the current literature and are probably related to the still-early developmental stage of the cryptocurrency market as a whole 
Overall, 36% of cryptocurrencies present trends that do not systematically contribute to increasing or decreasing their power-law exponents as they age and grow in market capitalization  On the other hand, for 26% of cryptocurrencies, aging and growing market capitalization are both associated with a reduction in their power-law exponents, thus contributing to the rise in the frequency of large price variations in their dynamics 
Only about 28% of cryptocurrencies present trends in which the power-law exponents increase with age and market capitalization, favoring thus large price variations to become less likely  These results somehow juxtapose with findings about the increasing informational efficiency of the cryptocurrency market  
In fact, if on the one hand the cryptocurrency market is becoming more informationally efficient, then on the other our findings indicate that there is no clear trend toward decreasing the risks of sizable variations in the prices of most considered cryptoassets  In other words, risk and efficiency thus appear to be moving towards different directions in the cryptocurrency market 
To conclude, we hope that our findings will contribute significantly to the better understanding of the dynamics of large price variations in the cryptocurrency market as a whole, and not just for a small subset of selected digital assets, which is especially relevant due to the diminishing concentration of market capitalization among the top digital currencies, and also because of the considerable impact these new assets may have in our increasingly digital economy 
Our results are based on time series of the daily closing prices (in USD) for all cryptoassets listed on CoinMar-ketCap (coinmarketcap com) as of 25 July 2022 [see Supplementary Figure (a) for a visualization of the increasing number cryptoassets listed on CoinMarketCap since 2013]  These time series were automatically gathered using the cryptoCMD Python package and other information such as the tags associated with each cryptoasset were obtained via the CoinMarketCap API  
In addition, we have also obtained the daily market capitalization time series (in USD) from all cryptoassets which had this information available at the time  Earliest records available from CoinMarketCap date from 29 April 2013 and the latest records used in our analysis correspond to 25 July 2022  Out of 9943 cryptocurrencies, we have restricted our analysis to the 7111 with at least 200 price-return observations 
The median length of these time series is 446 observations [see the distribution of series length in Supplementary Figure   We have estimated the power-law behavior of the return distributions by applying the Clauset-Shalizi-Newman method to the return time series r t   In particular, we have sampled each of these time series using an expanding time window that starts at the hundredth observation and grows in weekly steps (seven data points each step) 
For each position of the expanding time window, we have separated the positive returns from the negative ones and applied the Clauset-Shalizi-Newman method to each set  This approach consists of obtaining the maximum likelihood estimate for the power-law exponent, α = 1 + n/ (∑ n t=1 ln r t /r min ) , where r min is the lower bound of the power-law regime and n is the number of (positive or negative) return observations in the power-law regime for a given position of the expanding time window 
The value r min is estimated from data by minimizing the Kolmogorov-Smirnov statistic between the empirical distribution and the power-law model  The Clauset-Shalizi-Newman method yields an unbiased and consistent estimator , in a sense that as the sample increases indefinitely, the estimated power-law exponent converges in distribution to the actual value 
Moreover, we have used the implementation available on the powerlaw Python package   In addition to obtaining the power-law exponents, we have also verified the adequacy of the power-law hypothesis using the procedure originally proposed by Clauset et al  as adapted by Preis et al    This procedure consists of generating synthetic samples under the power-law hypothesis with the same properties of the empirical data under analysis (that is, same length and parameters α and r min ), adjusting the simulated data with the power-law model via the Clauset-Shalizi-Newman method, and calculating the Kolmogorov-Smirnov statistic (κ syn ) between the distributions obtained from the simulated samples and the adjusted power-law model 
Next, the values of κ syn are compared to the Kolmogorov-Smirnov statistic calculated between empirical data and the power-law model (κ)  Finally, a p-value is defined by calculating the fraction of times for which κ syn > κ  We have used one thousand synthetic samples for each position of the expanding time window and the more conservative 90% confidence level (instead of the more lenient and commonly used 95% confidence level), such that the power-law hypothesis is rejected whenever p-value ≤ 0 1 
We have estimated the effects of age and market capitalization on the power-law exponents associated with positive or negative returns of a given cryptocurrency using the linear model where α t represents the power-law exponent, log c t is the logarithm of the market capitalization, and y t is the age (in years) of the cryptocurrency at t-th observation 
Moreover, K is the intercept of the association, while C and A are linear coefficients quantifying the effects of market capitalization and age, respectively  Finally, N (µ, σ ) stands for the normal distribution with mean µ and standard deviation σ , such that the parameter ε accounts for the unobserved determinants in the dynamics of the power-law exponents 
We have framed this problem using the hierarchical Bayesian approach such that each power-law exponent α t is nested within a cryptocurrency with model parameters considered as random variables normally distributed with parameters that are also random variables  Mathematically, for each cryptocurrency, we have
12/16 where µ K , σ K , µ C , σ C , µ A , and σ A are hyperparameters  These hyperparameters are assumed to be distributed according to distributions that quantify the overall impact of age and market capitalization on the cryptocurrency market as a whole  We have performed this Bayesian regression for exponents related to positive and negative returns separately, and used noninformative prior and hyperprior distributions in order not to bias the posterior estimation  
Specifically, we have considered and ε ∼ U (0, 10 2 ) , where U (a, b) stands for the uniform distribution in the interval [a, b] and Inv−Γ(θ , γ) represents the inverse gamma distribution with shape and scale parameters θ and γ, respectively  For the numerical implementation, we have relied on the PyMC Python package and sampled the posterior distributions via the gradient-based Hamiltonian Monte Carlo no-U-Turn-sampler method 
We have run four parallel chains with 2500 iterations each (1000 burn-in samples) to allow good mixing and estimated the Gelman-Rubin convergence statistic (R-hat) to ensure the convergence of the sampling approach (R-hat was always close to one)  In addition, we have also verified that models describing the power-law exponents as a function of only age (C → 0 in Eq  3) or only market capitalization (A → 0 in Eq  3) yield significantly worse descriptions of our data as quantified by the Widely Applicable Information Criterion (WAIC) and the Pareto Smoothed Importance Sampling Leave-One-Out cross-validation (PSIS-LOO) (see Supplementary Table )  ) is larger than r 90 estimated from negative returns (r − 90 ) 
This fraction is calculated only for weeks in which the power-law hypothesis is not rejected for both tails  The percentage of cryptoassets for which r + 90 > r − 90 is shown in the panels  The first column of panels depicts the results when considering data from all cryptocurrencies, while the second and third columns present the results for the top 2000 and top 200 cryptocurrencies by market capitalization, respectively 
Sampling issues refer to missing data and problems caused by prices of cryptoassets decreasing to zero  We note that these distributions barely change when considering only cryptocurrencies without any sampling issue  Indeed, the distributions in this figure are not significantly distinguishable from their counterparts in Fig  (two-sample Kolmogorov-Smirnov test, p > 0 05) 
)  Each of the previous three levels is further classified regarding whether both positive and negative returns are simultaneously affected or whether the effect involves only positive or only negative returns  Finally, the former levels are classified regarding whether the power-law exponents increase, decrease or have a mixed trend with the predictive variables 
Overall, 35% of the associations are classified as mixed trends (green rectangles), 37% are increasing trends (blue rectangles), and 18% are decreasing trends (red rectangles) 



ground_truth: Power-law functions.