D2.2 Decadal Predictions
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,
Horizon 2020 Societal challenge 5:
Climate action, environment, resource
efficiency and raw materials
BINGO
Bringing INnovation to onGOing water management –
a better future under climate change
Grant Agreement n° 641739, Research and Innovation Action
Deliverable number: D2.2
Deliverable name: Data downscaled to 12km/daily, Europe, for the period 2015-2024
WP / WP number: WP2: Climate predictions and downscaling to extreme weather
Delivery due date: Project month 12 (30/06/2016)
Actual date of submission: 30/06/2016
Dissemination level: Public
Lead beneficiary: FUB
Responsible scientist/administrator: Uwe Ulbrich, Henning Rust
Estimated effort (PM): 12PM
Contributor(s): Komlan A. Kpogo-Nuwoklo, Edmund Meredith, Henning Rust, Uwe Ulbrich
(all FUB)
Estimated effort contributor(s) (PM): 12PM
Internal reviewer: Paula Lorza, March Scheibel (both Wupperverband), George Zittis (CYI)
Ref. Ares(2016)3128411 - 30/06/2016
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Changes with respect to the DoW
With justification if applicable In the DoW, it was stated that the decadal climate
predictions (2015-2024) would be downscaled to 12km/1d over the entire EURO-
CORDEX region. In order to reduce computational cost, we have instead carried out
the downscaling over two European sub-regions (see Figure 1, page 7). These regions
cover Iberia and north-west Europe, encompassing all five research sites that the FUB
is responsible for providing data for. An additional benefit of this approach is that the
reduced computational expense allows us to downscale more realizations of the
decadal predictions than would be possible for the whole EURO-CORDEX domain.
Dissemination and uptake
These data can be used by all partners within the project, though cannot be publicly
disseminated without prior consent.
Short Summary of results
This deliverable describes the decadal predictions (2015-2024) produced by WP2, to be
subsequently used as input data for the hydrological models used in WP3. The data
have been dynamically downscaled to a horizontal resolution of 0.11° (12 km) and are
available at a daily frequency. As with all data produced in Work Package 2 (see, e.g.,
Deliverable 2.1), the data are available to all project partners via the online Freva
portal, where the data is converted to a format suitable for specific hydrological
models and the option of applying a bias correction to the data is also available.
Evidence of accomplishment
1. BINGO-DECO plug-in of the FreVa evaluation system https://freva.met.fu-
berlin.de/plugins/bingo_deco/detail/ (log-in required)
2. DECO Documentation: DECO – A plug-in for data extraction and conversion
developed within and for BINGO, H.W. Rust, A. Richling, E. Meredith, M. Fischer, C.
Vagenas, C. Kadow, and U. Ulbrich, 2016, Technical Report. Available online at
http://users.met.fu-berlin.de/~HenningRust/BINGO/DECO_docu.pdf (See also
Appendix 2)
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TABLE OF CONTENTS
1. Introduction ..................................................................................................................................... 4
2. Data downscaled to 12km/daily, Europe, for the period 2015-2024 ........................................... 5
2.1. MiKlip forced decadal predictions ................................................................................................. 5
2.2. Bias correction of decadal predictions .......................................................................................... 8
2.3. Data dissemination ....................................................................................................................... 8
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1. Introduction
Work Package 2 – Climate predictions and downscaling to extreme weather – of the
BINGO Project is tasked with producing high-resolution climate data, which will be
subsequently used as input data for the hydrological models being used in the other
work packages. Deliverable 2.2, the focus of this document, is specifically tasked with
providing these data for the period 2015-2024, based on decadal climate predictions of
the MiKlip decadal prediction system.
The work carried out for Deliverable 2.2 builds on what was previously implemented
for Deliverable 2.1. As such, the same approach to data processing, storage and
distribution is adopted, which can be read in detail in Deliverable 2.1.
This document describes the data produced for Deliverable 2.2, how it was produced,
and how it can be accessed by project partners.
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2. Data downscaled to 12km/daily, Europe, for the period
2015-2024
This chapter describes the regional climate simulations carried out for Deliverable 2.2,
the data produced for BINGO partners (including their bias correction), and how these
data can be accessed by project partners.
2.1. MiKlip forced decadal predictions
The relatively new field of decadal climate prediction, e.g. Smith et al. (2007), aims to
simulate both the climate response to future anthropogenic forcing and the future
evolution (from the present) of the climate due to internal climate variability
(Marotzke et al., 2016). This differs from the approach taken in climate projections,
e.g. the CMIP5 project (Taylor et al., 2012), where the focus is on the response of the
climate to anthropogenic forcing and the impacts of internal climate variability are
(supposed to be) nullified via multi-decadal climate model integrations. The earth
system models (ESMs) used in decadal prediction systems are initialized with an
observed state of the climate system, i.e. ocean, atmosphere, soil, ice, etc. Skill in
predicting internal climate variability on a decadal scale is derived from the long-term
memory (i.e. sensitivity to the initial state) of certain components of the climate
system, predominantly the ocean. As such, decadal predictions (unlike climate
projections) are reliant on a high-quality initialization of the ESM for those components
which exhibit long-term memory.
The MiKlip project (http://www.fona-miklip.de) is funded by the German Ministry for
Education and Research with the aim of developing a world-class decadal prediction
system. The MiKlip decadal prediction system is based on the Max Planck Institute's
earth system model, MPI-ESM (http://www.mpimet.mpg.de/en/science/models/mpi-
esm/), and has an atmospheric horizontal resolution of T63 (1.875°). The first phase of
the MiKlip project showed significant skill (e.g. Müller et al., (2012), Pohlmann et al.,
(2013)) in the MiKlip system, based on the evaluation of decadal hindcast simulations
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which were initialized yearly between 1960 and 2010. In addition to this, the MiKlip
system was also used for future decadal prediction running up to 2024, for 10
realizations and with an initialization in 2015. Module C of the first phase of the MiKlip
project was devoted to the regionalisation of the MiKlip global model output, via
dynamical downscaling. This was carried out over a European domain for the entire
MiKlip period (1960-2024) using the CCLM at 0.44° resolution.
For the BINGO project, the FUB have further dynamically downscaled the first four
realizations of the future decadal predictions (2015-2024) from 0.44° to 0.11° using the
CCLM (see the attached Technical Report (Rust et al.), Appendix 2, for a description of
the CCLM). To reduce computational expense, this has been carried out over two sub-
domains (Fig. 1):
(1) NW-EUR-11: which contains the research sites at Bergen, Veluwe and Wupper.
(2) IBERIA-11: which contains the research sites at Tagus and Badalona.
The 0.11° resolution matches that used in the downscaling carried out for D2.1,
creating a total set of simulations spanning 1979-2024, crucially all at the same spatial
resolution.
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Figure 1 | BINGO domains for MiKlip decadal predictions. The area covered by the MiKlip 0.44°
regionalisation is shown in colour, with red representing the 0.44° land mask and blue the sea. The
IBERIA-11 and NW-EUR-11 domains of the BINGO project are shown in green and cyan.
The variables, all of which can be bias corrected, produced for BINGO partners and
their temporal resolution also match those of D2.1. That is, D2.2 provides the following
variables at a daily frequency, as well as their daily min/max values:
Total Cloud Fraction
Near-Surface Relative Humidity
Near-Surface Specific Humidity
Precipitation
Surface Air Pressure
Sea Level Pressure
Surface Downwelling Longwave Radiation
Surface Downwelling Shortwave Radiation
Near-Surface Wind Speed
Near-Surface Air Temperature
Near-Surface Dew Point Temperature
Eastward Near-Surface Wind
Northward Near-Surface Wind
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2.2. Bias correction of decadal predictions
As discussed in detail in Deliverable 2.1, climate models often show systematic biases with
respect to observations in their representation of certain variables. As such, the later work
packages are best served by having the option to input bias corrected data to their
hydrological models.
Bias correction of the 0.11° decadal predictions is carried out using a method based on the
cumulative distribution functions of the model output and historical observations. Broadly
speaking, this involves estimating the bias of historical MiKlip data and bias correcting the
future MiKlip data based on this. This method also takes account of the fact that the
highest resolution historical data available from the MiKlip project is 0.44°, and that
having produced 0.11° data for the decadal future predictions, BINGO does not have the
computational resources to additionally produce 0.11° resolution data for the historical
period. The concept behind the method is described in detail in Appendix 1 and in section
3.3 of Appendix 2.
2.3. Data dissemination
The dissemination method for the data provided for D2.2 is via the Freva system, using
the DECO plugin. This is identical to the method adopted for D2.1; users simply need to
select the correct experi e t decadal-predictio s from the DECO menu. As such, the
method will not be described in detail again here. For a recap, the reader is referred to
either Appendix 2 or Deliverable 2.1.
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3. References
J Marotzke, WA Müller, FSE Vamborg, P Becker, U Cubasch, H Feldmann, F Kaspar, C
Kottmeier, C Marini, I Polkova. Miklip – a national research project on decadal climate
prediction. Bulletin of the American Meteorological Society, 2016.
WA Mueller, J Baehr, H Haak, JH Jungclaus, J Kröger, D Matei, H Pohlmann, JS Storch, and J
Marotzke. Forecast skill of multi-year seasonal means in the decadal prediction system of
the max planck institute for meteorology. Geophysical Research Letters, 39(22), 2012.
H. Pohlmann, W. A. Mueller, K. Kulkarni, M. Kameswarrao, D. Matei, FSE Vamborg, C.
Kadow, S. Illing, and J. Marotzke. Improved forecast skill in the tropics in the new miklip
decadal climate predictions. Geophysical Research Letters, 40(21):5798-5802, 2013.
D. M. Smith, S. Cusack, A. W. Colman, C. K. Follard, G. R. Harris, and J. M. Murphy.
Improved surface temperature prediction for the coming decade from a global climate
model. Science, 317(5839):796-799, 2007.
K. E. Taylor, R. J. Stouffer, and G. A. Mehl. An overview of CMIP5 and the experiment
design. Bull. Amer. Meteor. Soc., 94(4):485-498, 2012.
Appendix 1
Bias Correction of MiKlip Decadal Predictions
❆ ♣r♦♣♦s❡❞ s❝❤❡♠❡ ❢♦r ▼✐❑❧✐♣ ❢✉t✉r❡ s✐♠✉❧❛t✐♦♥s ❜✐❛s ❝♦rr❡❝t✐♦♥
❏✉♥❡ ✷✾✱ ✷✵✶✻
❖✉r ❣♦❛❧ ✐s t♦ ❜✐❛s ❝♦rr❡❝t t❤❡ ▼✐❦❧✐♣ ❢✉t✉r❡ s✐♠✉❧❛t✐♦♥s ❢♦r ❛ s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢ 0.11◦ ✉s✐♥❣ t❤❡❈❉❋✲❚r❛♥s❢♦r♠ ♠❡t❤♦❞✳ ❚❤✐s ❜✐❛s ❝♦rr❡❝t✐♦♥ ♠❡t❤♦❞ ❝❛♥ ❜❡ s❡❡♥ ❛s ❛♥ ❡①t❡♥s✐♦♥ ♦❢ t❤❡ ❝❧❛ss✐❝❛❧
q✉❛♥t✐❧❡ ♠❛♣♣✐♥❣ ✐♥ ✇❤✐❝❤ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥s ❛r❡ ❝♦rr❡❝t❡❞ s♦ t❤❛t t❤❡✐r ❈✉♠✉❧❛t✐✈❡ ❉✐str✐❜✉t✐♦♥
❋✉♥❝t✐♦♥s ✭❈❉❋✮ ♠❛t❝❤ t❤❡ ♦♥❡s ♦❢ t❤❡ ♦❜s❡r✈❛t✐♦♥s✳ ❚❤❡ ❈❉❋✲❚r❛♥s❢♦r♠ ♠❡t❤♦❞✱ ✐♥ ❛❞❞✐t✐♦♥✱
❛✐♠s t♦ ♣r♦✈✐❞❡ ❛♣♣r♦①✐♠❛t✐✈❡ ❈❉❋ ♦❢ t❤❡ ♦❜s❡r✈❛t✐♦♥s ❢♦r t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞ ❜❛s❡❞ ♦♥ ✐♥❢♦r♠❛t✐♦♥
❧❡❛r♥❡❞ ❢r♦♠ t❤❡ ❤✐st♦r✐❝❛❧ ♣❡r✐♦❞ ✭s❡❡ ❆♣♣❡♥❞✐① ✷✱ s❡❝t✐♦♥ ✸✳✸✱ ❢♦r ♠♦r❡ ❞❡t❛✐❧s✮✳
■♥ t❤❡ ❚❛❜❧❡ ✶✱ t❤❡ ❛✈❛✐❧❛❜❧❡ ❞❛t❛ ❢♦r ❤✐st♦r✐❝❛❧ ❛♥❞ ❢✉t✉r❡ ♣❡r✐♦❞s ❛r❡ s✉♠♠❛r✐③❡❞✳ ❲❆❚❈❍
❞❛t❛ s❡r✈❡s ❤❡r❡ ❛s ♦❜s❡r✈❛t✐♦♥s✳
❘❡s♦❧✉t✐♦♥ 0.44◦ ❘❡s♦❧✉t✐♦♥ 0.11◦
❍✐st♦r✐❝❛❧ ❋✉t✉r❡ ❍✐st♦r✐❝❛❧ ❋✉t✉r❡
▼✐❑❧✐♣ F(M44)h
F(M44)f F
(M11)h
F(M11)f
❲❆❚❈❍ F(W44)h
F(W44)f F
(W11)h
F(W11)f
❚❛❜❧❡ ✶✿ ❚❛❜❧❡ s✉♠♠❛r✐③✐♥❣ t❤❡ ❞❛t❛✿ ❋ st❛♥❞s ❢♦r ❈❉❋s✳ ❈❉❋s t❤❛t ❝❛♥ ♥♦t ❜❡ ❝♦♠♣✉t❡❞ ❞✐r❡❝t❧②
❢r♦♠ t❤❡ ❛✈❛✐❧❛❜❧❡ ❞❛t❛ ❛r❡ ✐♥❞✐❝❛t❡❞ ✐♥ ❜❧✉❡✳
❚❤❡ ❜✐❛s ❝♦rr❡❝t✐♦♥ ♦❢ ▼✐❑❧✐♣ ❢✉t✉r❡ s✐♠✉❧❛t✐♦♥s ❢♦r s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢ 0.11◦ ✐s q✉✐t❡ ❝❤❛❧❧❡♥❣✐♥❣❜❡❝❛✉s❡ ❤✐st♦r✐❝❛❧ s✐♠✉❧❛t✐♦♥s ❢♦r t❤❡ s❛♠❡ r❡s♦❧✉t✐♦♥ ❛r❡ ♥♦t ❛✈❛✐❧❛❜❧❡✳ ❍♦✇❡✈❡r✱ ✇❡ ❤❛✈❡ ▼✐❦❧✐♣
s✐♠✉❧❛t✐♦♥s ❢♦r ❜♦t❤ ❤✐st♦r✐❝❛❧ ❛♥❞ ❢✉t✉r❡ ♣❡r✐♦❞s ❛t ❛ s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢ 0.44◦✳ ❚❤❛♥❦s t♦ t❤❡ ❈❉❋✲❚r❛♥s❢♦r♠✱ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ❡st✐♠❛t❡ ❈❉❋s ♦❢ ▼✐❑❧✐♣ ❤✐st♦r✐❝❛❧ s✐♠✉❧❛t✐♦♥s ❢♦r s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢
0.11◦ ❜② ♠♦❞❡❧❧✐♥❣ t❤❡ ♠❛t❤❡♠❛t✐❝❛❧ ❧✐♥❦ ❜❡t✇❡❡♥ t❤❡s❡ t✇♦ r❡s♦❧✉t✐♦♥s✳ ❚❤✉s✱ t❤❡ ♣r♦♣♦s❡❞ ♠❡t❤♦❞
t♦ ❝♦rr❡❝t t❤❡ ▼✐❑❧✐♣ ❢✉t✉r❡ s✐♠✉❧❛t✐♦♥s ❢♦r s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢ 0.11◦✱ ✉s✐♥❣ ❈❉❋✲❚r❛♥s❢♦r♠ ❝❛♥
❜❡ ❧✐st❡❞ ❛s ❢♦❧❧♦✇❡❞ ✭s❡❡ ❋✐❣✉r❡ ✶ ❢♦r ❣r❛♣❤✐❝ ✐❧❧✉str❛t✐♦♥✮✿
✶✳ ❊st✐♠❛t❡ ❈❉❋s ♦❢ t❤❡ ▼✐❑❧✐♣ ❤✐st♦r✐❝❛❧ s✐♠✉❧❛t✐♦♥s ❢♦r ❛ s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢ 0.11◦ ✭F(M11)h (x)✮
✉s✐♥❣ ✐♥❢♦r♠❛t✐♦♥ ♣r♦✈✐❞❡❞ ❜② t❤❡ ❧❛r❣❡ s❝❛❧❡ ✭0.44◦✮ ▼✐❑❧✐♣ ❞❛t❛ ✭❙❡❝t✐♦♥ ✶✮✳
✷✳ ❊st✐♠❛t❡ ❈❉❋s ♦❢ t❤❡ ❲❆❚❈❍ ❞❛t❛ ✭0.11◦✮ ❢♦r t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞ ✭F(W11)f (x)✮ ✉s✐♥❣ t❤❡ ▼✐❑❧✐♣
❤✐st♦r✐❝❛❧ ❛♥❞ ❢✉t✉r❡ s✐♠✉❧❛t✐♦♥s ❛♥❞ ❲❆❚❈❍ ❤✐st♦r✐❝❛❧ ❞❛t❛ ❢♦r s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢ 0.11◦
✭❙❡❝t✐♦♥ ✷✮✳
✸✳ ❖♥❝❡ ❈❉❋s ♦❢ t❤❡ ❲❆❚❈❍ ❞❛t❛ ✭0.11◦✮ ❢♦r t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞ ❛r❡ ❡st✐♠❛t❡❞✱ ❛ q✉❛♥t✐❧❡ ♠❛♣♣✐♥❣
❝❛♥ ✜♥❛❧❧② ❜❡ ❛♣♣❧✐❡❞ ❜❡t✇❡❡♥ F(M11)f (x) ❛♥❞ F
(W11)f (x)✳ ❚❤❡ ❝♦rr❡❝t❡❞ ✈❛❧✉❡ xbc ✐s t❤❡♥
xbc = F(W11)
−1f
[
F(M11)f (x)
]
. ✭✶✮
✶
❋✐❣✉r❡ ✶✿ ■❧❧✉str❛t✐♦♥ ♦❢ tr❛♥s❢♦r♠❛t✐♦♥s ✐♥✈♦❧✈❡❞ ✐♥ t❤❡ ♣r♦♣♦s❡❞ ♠❡t❤♦❞
✷
✶ ❊st✐♠❛t✐♦♥ ♦❢ ▼✐❑❧✐♣ ❤✐st♦r✐❝❛❧ ❈❉❋ ✭F(M11)h (x)✮ ❢r♦♠ t❤❡ ▼✐❑❧✐♣
0.44◦ ❞❛t❛✿ ♣r♦❜❛❜✐❧✐st✐❝ ❞♦✇♥s❝❛❧✐♥❣
❲❡ ❛❧s♦ ♠❛❦❡ t❤❡ ❛ss✉♠♣t✐♦♥ t❤❛t t❤❡r❡ ✐s ❛ ♠❛t❤❡♠❛t✐❝❛❧ tr❛♥s❢♦r♠❛t✐♦♥ T (44−11) t❤❛t ❛❧❧♦✇s t♦
❣♦ ❢r♦♠ t❤❡ ❈❉❋ ♦❢ t❤❡ ❧❛r❣❡ s❝❛❧❡ ▼✐❑❧✐♣ ❤✐st♦r✐❝❛❧ ❞❛t❛ ✭F(M44)h (x)✮ t♦ t❤❡ ❈❉❋ ♦❢ t❤❡ s♠❛❧❧ s❝❛❧❡
▼✐❑❧✐♣ ❤✐st♦r✐❝❛❧ ❞❛t❛ ✭F(M11)h (x)✮ ✱
T (44−11)[
F(M44)h (x)
]
= F(M11)h (x). ✭✷✮
❯♥❞❡r ❛ss✉♠♣t✐♦♥ t❤❛t T (11−44) st✐❧❧ ✈❛❧✐❞ ❢♦r t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞✱
T (44−11)[
F(M44)f (x)
]
= F(M11)f (x), ✭✸✮
✐t ❝❛♥ ❜❡ ♠♦❞❡❧❧❡❞ ❜② r❡♣❧❛❝✐♥❣ x ❜② F(M44)
−1f (u) ✐♥ ✭✸✮✱ ✇❤❡r❡ u ✐s ❛♥② ♣r♦❜❛❜✐❧✐t② ✐♥ [0, 1]✱
T (44−11)(u) = F(M11)f
[
F(M44)
−1f (u)
]
. ✭✹✮
■♥s❡rt✐♥❣ ✭✹✮ ✐♥ ✭✷✮ ❧❡❛❞s t♦ ❛ ♠♦❞❡❧❧✐♥❣ ♦❢ F(M11)h (x)✱
F(M11)h (x) = F
(M11)f
{
F(M44)
−1f
[
F(M44)h (x)
]}
. ✭✺✮
✷ ❊st✐♠❛t✐♦♥ ♦❢ ❲❆❚❈❍ ❢✉t✉r❡ ❈❉❋ ✭F(W11)f (x)✮
❲❡ ♠❛❦❡ ❛ss✉♠♣t✐♦♥ t❤❛t t❤❡r❡ ✐s ❛ ♠❛t❤❡♠❛t✐❝❛❧ tr❛♥s❢♦r♠❛t✐♦♥ T (MW ) t❤❛t ❛❧❧♦✇s t♦ ❣♦ ❢r♦♠
t❤❡ ❈❉❋ ♦❢ t❤❡ ▼✐❑❧✐♣ ❤✐st♦r✐❝❛❧ ❞❛t❛ ✭F(M11)h (x)✮ t♦ t❤❡ ❈❉❋ ♦❢ t❤❡ ❲❆❚❈❍ ❤✐st♦r✐❝❛❧ ❞❛t❛
✭F(W11)h (x)✮✱
T (MW )[
F(M11)h (x)
]
= F(W11)h (x). ✭✻✮
❲❡ s✉♣♣♦s❡ t❤❛t t❤✐s tr❛♥s❢♦r♠❛t✐♦♥ ✐s st✐❧❧ ✈❛❧✐❞ ❢♦r t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞✱
T (MW )[
F(M11)f (x)
]
= F(W11)f (x). ✭✼✮
❇② ♠♦❞❡❧❧✐♥❣ T (MW )✱ ✐t ✐s t❤❡♥ ♣♦ss✐❜❧❡ t♦ ❛♣♣r♦①✐♠❛t❡ t❤❡ ❈❉❋ ♦❢ ❲❆❚❈❍ ❢✉t✉r❡ ❞❛t❛
✭F(W11)f (x)✮✳ ❚❤❡ s✐♠♣❧❡ ✇❛② t♦ ♠♦❞❡❧ T (MW ) ✐s t♦ r❡♣❧❛❝❡ x ❜② F
(M11)−1
h (u) ✐♥ ✭✻✮✱ ✇❤❡r❡ u ✐s
❛♥② ♣r♦❜❛❜✐❧✐t② ✐♥ [0, 1]✳ ❲❡ t❤❡♥ ♦❜t❛✐♥
T (MW )(u) = F(W11)h
[
F(M11)
−1h (u)
]
, ✭✽✮
❝♦rr❡s♣♦♥❞✐♥❣ t♦ t❤❡ s✐♠♣❧❡ ❞❡✜♥✐t✐♦♥ ♦❢ T (MW )✳ ■♥s❡rt✐♥❣ ✭✽✮ ✐♥ ✭✼✮ ❧❡❛❞s t♦ ❛ ♠♦❞❡❧❧✐♥❣ ♦❢
F(W11)f (x)✱
F(W11)f (x) = F
(W11)h
{
F(M11)
−1h
[
F(M11)f (x)
]}
. ✭✾✮
■♥ ❡q✉❛t✐♦♥ ✭✾✮ t❤❡ ✐♥✈❡rs❡ ❈❉❋ ♦❢ t❤❡ ❤✐st♦r✐❝❛❧ ▼✐❦❧✐♣ ❞❛t❛ F(M11)
−1h ✐s ✉♥❦♥♦✇♥ ❛♥❞ ♥❡❡❞s t♦
❜❡ ❡st✐♠❛t❡❞✳ ❖♥❡ ✇❛② t♦ ❞♦ s♦ ✐s t♦ ❛♣♣❧② t❤❡ ❈❉❋✲t ❛s ❛ ♣r♦❜❛❜✐❧✐st✐❝ ❞♦✇♥s❝❛❧✐♥❣ t♦ r❡❧❛t❡ ❈❉❋s
❢r♦♠ t❤❡ ❧❛r❣❡ s❝❛❧❡ ✭0.44◦✮ t♦ ❈❉❋s ❢r♦♠ t❤❡ s♠❛❧❧ s❝❛❧❡ ✭0.11◦✮✳
✸
Appendix 2
Technical Report: Available data and the Freva system/DECO
plugin through which it is distributed
❇■◆●❖ ❲♦r❦ ♣❛❝❦❛❣❡ ✷❈❧✐♠❛t❡ ♣r❡❞✐❝t✐♦♥s ❛♥❞ ❞♦✇♥s❝❛❧✐♥❣ t♦ ❡①tr❡♠❡ ✇❡❛t❤❡r
❉❊❈❖
✕❆ ♣❧✉❣✲✐♥ ❢♦r ❞❛t❛ ❡①tr❛❝t✐♦♥ ❛♥❞ ❝♦♥✈❡rs✐♦♥
❞❡✈❡❧♦♣❡❞ ✇✐t❤✐♥ ❛♥❞ ❢♦r
❇■◆●❖
❍❡♥♥✐♥❣ ❲✳ ❘✉st✱ ❆♥❞② ❘✐❝❤❧✐♥❣✱ ❊❞♠✉♥❞ ▼❡r❡❞✐t❤✱
▼❛❞❧❡♥ ❋✐s❝❤❡r✱ ❈❤r✐st♦s ❱❛❣❡♥❛s✱
❈❤r✐st♦♣❤❡r ❑❛❞♦✇ ❛♥❞ ❯✇❡ ❯❧❜r✐❝❤
❱❡rs✐♦♥ ❢r♦♠ ❏✉♥❡ ✷✽✱ ✷✵✶✻
❚❤❡ ❇■◆●❖ ♣r♦❥❡❝t ❤❛s r❡❝❡✐✈❡❞ ❢✉♥❞✐♥❣ ❢r♦♠ t❤❡ ❊✉r♦♣❡❛♥ ❯♥✐♦♥✬s❍♦r✐③♦♥ ✷✵✷✵ ❘❡s❡❛r❝❤ ❛♥❞ ■♥♥♦✈❛t✐♦♥ ♣r♦❣r❛♠♠❡✱ ✉♥❞❡r t❤❡ ●r❛♥t❆❣r❡❡♠❡♥t ♥✉♠❜❡r ✻✹✶✼✸✾✳
❆❜str❛❝t
❉❊❈❖ ✐s ❛ ♣❧✉❣✲✐♥ t♦ t❤❡ ❋r❡✐❡ ❯♥✐✈❡rs✐tät ❇❡r❧✐♥ ❊✈❛❧✉❛t✐♦♥ ❋r❛♠❡✇♦r❦ ❢♦r ❊❛rt❤ ❙②s✲
t❡♠ ❙❝✐❡♥❝❡ ✭❋r❡❱❛✮ ❛♥❞ ❛✐♠s ❛t ❡①tr❛❝t✐♥❣ ❛♥❞ ❝♦♥✈❡rt✐♥❣ ❈❖❙▼❖✲❈▲▼ r❡❣✐♦♥❛❧ ❝❧✐✲♠❛t❡ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥s ❢r♦♠ ❛ ❝❡♥tr❛❧ ❞❛t❛ st♦r❛❣❡ ♦♥ ❞❡♠❛♥❞ ✈✐❛ ❛ ✇❡❜✲❜❛s❡❞ ♣❧❛t❢♦r♠✳❚❤❡ ❞❛t❛ ✐s t♦ ❜❡ ✉s❡❞ ❛s ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞r✐✈✐♥❣ ❞❛t❛ ❢♦r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s ❛t t❤❡ s✐①❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s ✭❇■◆●❖ ❞❡❧✐✈❡r❛❜❧❡ ❉✷✳✶✮✳ ❈✉rr❡♥t❧②✱ t❤❡ s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢t❤❡ r❡❣✐♦♥❛❧ ♠♦❞❡❧ ✐s ✶✷❦♠ ❛♥❞ ❞❛t❛ ✇✐❧❧ ❜❡ ♠❛❞❡ ❛✈❛✐❧❛❜❧❡ ❛s ❞❛✐❧② ✈❛❧✉❡s✳ ❚❤❡ ❝❧✐♠❛✲t♦❧♦❣② ❢♦r t❤❡ s✐♠✉❧❛t❡❞ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ♣❛r❛♠❡t❡rs✱ ✐✳❡✳ t❤❡✐r s❡❛s♦♥❛❧❧② ✈❛r②✐♥❣ ♠❡❛♥✭❛♥❞ ❤✐❣❤❡r ♠♦♠❡♥ts✮ ❞✐✛❡r ❢r♦♠ t❤❡ ♦❜s❡r✈❡❞ ♦♥❡✱ ❛ ❜✐❛s ❝♦rr❡❝t✐♦♥ ❝❛♥ ❜❡ ♦♣t✐♦♥❛❧❧②❛♣♣❧✐❡❞ ❜❡❢♦r❡ ❝♦♥✈❡rt✐♥❣ t❤❡ ❞❛t❛ ❛♥❞ ✜❧❡ ❢♦r♠❛t t♦ t❤❡ ♣❛rt✐❝✉❧❛r ♥❡❡❞s ♦❢ t❤❡ ✐♥❞✐✲✈✐❞✉❛❧ ♠♦❞❡❧✐♥❣ ❣r♦✉♣s ❛t t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡s✳ ❚❤❡ ❧❛tt❡r ✐♠♣❧✐❡s ❛ ❝♦♥✈❡rs✐♦♥ ❢r♦♠ t❤❡♥❛t✐✈❡ ❈❖❙▼❖✲❈▲▼ ❣r✐❞ t♦ st❛t✐♦♥ ❧♦❝❛t✐♦♥s ♦r t♦ ❛ ❞✐✛❡r❡♥t ❣r✐❞✱ ❛ ❝❤❛♥❣❡ ♦❢ ✉♥✐ts✱❛s ✇❡❧❧ ❛s ✇r✐t✐♥❣ t❤❡ ❞❛t❛ t♦ t❤❡ ❞❡s✐r❡❞ ✜❧❡ ❢♦r♠❛t✳ ❚❤✐s ♦♥✲❞❡♠❛♥❞ ♣♦st✲♣r♦❝❡ss✐♥❣❛♥❞ ❝♦♥✈❡rs✐♦♥ ❛♣♣r♦❛❝❤ ❛❧❧♦✇s ❢♦r ❛♥ ❡✣❝✐❡♥t ❞❛t❛ st♦r❛❣❡✱ ♠❛①✐♠❛❧ r❡♣r♦❞✉❝✐❜✐❧✐t②❛♥❞ tr❛♥s♣❛r❡♥❝②✱ ❛s ✇❡❧❧ ❛s tr❛♥s❢❡r❛❜✐❧✐t② t♦ ♥❡✇ ❞❛t❛ s❡ts✳ ❚❤❡ ❛♣♣❧✐❝❛t✐♦♥ ❞❡✈❡❧♦♣❡❞❤❡r❡ ❝❛♥ ❜❡ ❛❝❝❡ss❡❞ ✈✐❛ ❛ ✇❡❜✲♣❧❛t❢♦r♠ ♦r ❛ ❝♦♠♠❛♥❞ ❧✐♥❡ ✐♥t❡r❢❛❝❡✳ ❉❡✈❡❧♦♣♠❡♥t ✐ss✉❜❥❡❝t❡❞ t♦ ❛ str✐❝t ✈❡rs✐♦♥ ❝♦♥tr♦❧ t♦ ❡♥s✉r❡ r❡♣r♦❞✉❝✐❜✐❧✐t②✳
✸
❈♦♥t❡♥ts
✶ ❉❊❈❖ ✕ ❆✐♠s ❛♥❞ str❛t❡❣② ✻
✷ ❉❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❝❧✐♠❛t❡ s✐♠✉❧❛t✐♦♥s ✽✷✳✶ ▼♦❞❡❧ ❉❡s❝r✐♣t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷✳✷ ❉❡s❝r✐♣t✐♦♥ ♦❢ ❙✐♠✉❧❛t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽
✷✳✷✳✶ ❘❡❛♥❛❧②s✐s✲❢♦r❝❡❞ ❡✈❛❧✉❛t✐♦♥ r✉♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷✳✷✳✷ ❍✐❣❤✲r❡s♦❧✉t✐♦♥ ✭t❡st✮ s✐♠✉❧❛t✐♦♥s ♦❢ ❡①tr❡♠❛❧ ❡♣✐s♦❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷✳✷✳✸ ▼✐❑❧✐♣ ❢♦r❝❡❞ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷
✸ ❇✐❛s ❝♦rr❡❝t✐♦♥ ✶✹✸✳✶ ❘❡❢❡r❡♥❝❡ ❞❛t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✸✳✷ ❙❡❛s♦♥❛❧ ●❡♥❡r❛❧✐③❡❞ ▲✐♥❡❛r ▼♦❞❡❧ ♠❡t❤♦❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✸✳✷✳✶ ❯♥❞❡r❧②✐♥❣ ♣r✐♥❝✐♣❧❡ ❛♥❞ ♠♦❞❡❧✐♥❣ ❛♣♣r♦❛❝❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✸✳✷✳✷ ❆t ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✸✳✸ ❈✉♠✉❧❛t✐✈❡ ❉✐str✐❜✉t✐♦♥ ❋✉♥❝t✐♦♥ ❚r❛♥s❢♦r♠ ♠❡t❤♦❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷✸✳✸✳✶ ◗✉❛♥t✐❧❡✲▼❛♣♣✐♥❣ ▼❡t❤♦❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷✸✳✸✳✷ ❈❉❋✲❚r❛♥s❢♦r♠ ▼❡t❤♦❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷✸✳✸✳✸ ❆♣♣❧✐❝❛t✐♦♥ ♦❢ ❈❉❋✲t ❛t ❇■◆●❖ r❡s❡❛r❝❤ s✐t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✹ ❉❊❈❖ ✕ ❆ ❇■◆●❖ ♣❧✉❣✲✐♥ ❢♦r ❋r❡❱❛ ✷✽✹✳✶ ❋r❡❱❛ ✕ ❋r❡✐❡ ❯♥✐✈❡rs✐tät ❇❡r❧✐♥ ❡✈❛❧✉❛t✐♦♥ s②st❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽✹✳✷ ❉♦❝✉♠❡♥t❛t✐♦♥ ♦❢ ❉❊❈❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✹✳✷✳✶ ■♥tr♦❞✉❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾✹✳✷✳✷ Pr❡♣r♦❝❡ss✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵✹✳✷✳✸ ■♥♣✉t ♣❛r❛♠❡t❡rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶✹✳✷✳✹ ❖✉t♣✉t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✺ ❙✉♠♠❛r② ✸✼
❇✐❜❧✐♦❣r❛♣❤② ✸✽
✺
❈❤❛♣t❡r ✶
❉❊❈❖ ✕ ❆✐♠s ❛♥❞ str❛t❡❣②
❚❤❡ ❇■◆●❖❲♦r❦ P❛❝❦❛❣❡ ❲P✷ ❈❧✐♠❛t❡ ♣r❡❞✐❝t✐♦♥s ❛♥❞ ❞♦✇♥s❝❛❧✐♥❣ t♦ ❡①tr❡♠❡ ✇❡❛t❤❡r
❛✐♠s ❛t ♣r♦✈✐❞✐♥❣ ❤✐❣❤ r❡s♦❧✉t✐♦♥ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞r✐✈✐♥❣ ❞❛t❛ ❢♦r ✈❛r✐♦✉s ❤②❞r♦❧♦❣✐❝❛❧♠♦❞❡❧s✳ ❋♦r ♠♦st ♠♦❞❡❧s✱ t❤✐s ✐♥❝❧✉❞❡s ♣r❡❝✐♣✐t❛t✐♦♥✱ t❡♠♣❡r❛t✉r❡✱ ♣r❡ss✉r❡✱ ✇✐♥❞ s♣❡❡❞✱✐♥❝♦♠✐♥❣ s♦❧❛r r❛❞✐❛t✐♦♥ ❛♥❞ ♦t❤❡rs✳ ❚❤✐s ❞❛t❛ ✐s ❣❡♥❡r❛t❡❞ ♦♥ ❛ r❡❣✐♦♥❛❧ ❧❡✈❡❧ ✭❢♦r t❤✐s❞❡❧✐✈❡r❛❜❧❡ ❛t ❛ ❊✉r♦♣❡❛♥ ❧❡✈❡❧✮ ❜② ❞②♥❛♠✐❝❛❧❧② ❞♦✇♥s❝❛❧✐♥❣ ❝♦❛rs❡ r❡s♦❧✉t✐♦♥ ❣❧♦❜❛❧❞❛t❛✱ s❡❡ ❛❧s♦ t❤❡ r❡❞ ❜♦① ♦❢ ❋✐❣✳ ✶✳✶✳ ❚♦ ❜❡ ✉s❛❜❧❡ ❢♦r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✱ t❤✐s ❞❛t❛
❋✐❣✉r❡ ✶✳✶✿ ❙❦❡t❝❤ ♦❢ t❤❡ str❛t❡❣② ✐♥ ❲P✷✳
♥❡❡❞s t♦ ❜❡ ❛♣♣r♦♣r✐❛t❡❧② ♣♦st✲♣r♦❝❡ss❡❞ ❛♥❞ ❝♦♥✈❡rt❡❞ t♦ t❤❡ ♥❡❡❞s ♦❢ t❤❡ ✶✺ ❛♥❞ ♠♦r❡✐♥❞✐✈✐❞✉❛❧ ♠♦❞❡❧s ✉s❡❞ ❛t t❤❡ ✻ ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s✳
❋♦r tr❛♥s♣❛r❡♥❝② ❛♥❞ r❡♣r♦❞✉❝✐❜✐❧✐t② ✇✐t❤✐♥ ❇■◆●❖✱ ✇❡ ♠✉st ❡♥s✉r❡ t❤❛t t❤❡ ✈❡r②s❛♠❡ ❞r✐✈✐♥❣ ❞❛t❛ ✐s ❛✈❛✐❧❛❜❧❡ t❤r♦✉❣❤♦✉t t❤❡ ♣r♦❥❡❝t ❛♥❞ ❜❡②♦♥❞✳ ❚❤✉s✱ ✐t ♠✉st ❜❡ ❡✐t❤❡rst♦r❡❞ ✐♥ t❤❡ ✈❛r✐♦✉s ❞✐✛❡r❡♥t ✜❧❡ ❢♦r♠❛ts ♥❡❡❞❡❞ ❜② t❤❡ ✐♥❞✐✈✐❞✉❛❧ ♠♦❞❡❧s✱ ♦r ✕ t♦ ❜❡♠♦r❡ ❡✣❝✐❡♥t ♦♥ ♠❡♠♦r② ❝♦♥s✉♠♣t✐♦♥ ✕ ♦♥❡ ❞❛t❛ s❡t ✐s st♦r❡❞ ✐♥ ❛ ❝♦♠♠♦♥ st❛♥❞❛r❞✐③❡❞❢♦r♠❛t ❢♦r ❝❧✐♠❛t❡ ♠♦❞❡❧s ❛♥❞ ❛❞❞✐t✐♦♥❛❧❧② ❞❛t❛ ❝♦♥✈❡rs✐♦♥ ❛❧❣♦r✐t❤♠s ❛r❡ s♣❡❝✐✜❝❛❧❧②t❛✐❧♦r❡❞ ❢♦r ❛❧❧ t❤❡ ✐♥❞✐✈✐❞✉❛❧ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✳ ❇❡s✐❞❡s t❤❡ ❡✣❝✐❡♥t ✉s❡ ♦❢ ♠❡♠♦r②✱t❤❡r❡ ❛r❡ ♦t❤❡r ❛❞✈❛♥t❛❣❡s t♦ t❤❡ ❧❛tt❡r ♣r♦❝❡❞✉r❡✿ ■✮ t❤❡s❡ ❝♦♥✈❡rs✐♦♥ ❛❧❣♦r✐t❤♠s ❝❛♥
✻
❜❡ r❡✉s❡❞ ❢♦r ♠♦r❡ ❞❛t❛ t♦ ❝♦♠❡ ✇✐t❤ t❤❡ ❢♦❧❧♦✇✐♥❣ ❞❡❧✐✈❡r❛❜❧❡s ❛ss♦❝✐❛t❡❞ ✇✐t❤ ❲P✷✱■■✮ ❜✐❛s ❝♦rr❡❝t✐♦♥ ❝❛♥ ❜❡ ❡①❝❤❛♥❣❡ ✇✐t❤ ❛ ♠♦r❡ s♦♣❤✐st✐❝❛t❡❞ ♦♥❡ ✐❢ ❛✈❛✐❧❛❜❧❡✱ ❛♥❞ ■■■✮♠❛♥② ♦t❤❡r ❛✈❛✐❧❛❜❧❡ ❞❛t❛ s❡ts ✐♥ t❤✐s st❛♥❞❛r❞✐③❡❞ ❢♦r♠❛t ❝❛♥ ❜❡ ✉s❡❞ ❛❞❞✐t✐♦♥❛❧❧② t♦t❤❡ ❞❛t❛ ♣r♦❞✉❝❡❞ ♣❛rt✐❝✉❧❛r❧② ❢♦r ❇■◆●❖✳
●✐✈❡♥ t❤❡s❡ ❛❞✈❛♥t❛❣❡s✱ ❲P✷ ❧❡❛❞❡rs ❞❡❝✐❞❡❞ t♦ ❞❡✈❡❧♦♣ ❛ ❤②❜r✐❞ ❛♣♣❧✐❝❛t✐♦♥ ✭❝♦♠♠❛♥❞✲❧✐♥❡✲✐♥t❡r❢❛❝❡ ❛♥❞ ✇❡❜✲❜❛s❡❞✮ t♦ ❡①tr❛❝t t❤❡ ❞❛t❛ ♥❡❡❞❡❞ ❢♦r t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡s✱ ♣♦st✲♣r♦❝❡ss ❛♥❞ ❝♦♥✈❡rt ✐t t♦ t❤❡ ♥❡❡❞s ♦❢ ❛❧❧ ✐♥❞✐✈✐❞✉❛❧ ♠♦❞❡❧✐♥❣ ❣r♦✉♣s✳ ❚❤❡s❡ ❝♦♥✈❡rs✐♦♥r♦✉t✐♥❡s ❝❛♥ ❛❧s♦ ❜❡ ❛❞❛♣t❡❞ t♦ ✐♥❝♦r♣♦r❛t❡ ♥❡✇ ♠♦❞❡❧s ♦r t♦ ❝❤❛♥❣✐♥❣ ♥❡❡❞s ♦❢ ❡①✐st✐♥❣♠♦❞❡❧s✳ ❋✉rt❤❡r♠♦r❡✱ ✉s❡rs ❝❛♥ ❛❧s♦ ❣❡t ❜❛❝❦ t♦ ❞❛t❛ ❣❡♥❡r❛t❡❞ ❡❛r❧✐❡r ❛♥❞ ❡①tr❛❝t t❤❡s❡✉s✐♥❣✱ ❡✳❣✳✱ ❛ ♥❡✇ ❜✐❛s ❝♦rr❡❝t✐♦♥ ♠❡t❤♦❞ ♦r ❛ s❧✐❣❤t❧② ❝❤❛♥❣❡❞ ❝♦♥✈❡rs✐♦♥ r♦✉t✐♥❡✳ ❆❞✲❞✐t✐♦♥❛❧❧② t♦ ❡✣❝✐❡♥t❧② ❛r❝❤✐✈✐♥❣ ❝❧✐♠❛t❡ ❞❛t❛ ✐♥ ❛ ❝❡♥tr❛❧ ♣❧❛❝❡✱ t❤❡ ♣❧✉❣✲✐♥ ❞❡✈❡❧♦♣❡rs✐♥ ❲P✷ ✉s❡ ❣✐t✶ t♦ ❡♥s✉r❡s ❛ ♣r♦♣❡r ✈❡rs✐♦♥✐♥❣ ♦❢ t❤❡ ❜✐❛s ❝♦rr❡❝t✐♦♥ ❛♥❞ ❝♦♥✈❡rs✐♦♥❛❧❣♦r✐t❤♠s✳
❉✉r✐♥❣ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ♣❧✉❣✲✐♥ ❝♦♠♠❡♥ts ✇❡r❡ r❡q✉❡st❡❞ ❞✐r❡❝t❧② ❢r♦♠ t❤❡♠♦❞❡❧✐♥❣ ❣r♦✉♣s ❛t t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡✳ ❍②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧❡rs ✇❡r❡ ❛❧s♦ ❛s❦❡❞ t♦ t❡st t❤❡♦✉t♣✉t ♦❢ t❤❡ ♣❧✉❣✲✐♥ ✇✐t❤ t❤❡✐r ♠♦❞❡❧s ❛♥❞ r❡✈✐❡✇ t❤❡ ♣❧✉❣✲✐♥ ❞✉r✐♥❣ ❞❡✈❡❧♦♣♠❡♥t✳ ❆s❢♦r ❛❧❧ ♣✐❡❝❡s ♦❢ s♦❢t✇❛r❡✱ ❛❧s♦ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❉❊❈❖ ✐s ♥♦t ✜♥✐s❤❡❞ ❜✉t ♦♣❡♥ t♦ ❜❡✐♥❣❝♦♥t✐♥✉❡❞✳ ❈♦♥✈❡rs✐♦♥ r♦✉t✐♥❡s ❢♦r ♦t❤❡r ♠♦❞❡❧s ❝♦✉❧❞ ❜❡ ✐♥t❡❣r❛t❡❞✱ ❛s ✇❡❧❧ ❛s ♥❡✇ ❜✐❛s❝♦rr❡❝t✐♦♥ s❝❤❡♠❡s✳
❚❤✐s ❞♦❝✉♠❡♥t ❞❡s❝r✐❜❡s t❤❡ ❞❛t❛ ❣❡♥❡r❛t❡❞ ✇✐t❤ t❤❡ ❈❖❙▼❖✲❈▲▼ ❞r✐✈❡♥ ❜② ❊❘❆✲■♥t❡r✐♠ ✭❙❡❝t✳ ✷✮✱ t❤❡ ❜✐❛s ❝♦rr❡❝t✐♦♥ ✉s❡❞ ✭❙❡❝t✳ ✸✮ ❛♥❞ t❤❡ ❡①tr❛❝t✐♦♥ ❛♥❞ ❝♦♥✈❡rs✐♦♥❛❧❣♦r✐t❤♠s ❢♦r t❤❡ ✐♥❞✐✈✐❞✉❛❧ ♠♦❞❡❧s ❛t t❤❡ r❡s❡❛r❝❤ ❙✐t❡s ✭❙❡❝t✳ ✹✮✳
✶❤tt♣s✿✴✴❡♥✳✇✐❦✐♣❡❞✐❛✳♦r❣✴✇✐❦✐✴●✐t❴✪✷✽s♦❢t✇❛r❡✪✷✾
✼
❈❤❛♣t❡r ✷
❉❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❝❧✐♠❛t❡
s✐♠✉❧❛t✐♦♥s
❆❧❧ s✐♠✉❧❛t✐♦♥s ❞❡s❝r✐❜❡❞ ✐♥ t❤✐s ❝❤❛♣t❡r ❤❛✈❡ ❜❡❡♥ ❝❛rr✐❡❞ ♦✉t ✉s✐♥❣ t❤❡ ❈❖❙▼❖✲❈▲▼r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧ ✭❘♦❝❦❡❧ ❡t ❛❧✳✱ ✷✵✵✽✮✱ ❢♦r ❛ ❞♦♠❛✐♥ ❝❡♥tr❡❞ ♦✈❡r ❊✉r♦♣❡✳ ■♥ t❤✐s❝❤❛♣t❡r✱ ❛ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❈❖❙▼❖✲❈▲▼ r❡❣✐♦♥❛❧ ♠♦❞❡❧ ✐s ♣r♦✈✐❞❡❞✱ ❢♦❧❧♦✇❡❞ ❜② ❞❡t❛✐❧s♦❢ t❤❡ s✐♠✉❧❛t✐♦♥s ♣❡r❢♦r♠❡❞✳
✷✳✶ ▼♦❞❡❧ ❉❡s❝r✐♣t✐♦♥
❚❤❡ ❈❖❙▼❖✲❈▲▼ ✭❈❈▲▼✮ ✐s ❛ st❛t❡✲♦❢✲t❤❡✲❛rt ♥♦♥❤②❞r♦st❛t✐❝ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧✱t❤❛t ✐s t❤❡ ❝❧✐♠❛t❡ ✈❡rs✐♦♥ ♦❢ t❤❡ ❈❖❙▼❖ ♥✉♠❡r✐❝❛❧ ✇❡❛t❤❡r ♣r❡❞✐❝t✐♦♥ ♠♦❞❡❧ ✉s❡❞❜② t❤❡ ●❡r♠❛♥ ❲❡❛t❤❡r ❙❡r✈✐❝❡ ✭❉❲❉✮✳ ❈❈▲▼ ✐s ❞❡✈❡❧♦♣❡❞ ❢♦r ❝❧✐♠❛t❡ ♣✉r♣♦s❡s ❜②t❤❡ ❈▲▼✲❈♦♠♠✉♥✐t② ✭❤tt♣✿✴✴✇✇✇✳❝❧♠✲❝♦♠♠✉♥✐t②✳❡✉✴✮ ❛♥❞ ❢❡❛t✉r❡s ❛ s♦❢t✇❛r❡ ❛r❝❤✐✲t❡❝t✉r❡ ❛❧❧♦✇✐♥❣ ❢♦r ❝♦♠♣✉t❛t✐♦♥❛❧ ♣❛r❛❧❧❡❧✐s♠ ❛♥❞ s②st❡♠ ❡①t❡♥s✐❜✐❧✐t②✳ ■t ✐s s✉✐t❛❜❧❡❢♦r ❛ ❜r♦❛❞ s♣❡❝tr✉♠ ♦❢ ❛♣♣❧✐❝❛t✐♦♥s ❛❝r♦ss s❝❛❧❡s r❛♥❣✐♥❣ ❢r♦♠ ❤✉♥❞r❡❞s ♦❢ ♠❡tr❡s t♦t❤♦✉s❛♥❞s ♦❢ ❦✐❧♦♠❡tr❡s✳ ❚❤❡ ♠♦❞❡❧ ❝♦♠♣♦♥❡♥ts ✐♥❝❧✉❞❡ ❛♥ ❛t♠♦s♣❤❡r✐❝ ♠♦❞❡❧ ❞✐r❡❝t❧②❝♦✉♣❧❡❞ t♦ ❛ ❧❛♥❞✲s✉r❢❛❝❡✴s♦✐❧ ♠♦❞❡❧✱ ❛♥❞ ❛♥ ❛❡r♦s♦❧ ♠♦❞❡❧✳ ❙❡❛ s✉r❢❛❝❡ t❡♠♣❡r❛t✉r❡s♠✉st ❜❡ ♣r❡s❝r✐❜❡❞ ❛s ❛ ❜♦✉♥❞❛r② ❝♦♥❞✐t✐♦♥✳
✷✳✷ ❉❡s❝r✐♣t✐♦♥ ♦❢ ❙✐♠✉❧❛t✐♦♥s
✷✳✷✳✶ ❘❡❛♥❛❧②s✐s✲❢♦r❝❡❞ ❡✈❛❧✉❛t✐♦♥ r✉♥s
❚♦ ❝r❡❛t❡ ❛ ❝❧✐♠❛t♦❧♦❣② ❛♥❞ ❝♦♥t✐♥✉♦✉s t✐♠❡ s❡r✐❡s ♦❢ ❦❡② ❤②❞♦r♦❧♦❣✐❝❛❧ ✈❛r✐❛❜❧❡s✱ ❞♦✇♥✲s❝❛❧✐♥❣ s✐♠✉❧❛t✐♦♥s ❤❛✈❡ ❜❡❡♥ ❝❛rr✐❡❞ ♦✉t ✇✐t❤ t❤❡ ❈❈▲▼ ♦✈❡r t❤❡ ❊❯❘❖✲❈❖❘❉❊❳❞♦♠❛✐♥ ✭❋✐❣✳ ✷✳✶✮✱ ✇✐t❤ ❛ ❤♦r✐③♦♥t❛❧ r❡s♦❧✉t✐♦♥ ♦❢ ✵✳✶✶➦ ✭❛❜♦✉t ✶✷❦♠✮ ❛♥❞ s♣❛♥♥✐♥❣ t❤❡t✐♠❡ ♣❡r✐♦❞ ✶✾✼✾✲✷✵✶✺✳ ❆t t❤❡ ❞♦♠❛✐♥ ❧❛t❡r❛❧ ❜♦✉♥❞❛r✐❡s✱ t❤❡ ♠♦❞❡❧ ✐s ❝♦♥str❛✐♥❡❞ ❜②t❤❡ ❧❛t❡st ❣❡♥❡r❛t✐♦♥ ♦❢ r❡❛♥❛❧②s❡s ❢r♦♠ t❤❡ ❊✉r♦♣❡❛♥ ❈❡♥tr❡ ❢♦r ▼❡❞✐✉♠✲r❛♥❣❡ ❲❡❛t❤❡r❋♦r❡❝❛st✐♥❣✱ ❊❘❆✲■♥t❡r✐♠ ✭❉❡❡ ❡t ❛❧✳✱ ✷✵✶✶✮✱ ✇❤✐❝❤ ♣r♦✈✐❞❡ ✉♣❞❛t❡❞ ❧❛t❡r❛❧ ❜♦✉♥❞❛r②❝♦♥❞✐t✐♦♥s ❡✈❡r② ✻ ❤♦✉rs✳ ❚❤❡ ❡♥t✐r❡ ♣❡r✐♦❞ ❝♦✈❡r❡❞ ❜② t❤❡ ❊❘❆✲■♥t❡r✐♠ r❡❛♥❛❧②s✐s ❤❛s
✽
❜❡❡♥ ❞♦✇♥s❝❛❧❡❞ ✭✶✾✼✾✲✷✵✶✺✮✳ ■♥✐t✐❛❧ ❝♦♥❞✐t✐♦♥s✱ s❡❛ s✉r❢❛❝❡ t❡♠♣❡r❛t✉r❡✱ ❛♥❞ s❡❛✲✐❝❡❝♦✈❡r ❛❧s♦ ❝♦♠❡ ❢r♦♠ t❤❡ ❊❘❆✲■♥t❡r✐♠ r❡❛♥❛❧②s✐s✳
❋✐❣✉r❡ ✷✳✶✿ ❊❯❘❖✲❈❖❘❉❊❳ ❉♦♠❛✐♥✳ ❚❤❡ ❊❯❘❖✲❈❖❘❉❊❳ ❞♦♠❛✐♥ ✐s ❛ st❛♥❞❛r❞ r❡❢❡r❡♥❝❡❞♦♠❛✐♥ ❢♦r ❊✉r♦♣❡ ❞❡✜♥❡❞ ❛s ♣❛rt ♦❢ t❤❡ ❈❖❘❉❊❳ ❊①♣❡r✐♠❡♥t ✭❤tt♣✿✴✴✇✇✇✳❝♦r❞❡①✳♦r❣✴✮✳
❈♦♠♣✉t❛t✐♦♥❛❧ ❧✐♠✐t❛t✐♦♥s ♣r♦❤✐❜✐t s✐♠✉❧❛t✐♦♥ ❛t t❤❡ ❦✐❧♦♠❡tr❡✲s❝❛❧❡ ♦✈❡r s✉❝❤ ❛ ❧❛r❣❡❞♦♠❛✐♥ ❛♥❞ t✐♠❡ ♣❡r✐♦❞✳ ❆ ❤♦r✐③♦♥t❛❧ r❡s♦❧✉t✐♦♥ ♦❢ ✵✳✶✶➦ ❤❛s t❤✉s ❜❡❡♥ ❝❤♦s❡♥✱ ✇❤✐❝❤r❡♣r❡s❡♥ts s♦♠❡✇❤❛t ♦❢ ❛ ✏❜r❡❛❦t❤r♦✉❣❤✑ r❡s♦❧✉t✐♦♥ ❛♥❞ ❤❛s ❜❡❡♥ s❤♦✇♥ t♦ ❛❞❞ s✐❣♥✐✜❝❛♥t✈❛❧✉❡ t♦ ❝♦❛rs❡r ❣❧♦❜❛❧ ♠♦❞❡❧ ♦✉t♣✉t ❢♦r t❤❡ s✐♠✉❧❛t✐♦♥ ♦❢ ✭♥♦♥✲❝♦♥✈❡❝t✐✈❡✮ ♣r❡❝✐♣✐t❛t✐♦♥❡①tr❡♠❡s ✭❍❡✐❦❦✐❧ä✳ ❡t ❛❧✳✱ ✷✵✶✶✮✱ ♣❛rt✐❝✉❧❛r❧② ✐♥ ♠♦✉♥t❛✐♥♦✉s r❡❣✐♦♥s✱ ❛♥❞ ❝❛♥ ♠♦❞✉❧❛t❡t❤❡ ❝❧✐♠❛t❡ ❝❤❛♥❣❡ s✐❣♥❛❧ ♦❢ ❝♦❛rs❡ r❡s♦❧✉t✐♦♥ ❣❧♦❜❛❧ ♠♦❞❡❧s ✭❚♦r♠❛ ❡t ❛❧✳✱ ✷✵✶✺✮✳
❚❤❡ s✐♠✉❧❛t✐♦♥s ❤❛✈❡ ❜❡❡♥ ❝❛rr✐❡❞ ♦✉t ✈✐❛ t❤r❡❡ s❡♣❛r❛t❡ ♠♦❞❡❧ r✉♥s✱ ❡❛❝❤ ♦❢ ✇❤✐❝❤ ✐s❝♦♥t✐♥✉♦✉s ❞✉r✐♥❣ t❤❡ t✐♠❡ ♣❡r✐♦❞ ✐♥❞✐❝❛t❡❞ ✐♥ ❚❛❜ ✷✳✶ ✭♠✐❞❞❧❡ ❝♦❧✉♠♥✮✳ ❘✉♥s ✶ ❛♥❞ ✸✇❡r❡ ❝❛rr✐❡❞ ♦✉t ❛t t❤❡ ❋r❡✐❡ ❯♥✐✈❡rs✐tät ❇❡r❧✐♥❀ r✉♥ ✷ ❤❛❞ ♣r❡✈✐♦✉s❧② ❜❡❡♥ ❝❛rr✐❡❞ ♦✉t ❜②t❤❡ ❈▲▼ ❝♦♠♠✉♥✐t②✱ ❛♥❞ ✇❡ ✉t✐❧✐s❡ t❤✐s t♦ ❦❡❡♣ ❝♦♠♣✉❛t✐♦♥❛❧ ❡①♣❡♥s❡ t♦ ❛ ♠✐♥✐♠✉♠✳❲✐t❤✐♥ ❡❛❝❤ ♠♦❞❡❧ r✉♥✱ ✐t ✐s ♥❡❝❡ss❛r② t♦ ❛❧❧♦✇ s✉✣❝✐❡♥t t✐♠❡ ❛❢t❡r ✐♥✐t✐❛❧✐s❛t✐♦♥ ❢♦r t❤❡s♣✐♥✲✉♣ ♦❢ s♦✐❧ ♠♦✐st✉r❡ ❛♥❞ s♦✐❧✲r❡❧❛t❡❞ ♣r♦❝❡ss❡s ✇✐t❤✐♥ t❤❡ ❤✐❣❤❡r r❡s♦❧✉t✐♦♥ ❈❈▲▼✳ ■♥❡❛❝❤ r✉♥✱ ❛ ♠✐♥✐♠✉♠ ♦❢ t✇♦ ♠♦♥t❤s ✐s ❛❧❧♦✇❡❞ ❢♦r s♣✐♥✲✉♣✳ ▼♦❞❡❧ ♦✉t♣✉t ❢r♦♠ t❤✐s ♣❡r✐♦❞✐s t❤✉s ♥♦t ✐♥❝❧✉❞❡❞ ✐♥ t❤❡ ✜♥❛❧ ❞❛t❛✱ ✐✳❡✳ t❤❡ ❞❛t❛ t♦ ❜❡ ✉s❡❞ ❢♦r r❡s❡❛r❝❤ ♣✉r♣♦s❡s✳ ❚❤❡✜♥❛❧ ❞❛t❛ t❤✉s ❝♦✈❡rs t❤❡ ♣❡r✐♦❞ ▼❛r❝❤ ✶✾✼✾ ✲ ❏✉❧② ✷✵✶✺✱ s✉♠♠❛r✐s❡❞ ✐♥ ❚❛❜ ✷✳✶ ✭r✐❣❤t❝♦❧✉♠♥✮✳ ❚❤❡ ♠♦❞❡❧ ♦✉t♣✉t ❝❛♥ ❜❡ ❡①t❡♥❞❡❞ ❜❡②♦♥❞ ❏✉❧② ✷✵✶✺ ✐❢ t❤❡r❡ ✐s ❛❣r❡❡♠❡♥t❛♠♦♥❣st ♣r♦❥❡❝t ♣❛rt♥❡rs ❛♥❞ ✐❢ r❡❛♥❛❧②s✐s ❞❛t❛ ❢♦r t❤❛t ♣❡r✐♦❞ ✐s ❛✈❛✐❧❛❜❧❡✳
❋♦r ♠♦st ❦❡② ❇■◆●❖ ✈❛r✐❛❜❧❡s✱ ✵✳✶✶➦ ❈❈▲▼ ♦✉t♣✉t ✐s ❛✈❛✐❧❛❜❧❡ ❛t ✸✲❤♦✉r❧② ❢r❡q✉❡♥❝②✳❚❤❡ ❡①❝❡♣t✐♦♥ t♦ t❤✐s ✐s ♣r❡❝✐♣✐t❛t✐♦♥✱ ✇❤✐❝❤ ✐s ❛✈❛✐❧❛❜❧❡ ❛t ❤♦✉r❧② ❢r❡q✉❡♥❝②✳ ❇■◆●❖✈❛r✐❛❜❧❡s ❛✈❛✐❧❛❜❧❡ ❛♥❞ t❤❡✐r t❡♠♣♦r❛❧ ❢r❡q✉❡♥❝✐❡s ❛r❡ s✉♠♠❛r✐s❡❞ ✐♥ ❚❛❜❧❡ ✷✳✷✳
✾
▼♦❞❡❧ ❘✉♥ P❡r✐♦❞ ♦❢ ❘✉♥ ❉❛t❛ ❆✈❛✐❧❛❜❧❡✶ ✵✶✳✵✶✳✶✾✼✾ ✲ ✵✶✳✵✹✳✶✾✽✾ ✵✶✳✵✸✳✶✾✼✾ ✲ ✵✶✳✵✸✳✶✾✽✾
✷ ✵✶✳✵✶✳✶✾✽✾ ✲ ✵✶✳✵✶✳✷✵✵✾ ✵✶✳✵✸✳✶✾✽✾ ✲ ✵✶✳✶✷✳✷✵✵✾
✸ ✵✶✳✵✾✳✷✵✵✽ ✲ ✵✶✳✵✽✳✷✵✶✺ ✵✶✳✶✷✳✷✵✵✾ ✲ ✵✶✳✵✽✳✷✵✶✺
❚❛❜❧❡ ✷✳✶✿ ▲✐st ♦❢ ♠♦❞❡❧ r✉♥s✳
✷✳✷✳✷ ❍✐❣❤✲r❡s♦❧✉t✐♦♥ ✭t❡st✮ s✐♠✉❧❛t✐♦♥s ♦❢ ❡①tr❡♠❛❧ ❡♣✐s♦❞❡s
❚❤❡♦r② ❛♥❞ ▼❡t❤♦❞s
❊①tr❡♠❛❧ ✇❡❛t❤❡r ♣❛tt❡r♥s ❛♥❞ ✐♥❞✐✈✐❞✉❛❧ ❡✈❡♥ts ♦❢ ❤②❞r♦❧♦❣✐❝❛❧ s✐❣♥✐✜❝❛♥❝❡ s❤❛❧❧ ❜❡✐❞❡♥t✐✜❡❞ ❢r♦♠ t❤❡ ✵✳✶✶➦ ❈❈▲▼ s✐♠✉❧❛t✐♦♥s✱ ❢♦r ❡❛❝❤ ♦❢ t❤❡ ✻ r❡s❡❛r❝❤ s✐t❡s✳ ❚❤❡s❡ s❤❛❧❧❜❡ s✉❜❥❡❝t❡❞ t♦ ♠♦r❡ ❞❡t❛✐❧❡❞ ❛♥❛❧②s✐s✳ ■♥ t❤❡ ❝❛s❡ ♦❢ ❡①tr❡♠❡ ♣r❡❝✐♣✐t❛t✐♦♥ ❡✈❡♥ts✱ ✇❤✐❝❤❛r❡ ❛ ♣❤❡♥♦♠❡♥♦♥ ✇✐t❤ ❤✐❣❤ s♣❛t✐❛❧ ✈❛r✐❛❜✐❧✐t②✱ t❤✐s ✐♥✈♦❧✈❡s ❢✉rt❤❡r ❞②♥❛♠✐❝ ❞♦✇♥s❝❛❧✐♥❣♦❢ t❤❡ ✐❞❡♥t✐✜❡❞ ❡✈❡♥ts ✉♣ t♦ ❛ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ r❡s♦❧✉t✐♦♥ ♦❢ ✵✳✵✷➦ ✭✷✳✷ ❦♠✮ t♦ ♣r♦✲✈✐❞❡ ❜❡tt❡r r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ❞②♥❛♠✐❝s ❞r✐✈✐♥❣ ❛♥② ❝❤❛♥❣❡s ✐♥ ❤②❞r♦❧♦❣✐❝❛❧ ❡①tr❡♠❡s❛♥❞ ❤❡♥❝❡ ❛ ♠♦r❡ ❞❡t❛✐❧❡❞ ✐♥♣✉t ❢♦r t❤❡ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✳ ■♥ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣s✐♠✉❧❛t✐♦♥s✱ ❞❡❡♣ ❝♦♥✈❡❝t✐✈❡ ♣r♦❝❡ss❡s ❝❛♥ ❜❡ ❡①♣❧✐❝✐t❧② s✐♠✉❧❛t❡❞ ❜② t❤❡ ♠♦❞❡❧✱ ✇❤❡r❡t❤❡② ❤❛✈❡ t♦ ❜❡ ♦t❤❡r✇✐s❡ ♣❛r❛♠❡tr✐③❡❞ ✐♥ ❧♦✇❡r✲r❡s♦❧✉t✐♦♥ s✐♠✉❧❛t✐♦♥s✱ ✐✳❡✳ ♦✉r ✵✳✶✶➦❈❈▲▼ ✐♥t❡❣r❛t✐♦♥✳ ❚❤❡ ❢✉rt❤❡r ❞♦✇♥s❝❛❧✐♥❣ t♦ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ r❡s♦❧✉t✐♦♥ ✐s ❛ ❦❡②st❡♣✱ ❛s r❡❝❡♥t st✉❞✐❡s ❤❛✈❡ s❤♦✇♥ t❤❛t ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ r❡s♦❧✉t✐♦♥ ✐s ❡ss❡♥t✐❛❧ t♦❛❝❝✉r❛t❡❧② ❝❛♣t✉r❡ t❤❡ r❡s♣♦♥s❡ ♦❢ ❝♦♥✈❡❝t✐✈❡ ♣r❡❝✐♣✐t❛t✐♦♥ ❡①tr❡♠❡s t♦ ❝❧✐♠❛t✐❝ ❝❤❛♥❣❡s✭❑❡♥❞♦♥ ❡t ❛❧✳✱ ✷✵✶✹❀ ❇❛♥ ❡t ❛❧✳✱ ✷✵✶✺✮✱ ✇❤✐❝❤ ❝❛♥ ❜❡ ❤✐❣❤❧② ♥♦♥❧✐♥❡❛r ✭▼❡r❡❞✐t❤ ❡t ❛❧✳✱✷✵✶✺✮✳
❚❤❡ ✐ss✉❡ ♦❢ s♣❛t✐❛❧ s♣✐♥✉♣ ✲ ♠❡❛♥✐♥❣ t❤❡ ❞✐st❛♥❝❡ ❢r♦♠ t❤❡ ❧❛t❡r❛❧ ❜♦✉♥❞❛r✐❡s ❛t ✇❤✐❝❤✜♥❡✲s❝❛❧❡ ❢❡❛t✉r❡s ❝❛♥ ❜❡ ❛❝❤✐❡✈❡❞ ✲ ✐s ❛♥ ✐♠♣♦rt❛♥t ❝♦♥s✐❞❡r❛t✐♦♥ ✇❤❡♥ ❞❡s✐❣♥✐♥❣ r❡✲❣✐♦♥❛❧ ❞♦✇♥s❝❛❧✐♥❣ ❡①♣❡r✐♠❡♥ts✳ ❋♦r ❝♦♥s✐st❡♥❝②✱ ✇❡ ✐♥t❡♥❞ t♦ ✉s❡ ❛ ❝♦♠♠♦♥ ❞♦♠❛✐♥ ❢♦r❛❧❧ ❤✐❣❤✲r❡s♦❧✉t✐♦♥ s✐♠✉❧❛t✐♦♥s ❛t ❡❛❝❤ r❡s❡❛r❝❤ s✐t❡✳ ❆s t❤❡ ❧❛r❣❡✲s❝❛❧❡ ❢♦r❝✐♥❣ ❜❡❤✐♥❞✐♥❞✐✈✐❞✉❛❧ ❡①tr❡♠❡s ❝❛♥ ❝♦♠❡ ❢r♦♠ ❛♥② s✐❞❡ ♦❢ t❤❡ ❞♦♠❛✐♥✱ ✇❡ ❝❡♥tr❡ ♦✉r ❤✐❣❤✲r❡s♦❧✉t✐♦♥❞♦♠❛✐♥s ♦✈❡r ❡❛❝❤ r❡s❡❛r❝❤ s✐t❡ ❛♥❞ ✉s❡ ❛ ✷✵✶ ① ✷✵✶ ❣r✐❞✱ ✇✐t❤ ✺✵ ✈❡rt✐❝❛❧ ❧❡✈❡❧s✳ ❚❤✐s❛❧❧♦✇s ❛t ❧❡❛st ✶✵✵ ❣r✐❞✲❧❡♥❣t❤s ❜❡t✇❡❡♥ t❤❡ ❧❛t❡r❛❧ ❜♦✉♥❞❛r✐❡s ❛♥❞ t❤❡ ❝❡♥tr❡ ♦❢ ❡❛❝❤r❡s❡❛r❝❤ s✐t❡✳ ❇r✐ss♦♥ ❡t ❛❧✳ ✭✷✵✶✺✮ ✐♥✈❡st✐❣❛t❡❞ t❤❡ ✐♠♣❛❝t ♦❢ ❞♦♠❛✐♥ s✐③❡ ♦♥ t❤❡ s✐♠✉❧❛✲t✐♦♥ ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ✐♥ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ ♠♦❞❡❧s✱ ✉s✐♥❣ ❛ ❤♦r✐③♦♥t❛❧ ❣r✐❞ s♣❛❝✐♥❣ ♦❢✸ ❦♠✳ ❚❤❡② ❝♦♥❝❧✉❞❡❞ t❤❛t ❛ s♣❛t✐❛❧ s♣✐♥✉♣ ♦❢ ❛t ❧❡❛st ✹✵ ❣r✐❞ ❝❡❧❧s ✐s ♥❡❝❡ss❛r② ❢♦r t❤❡r❡❛❧✐st✐❝ s✐♠✉❧❛t✐♦♥ ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ♣❛tt❡r♥s✳ ❋♦r ♠♦r❡ ❞❡t❛✐❧❡❞ ❞✐s❝✉ss✐♦♥ ♦❢ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ ♠♦❞❡❧❧✐♥❣ t❤❡ r❡❛❞❡r ✐s r❡❢❡rr❡❞ t♦ Pr❡✐♥ ❡t ❛❧✳ ✭✷✵✶✺✮✳
❚❤❡ ❙✐♠✉❧❛t✐♦♥s
❲✐t❤ t❤❡ ❛✐❞ ♦❢ t❤❡ q✉❡st✐♦♥♥❛✐r❡ r❡s♣♦♥s❡s ❢r♦♠ ❡❛❝❤ r❡s❡❛r❝❤ s✐t❡✱ ♦♥❡ ❡①tr❡♠❡ ♣r❡✲❝✐♣✐t❛t✐♦♥ ❡✈❡♥t ❤❛s ❜❡❡♥ ✐❞❡♥t✐✜❡❞ ❢r♦♠ t❤❡ ✵✳✶✶➦✲❈❈▲▼ s✐♠✉❧❛t✐♦♥s ❢♦r ❡❛❝❤ s✐t❡
✶✵
❱❛r✐❛❜❧❡❉❡s❝r✐♣t✐♦♥
❱❛r✐❛❜❧❡■❉
❋r❡q✉❡♥❝②
❚✐♠
❡▼❡t❤♦❞✯
▼✐♥✴▼❛①❸
❚♦t❛❧❈❧♦✉❞❋r❛❝t✐♦♥
❝❧t
✸✲❤r✱❞❛②
■♥st❛♥t❛♥❡♦✉s
❉❛✐❧②
◆❡❛r✲❙✉r❢❛❝❡❘❡❧❛t✐✈❡❍✉♠✐❞✐t②
❤✉rs
✸✲❤r✱❞❛②
■♥st❛♥t❛♥❡♦✉s
❉❛✐❧②
◆❡❛r✲❙✉r❢❛❝❡❙♣❡❝✐✜❝❍✉♠✐❞✐t②
❤✉ss
✸✲❤r✱❞❛②
■♥st❛♥t❛♥❡♦✉s
❉❛✐❧②
Pr❡❝✐♣✐t❛t✐♦♥
♣r
✶✲❤r✱✸✲❤r✱❞❛②
▼❡❛♥
❉❛✐❧②
❙✉r❢❛❝❡❆✐rPr❡ss✉r❡
♣s
✸✲❤r✱❞❛②
■♥st❛♥t❛♥❡♦✉s
❉❛✐❧②
❙❡❛
▲❡✈❡❧Pr❡ss✉r❡
♣s❧
✸✲❤r✱❞❛②
■♥st❛♥t❛♥❡♦✉s
❉❛✐❧②
❙✉r❢❛❝❡❉♦✇
♥✇❡❧❧✐♥❣▲♦♥❣✇
❛✈❡❘❛❞✐❛t✐♦♥
r❧❞s
✸✲❤r✱❞❛②
▼❡❛♥
❉❛✐❧②
❙✉r❢❛❝❡❉♦✇
♥✇❡❧❧✐♥❣❙❤♦rt✇❛✈❡❘❛❞✐❛t✐♦♥
rs❞s
✸✲❤r✱❞❛②
▼❡❛♥
❉❛✐❧②
◆❡❛r✲❙✉r❢❛❝❡❲✐♥❞❙♣❡❡❞
s❢❝❲
✐♥❞
✸✲❤r✱❞❛②
■♥st❛♥t❛♥❡♦✉s
❉❛✐❧②
◆❡❛r✲❙✉r❢❛❝❡❆✐r❚❡♠
♣❡r❛t✉r❡
t❛s
✸✲❤r✱❞❛②
■♥st❛♥t❛♥❡♦✉s
❉❛✐❧②
◆❡❛r✲❙✉r❢❛❝❡❉❡✇
P♦✐♥t❚❡♠
♣❡r❛t✉r❡
t❞♣s
✸✲❤r✱❞❛②
■♥st❛♥t❛♥❡♦✉s
❉❛✐❧②
❊❛st✇❛r❞◆❡❛r✲❙✉r❢❛❝❡❲✐♥❞
✉❛s
✸✲❤r✱❞❛②
■♥st❛♥t❛♥❡♦✉s
❉❛✐❧②
◆♦rt❤✇❛r❞◆❡❛r✲❙✉r❢❛❝❡❲✐♥❞
✈❛s
✸✲❤r✱❞❛②
■♥st❛♥t❛♥❡♦✉s
❉❛✐❧②
❚❛❜❧❡
✷✳✷✿❇■◆
●❖
❱❛r✐❛❜❧❡s✳
✯❚✐♠
❡♠❡t❤♦❞r❡❢❡rs
t♦t❤❡❤✐❣❤❡st❢r❡q✉❡♥
❝②❞❛t❛❀
❞❛✐❧②
♠❡❛♥s❛r❡❝❛❧❝✉❧❛t❡❞❜②❛✈❡r❛❣
✐♥❣t❤❡❤✐❣❤❡st
❢r❡q✉❡♥
❝②❞❛t❛✳
❸❱❛r✐❛❜❧❡
■❉s❢♦r❞❛✐❧②
♠✐♥✴♠
❛①❛r❡❢♦r♠
❡❞❜②❛♣
♣❡♥
❞✐♥❣❡✐t❤❡r
✬♠✐♥✬♦r
✬♠❛①
✬t♦
t❤❡✈❛r✐❛❜
❧❡■❉
✱❡✳❣✳
❝❧t❬♠✐♥⑤♠
❛①❪✳
❆✏❞❛②
✑✐s
❞❡✜
♥❡❞
❛s✷✹
✲❤♦✉
rs❢r♦♠
✵✵✿✵✵❯❚❈✳❆❧❧t✐♠❡✲st❛♠
♣s✐♥
t❤❡♦✉
t♣✉t❞❛t❛❛r❡✐♥
❯❚❈✳
✶✶
✭❡①❝❧✉❞✐♥❣ ❈②♣r✉s✮✱ ❛♥❞ ❤❛s ❜❡❡♥ ❢✉rt❤❡r ❞♦✇♥s❝❛❧❡❞ t♦ ✵✳✵✷➦ r❡s♦❧✉t✐♦♥ ✭✷✳✷ ❦♠✮ ✇✐t❤t❤❡ ❈❈▲▼✳ ❚❤❡ ❡✈❡♥ts ❢♦r t❤❡s❡ t❡st✲s✐♠✉❧❛t✐♦♥s ✇❡r❡ s✉❜❥❡❝t✐✈❡❧② ✐❞❡♥t✐✜❡❞ ❢r♦♠ t❤❡✵✳✶✶➦ ❞❡❣r❡❡ ♠♦❞❡❧ ♦✉t♣✉t✱ ❜❛s❡❞ ♦♥ t❤❡ q✉❡st✐♦♥♥❛✐r❡ ❞❡s❝r✐♣t✐♦♥s ♦❢ ♣❛st ❡①tr❡♠❡s ❛t❡❛❝❤ s✐t❡ ❛♥❞ t❤❡ ✵✳✶✶➦ ♠♦❞❡❧❧❡❞ ♣r❡❝✐♣✐t❛t✐♦♥✳
❚❤❡ ♦✉t♣✉t ✈❛r✐❛❜❧❡s ❛r❡ ❛t ❛♥ ❤♦✉r❧② ❢r❡q✉❡♥❝② ❛♥❞ ❤❛✈❡ ❜❡❡♥ ♠❛❞❡ ❛✈❛✐❧❛❜❧❡ ❢♦r t❤❡s❛♠❡ ♣❛r❛♠❡t❡rs ❛s s❤♦✇♥ ✐♥ ❚❛❜❧❡ ✷✳✷✱ t❤♦✉❣❤ t❤❡r❡ ❛r❡ ♦❜✈✐♦✉s❧② ♥♦ ❞❛✐❧② ♠✐♥✴♠❛①✬s♣r♦✈✐❞❡❞✳ ❆❧❧ ❞❛t❛ ❛r❡ ❛✈❛✐❧❛❜❧❡ t❤r♦✉❣❤ t❤❡ ❋r❡✈❛ ❉❊❈❖ ♣❧✉❣✐♥✱ ❛♥❞ ❛r❡ ❜❡st ❛❝❝❡ss❡❞❜② s❡❧❡❝t✐♥❣ ✏t❡st✲❡✈❡♥ts✑ ✐♥ t❤❡ ❡①♣❡r✐♠❡♥t ✜❡❧❞ ❛♥❞ t❤❡♥ t❤❡ ❛♣♣r♦♣r✐❛t❡ r❡s❡❛r❝❤ s✐t❡✭✐✳❡✳ ❇❛❞❛❧♦♥❛✱ ❇❡r❣❡♥✱ ❚❛❣✉s✱ ❱❡❧✉✇❡✱ ❲✉♣♣❡r✮ ✐♥ t❤❡ ♣r♦❞✉❝t ✜❡❧❞✳ ❆s ♦❢ ✶✵✲✵✻✲✷✵✶✻✱t❤❡ t❡st✲❡✈❡♥ts ❢♦r t❤❡ ❚❛❣✉s r❡s❡❛r❝❤ s✐t❡ ❛r❡ ♥♦t ②❡t ❛✈❛✐❧❛❜❧❡ t❤r♦✉❣❤ t❤❡ ❉❊❈❖ ♣❧✉❣✐♥✳❲❡ ❤♦♣❡ t♦ r❡♠❡❞② t❤✐s ❛s❛♣✱ ❛❢t❡r ❝❧❛r✐❢②✐♥❣ t❤❡ ✐♥♣✉t r❡q✉✐r❡♠❡♥ts ♦❢ t❤❡ ♣❛rt✐❝✉❧❛r❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧ ❜❡✐♥❣ ✉s❡❞ ❢♦r t❤❡ s✐t❡✳
Pr♦❥❡❝t ♣❛rt♥❡rs ❛r❡ ❛s❦❡❞ t♦ ❞♦✇♥❧♦❛❞ t❤❡ ❤✐❣❤✲r❡s♦❧✉t✐♦♥ t❡st✲s✐♠✉❧❛t✐♦♥s ❢♦r t❤❡✐r r❡✲s♣❡❝t✐✈❡ r❡s❡❛r❝❤ s✐t❡s ❛♥❞ t❡st t❤❡ ❞❛t❛ ♦♥ t❤❡✐r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✳ ❋❡❡❞❜❛❝❦ s❤♦✉❧❞t❤❡♥ ❜❡ ♣r♦✈✐❞❡❞ ❛s s♦♦♥ ❛s ♣♦ss✐❜❧❡✳ ❚❤❡ ❡❛r❧✐❡r ❢❡❡❞❛❝❦ ✐s r❡❝❡✐✈❡❞✱ t❤❡ ♠♦r❡ ❧✐❦❡❧② t❤❛t❛♥② ❝♦♥❝❡r♥s r❛✐s❡❞ ❝❛♥ ❜❡ s❛t✐s❢❛❝t♦r✐❧② ❛❞❞r❡ss❡❞✳ ❋❡❡❞❜❛❝❦ ♦♥ t❤❡ t❡st✲s✐♠✉❧❛t✐♦♥s ✐s❜❡st ♣r♦✈✐❞❡❞ t♦ ❊❞♠✉♥❞ ▼❡r❡❞✐t❤ ✭❡❞♠✉♥❞✳♠❡r❡❞✐t❤❅♠❡t✳❢✉✲❜❡r❧✐♥✳❞❡✮✳
✷✳✷✳✸ ▼✐❑❧✐♣ ❢♦r❝❡❞ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥s
❚❤❡ r❡❧❛t✐✈❡❧② ♥❡✇ ✜❡❧❞ ♦❢ ❞❡❝❛❞❛❧ ❝❧✐♠❛t❡ ♣r❡❞✐❝t✐♦♥✱ ❡✳❣✳ ❙♠✐t❤ ❡t ❛❧✳ ✭✷✵✵✼✮✱ ❛✐♠st♦ s✐♠✉❧❛t❡ ❜♦t❤ t❤❡ ❝❧✐♠❛t❡ r❡s♣♦♥s❡ t♦ ❢✉t✉r❡ ❛♥t❤r♦♣♦❣❡♥✐❝ ❢♦r❝✐♥❣ ❛♥❞ t❤❡ ❢✉t✉r❡❡✈♦❧✉t✐♦♥ ✭❢r♦♠ t❤❡ ♣r❡s❡♥t✮ ♦❢ t❤❡ ❝❧✐♠❛t❡ ❞✉❡ t♦ ✐♥t❡r♥❛❧ ❝❧✐♠❛t❡ ✈❛r✐❛❜✐❧✐t② ✭▼❛r♦t③❦❡❡t ❛❧✳✱ ✷✵✶✻✮✳ ❚❤✐s ❞✐✛❡rs ❢r♦♠ t❤❡ ❛♣♣r♦❛❝❤ t❛❦❡♥ ✐♥ ❝❧✐♠❛t❡ ♣r♦❥❡❝t✐♦♥s✱ ❡✳❣✳ t❤❡ ❈▼■P✺♣r♦❥❡❝t ✭❚❛②❧♦r ❡t ❛❧✳✱ ✷✵✶✷✮✱ ✇❤❡r❡ t❤❡ ❢♦❝✉s ✐s ♦♥ t❤❡ r❡s♣♦♥s❡ ♦❢ t❤❡ ❝❧✐♠❛t❡ t♦ ❛♥✲t❤r♦♣♦❣❡♥✐❝ ❢♦r❝✐♥❣ ❛♥❞ t❤❡ ✐♠♣❛❝ts ♦❢ ✐♥t❡r♥❛❧ ❝❧✐♠❛t❡ ✈❛r✐❛❜✐❧✐t② ❛r❡ ✭s✉♣♣♦s❡❞ t♦ ❜❡✮♥✉❧❧✐✜❡❞ ✈✐❛ ♠✉❧t✐✲❞❡❝❛❞❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧ ✐♥t❡❣r❛t✐♦♥s✳ ❚❤❡ ❡❛rt❤ s②st❡♠ ♠♦❞❡❧s ✭❊❙▼s✮✉s❡❞ ✐♥ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥ s②st❡♠s ❛r❡ ✐♥✐t✐❛❧✐③❡❞ ✇✐t❤ ❛♥ ♦❜s❡r✈❡❞ st❛t❡ ♦❢ t❤❡ ❝❧✐♠❛t❡s②st❡♠✱ ✐✳❡✳ ♦❝❡❛♥✱ ❛t♠♦s♣❤❡r❡✱ s♦✐❧✱ ✐❝❡✱ ❡t❝✳ ❙❦✐❧❧ ✐♥ ♣r❡❞✐❝t✐♥❣ ✐♥t❡r♥❛❧ ❝❧✐♠❛t❡ ✈❛r✐❛❜✐❧✲✐t② ♦♥ ❛ ❞❡❝❛❞❛❧ s❝❛❧❡ ✐s ❞❡r✐✈❡❞ ❢r♦♠ t❤❡ ❧♦♥❣✲t❡r♠ ♠❡♠♦r② ✭✐✳❡✳ s❡♥s✐t✐✈✐t② t♦ t❤❡ ✐♥✐t✐❛❧st❛t❡✮ ♦❢ ❝❡rt❛✐♥ ❝♦♠♣♦♥❡♥ts ♦❢ t❤❡ ❝❧✐♠❛t❡ s②st❡♠✱ ♣r❡❞♦♠✐♥❛♥t❧② t❤❡ ♦❝❡❛♥✳ ❆s s✉❝❤✱❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥s ✭✉♥❧✐❦❡ ❝❧✐♠❛t❡ ♣r♦❥❡❝t✐♦♥s✮ ❛r❡ r❡❧✐❛♥t ♦♥ ❛ ❤✐❣❤✲q✉❛❧✐t② ✐♥✐t✐❛❧✐③❛t✐♦♥♦❢ t❤❡ ❊❙▼ ❢♦r t❤♦s❡ ❝♦♠♣♦♥❡♥ts ✇❤✐❝❤ ❡①❤✐❜✐t ❧♦♥❣✲t❡r♠ ♠❡♠♦r②✳
❚❤❡ ▼✐❑❧✐♣ ♣r♦❥❡❝t ✭❤tt♣✿✴✴✇✇✇✳❢♦♥❛✲♠✐❦❧✐♣✳❞❡✮ ✐s ❢✉♥❞❡❞ ❜② t❤❡ ●❡r♠❛♥ ▼✐♥✐str②❢♦r ❊❞✉❝❛t✐♦♥ ❛♥❞ ❘❡s❡❛r❝❤ ✇✐t❤ t❤❡ ❛✐♠ ♦❢ ❞❡✈❡❧♦♣✐♥❣ ❛ ✇♦r❧❞✲❝❧❛ss ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥s②st❡♠✳ ❚❤❡ ▼✐❑❧✐♣ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥ s②st❡♠ ✐s ❜❛s❡❞ ♦♥ t❤❡ ▼❛① P❧❛♥❝❦ ■♥st✐t✉t❡✬s❡❛rt❤ s②st❡♠ ♠♦❞❡❧✱ ▼P■✲❊❙▼✱ ❛♥❞ ❤❛s ❛♥ ❛t♠♦s♣❤❡r✐❝ ❤♦r✐③♦♥t❛❧ r❡s♦❧✉t✐♦♥ ♦❢ ❚✻✸✭✶✳✽✼✺➦✮✳ ❚❤❡ ✜rst ♣❤❛s❡ ♦❢ t❤❡ ▼✐❑❧✐♣ ♣r♦❥❡❝t s❤♦✇❡❞ s✐❣♥✐✜❝❛♥t s❦✐❧❧ ✭❡✳❣✳ ▼✉❡❧❧❡r❡t ❛❧✳ ✭✷✵✶✷✮✱ P♦❤❧♠❛♥♥ ❡t ❛❧✳ ✭✷✵✶✸✮✮ ✐♥ t❤❡ ▼✐❑❧✐♣ s②st❡♠ ❜❛s❡❞ ♦♥ t❤❡ ❡✈❛❧✉❛t✐♦♥♦❢ ❞❡❝❛❞❛❧ ❤✐♥❞❝❛st s✐♠✉❧❛t✐♦♥s ✐♥✐t✐❛❧✐③❡❞ ②❡❛r❧② ❢r♦♠ ✶✾✻✵✲✷✵✶✵✳ ■♥ ❛❞❞✐t✐♦♥ t♦ t❤✐s✱
✶✷
t❤❡ ▼✐❑❧✐♣ s②st❡♠ ✇❛s ❛❧s♦ ✉s❡❞ ❢♦r ❢✉t✉r❡ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥ r✉♥♥✐♥❣ ✉♣ t♦ ✷✵✷✹✱ ❢♦r✶✵ r❡❛❧✐③❛t✐♦♥s ❛♥❞ ✇✐t❤ ❛♥ ✐♥✐t✐❛❧✐③❛t✐♦♥ ✐♥ ✷✵✶✺✳ ▼♦❞✉❧❡ ❈ ♦❢ t❤❡ ✜rst ♣❤❛s❡ ♦❢ t❤❡▼✐❑❧✐♣ ♣r♦❥❡❝t ✇❛s ❞❡✈♦t❡❞ t♦ t❤❡ r❡❣✐♦♥❛❧✐s❛t✐♦♥ ♦❢ t❤❡ ▼✐❑❧✐♣ ❣❧♦❜❛❧ ♠♦❞❡❧ ♦✉t♣✉t✱✈✐❛ ❞②♥❛♠✐❝❛❧ ❞♦✇♥s❝❛❧✐♥❣✳ ❚❤✐s ✇❛s ❝❛rr✐❡❞ ♦✉t ♦✈❡r ❛ ❊✉r♦♣❡❛♥ ❞♦♠❛✐♥ ❢♦r t❤❡ ❡♥t✐r❡▼✐❑❧✐♣ ♣❡r✐♦❞ ✭✶✾✻✵✲✷✵✷✹✮ ✉s✐♥❣ t❤❡ ❈❈▲▼ ❛t ✵✳✹✹➦ r❡s♦❧✉t✐♦♥✳
❋♦r t❤❡ ❇■◆●❖ ♣r♦❥❡❝t✱ t❤❡ ❋❯❇ ❤❛✈❡ ❢✉rt❤❡r ❞②♥❛♠✐❝❛❧❧② ❞♦✇♥s❝❛❧❡❞ ❢♦✉r r❡❛❧✐③❛t✐♦♥s♦❢ t❤❡ ❢✉t✉r❡ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥s ✭✷✵✶✺✲✷✵✷✹✮ ❢r♦♠ ✵✳✹✹➦ t♦ ✵✳✶✶➦ ✉s✐♥❣ t❤❡ ❈❈▲▼✳ ❚♦r❡❞✉❝❡ ❝♦♠♣✉t❛t✐♦♥❛❧ ❡①♣❡♥s❡✱ t❤✐s ❤❛s ❜❡❡♥ ❝❛rr✐❡❞ ♦✉t ♦✈❡r t✇♦ s✉❜✲❞♦♠❛✐♥s ✭❋✐❣✳ ✷✳✷✮✿
✭✶✮ ◆❲✲❊❯❘✲✶✶✿ ✇❤✐❝❤ ❝♦♥t❛✐♥s t❤❡ r❡s❡❛r❝❤ s✐t❡s ❛t ❇❡r❣❡♥✱ ❱❡❧✉✇❡ ❛♥❞❲✉♣♣❡r✳✭✷✮ ■❇❊❘■❆✲✶✶✿ ✇❤✐❝❤ ❝♦♥t❛✐♥s t❤❡ r❡s❡❛r❝❤ s✐t❡s ❛t ❚❛❣✉s ❛♥❞ ❇❛❞❛❧♦♥❛✳
❚❤❡ s❛♠❡ ✈❛r✐❛❜❧❡s ❛♥❞ ❢r❡q✉❡♥❝✐❡s ❛s ❧✐st❡❞ ✐♥ ❚❛❜❧❡ ✷✳✷ ❛r❡ ❛✈❛✐❧❛❜❧❡ ❛♥❞ ❛r❡ ❞♦✇♥❧♦❛❞✲❛❜❧❡ ✈✐❛ t❤❡ ♦♥❧✐♥❡ ❉❊❈❖ ♣❧✉❣✐♥✳
❋✐❣✉r❡ ✷✳✷✿ ❇■◆●❖ ❉♦♠❛✐♥s ❢♦r ▼✐❑❧✐♣ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥s ✭✷✵✶✺✲✷✵✷✹✮✳ ❚❤❡ ❛r❡❛❝♦✈❡r❡❞ ❜② t❤❡ ▼✐❑❧✐♣ ✵✳✹✹➦ r❡❣✐♦♥❛❧✐s❛t✐♦♥ ✐s s❤♦✇♥ ✐♥ ❝♦❧♦✉r✱ ✇✐t❤ r❡❞ r❡♣r❡s❡♥t✐♥❣ t❤❡ ✵✳✹✹➦❧❛♥❞ ♠❛s❦ ❛♥❞ ❜❧✉❡ t❤❡ s❡❛✳ ❚❤❡ ■❇❊❘■❆✲✶✶ ❛♥❞ ◆❲✲❊❯❘✲✶✶ ❞♦♠❛✐♥s ♦❢ t❤❡ ❇■◆●❖ ♣r♦❥❡❝t❛r❡ t❤❡♥ ♠❛r❦❡❞ ✐♥ ❣r❡❡♥ ❛♥❞ ❝②❛♥✳
✶✸
❈❤❛♣t❡r ✸
❇✐❛s ❝♦rr❡❝t✐♦♥
❚②♣✐❝❛❧❧②✱ s②st❡♠❛t✐❝ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ t❤❡ ❝❧✐♠❛t❡ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥ ❛♥❞ ♦❜s❡r✈❡❞❞❛t❛ ❡①✐st✳ ❚❤❡ ♠♦st ♣r♦♠✐♥❡♥t ❞✐✛❡r❡♥❝❡ ✐s ❛ s❤✐❢t ✐♥ t❤❡ ♠❡❛♥ ✈❛❧✉❡✳ ❈❧✐♠❛t❡ ♠♦❞❡❧s✐♠✉❧❛t✐♦♥s ❛r❡ t❤✉s t②♣✐❝❛❧❧② ♣♦st✲♣r♦❝❡ss❡❞ ✉s✐♥❣ ❛ ❜✐❛s ❝♦rr❡❝t✐♦♥✳ ❚❤✐s ❝❤❛♣t❡r ❛✐♠s❛t ♦✉t❧✐♥✐♥❣ t❤✐s ❦✐♥❞ ♦❢ ♣♦st✲♣r♦❝❡ss✐♥❣✳ ❚✇♦ ❞✐✛❡r❡♥t ❜✐❛s ❝♦rr❡❝t✐♦♥ ♠❡t❤♦❞s ❛r❡♣r❡s❡♥t❡❞ ✐♥ t❤✐s ❝❤❛♣t❡r✿ ❙❡❛s♦♥❛❧ ●❡♥❡r❛❧✐③❡❞ ▲✐♥❡❛r ▼♦❞❡❧ ♠❡t❤♦❞ ❛♥❞ ❈✉♠✉❧❛t✐✈❡❉✐str✐❜✉t✐♦♥ ❋✉♥❝t✐♦♥ ❚r❛♥s❢♦r♠ ♠❡t❤♦❞✳
❚❤❡ ✜rst ❙❡❝t✐♦♥ ✸✳✶ ❝♦✈❡rs t❤❡ r❡❢❡r❡♥❝❡ ❞❛t❛s❡ts ✉s❡❞✳ ❚❤❡ ❙❡❛s♦♥❛❧ ●❡♥❡r❛❧✐③❡❞▲✐♥❡❛r ▼♦❞❡❧ ♠❡t❤♦❞ ✐s ❞❡s❝r✐❜❡ ✐♥ ✸✳✷ ❢♦❧❧♦✇❡❞ ❜② ❛ ❞❡s❝r✐♣t✐♦♥ ♦❢ ❈✉♠✉❧❛t✐✈❡ ❉✐str✐✲❜✉t✐♦♥ ❋✉♥❝t✐♦♥ ❚r❛♥s❢♦r♠ ♠❡t❤♦❞ ✐♥ ❙❡❝t✐♦♥ ✸✳✸✳
✸✳✶ ❘❡❢❡r❡♥❝❡ ❞❛t❛
❉❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡s ❛♥❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✱ t❤❡ r❡❢❡r❡♥❝❡ ❞❛t❛ ❢♦r ❜✐❛s❝♦rr❡❝t✐♦♥ ✈❛r✐❡s✳ ■♥ ❝❛s❡ t❤❡ ❞r✐✈✐♥❣ ❞❛t❛ ✐s r❡q✉❡st❡❞ ❣❛✉❣❡ ❜❛s❡❞ ❛♥❞ ❣❛✉❣❡s ❜❛s❡❞r❡❢❡r❡♥❝❡ ❞❛t❛ ✐s ❛✈❛✐❧❛❜❧❡✱ ✇❡ ✉s❡ t❤✐s ❞❛t❛ ❢♦r ❜✐❛s ❝♦rr❡❝t✐♦♥✳ ❋♦r ❣r✐❞❞❡❞ ♣r♦❞✉❝ts✱ ✇❡✉s❡ t❤❡ ❲❆❚❈❍ ❢♦r❝✐♥❣ ❞❛t❛ ❊❘❆✲■♥t❡r✐♠ ✭❲❋❉❊■✱ ❲❡❡❞♦♥ ❡t ❛❧✳✱ ✷✵✶✹✮ ❛s ❛ r❡❢❡r❡♥❝❡✐♥ ❝❛s❡ ♥♦ ♦t❤❡r ❣r✐❞❞❡❞ r❡❢❡r❡♥❝❡ ♣r♦❞✉❝t ✇❛s ♣r♦✈✐❞❡❞✳ ❆s ❜✐❛s ❝♦rr❡❝t✐♦♥ ♦❢ ❣r✐❞❞❡❞♣r♦❞✉❝ts ❜❛s❡❞ ♦♥ ❣❛✉❣❡✲❜❛s❡❞ r❡❢❡r❡♥❝❡ ❞❛t❛ ✐s ❛ ❧♦t ❧❡ss str❛✐❣❤t❢♦r✇❛r❞✱ t❤✐s ✇✐❧❧ ♥♦t❜❡ ✐♥❝❧✉❞❡❞ ✐♥ t❤✐s ❞❡❧✐✈❡r❛❜❧❡✳ ❚❤❡ ❢♦❧❧♦✇✐♥❣ ❧✐st ❣✐✈❡s ❛♥ ♦✈❡r✈✐❡✇ ♦✈❡r t❤❡ r❡❢❡r❡♥❝❡❞❛t❛ ✉s❡❞ ❛t ❞✐✛❡r❡♥t ❘❡s❡❛r❝❤ ❙✐t❡s✳
❘❙✶ ❇❡r❣❡♥ ❛ ❣r✐❞❞❡❞ ❞❛t❛ ♣r♦❞✉❝t ✐s r❡q✉❡st❡❞ ❛♥❞ t❤✉s ❲❋❉❊■ ❞❛t❛s❡t ✐s ✉s❡❞ ❛sr❡❢❡r❡♥❝❡✳
❘❙✷ ❱❡❧✉✇❡ ❛ ❣r✐❞❞❡❞ ❞❛t❛ ♣r♦❞✉❝t ✐s r❡q✉❡st❡❞ ❛♥❞ t❤✉s ❲❋❉❊■ ❞❛t❛s❡t ✐s ✉s❡❞ ❛sr❡❢❡r❡♥❝❡✳
❘❙✸ ❲✉♣♣❡r ❛ ❣r✐❞❞❡❞ ❞❛t❛ ♣r♦❞✉❝t ✐s r❡q✉❡st❡❞ ❛♥❞ t❤✉s ❲❋❉❊■ ❞❛t❛s❡t ✐s ✉s❡❞ ❛sr❡❢❡r❡♥❝❡✳
❘❙✹ ❇❛❞❛❧♦♥❛ ❛ ❣r✐❞❞❡❞ ❞❛t❛ ♣r♦❞✉❝t ✐s r❡q✉❡st❡❞ ❛♥❞ t❤✉s ❲❋❉❊■ ❞❛t❛s❡t ✐s ✉s❡❞❛s r❡❢❡r❡♥❝❡✳
✶✹
❘❙✺ ❚❛❣✉s✲❘✐✈❡r ✭P♦rt✉❣❛❧✮ ❛ ❣❛✉❣❡✲❜❛s❡❞ ❞❛t❛ ♣r♦❞✉❝t ❢♦r t❤❡ t❤❡ ✈❛r✐❛❜❧❡s ♣r❡✲❝✐♣✐t❛t✐♦♥ ✭♠♠✴❞❛②✮✱ ❞❛✐❧② ♠❛①✐♠✉♠ ❛♥❞ ♠✐♥✐♠✉♠ ♥❡❛r✲s✉r❢❛❝❡ ❛✐r t❡♠♣❡r❛t✉r❡✭◦❈✮✱ s✉r❢❛❝❡ ❞♦✇♥✇❡❧❧✐♥❣ s❤♦rt✇❛✈❡ ✢✉① ✐♥ ❛✐r ✭❲✴♠2✮✱ ✇✐♥❞ s♣❡❡❞ ✭♠✴s✮ ❛♥❞ s✉r✲❢❛❝❡ ❛✐r ♣r❡ss✉r❡ ✭❦P❛✮ ❛t ❞❛✐❧② r❡s♦❧✉t✐♦♥ ✐s t♦ ❜❡ ♣r♦✈✐❞❡❞✳ ●❛✉❣❡ ❧♦❝❛t✐♦♥s ❤❛✈❡❜❡❡♥ ♣r♦✈✐❞❡❞ ❜✉t ♥♦t ❛❧❧ ❣❛✉❣❡s r❡❝♦r❞ ❛❧❧ t❤❡ r❡q✉❡st❡❞ ✈❛r✐❛❜❧❡s✳ ❈♦♥s❡q✉❡♥t❧②✱❜✐❛s ❝♦rr❡❝t✐♦♥ ❝❛♥ ♦♥❧② ❜❡❡♥ ♠❛❞❡ ❢♦r t❤♦s❡ q✉❛♥t✐t✐❡s ✇❤❡r❡ r❡❢❡r❡♥❝❡ ❤❛s ❜❡❡♥♣r♦✈✐❞❡❞✳ ❚❤❛t ✐s
❼ ▼❛①✐♠✉♠ ❛♥❞ ♠✐♥✐♠✉♠ t❡♠♣❡r❛t✉r❡✱ ✇✐♥❞ s♣❡❡❞ ✭♠♦♥t❤❧②✮ ❢♦r ❚❛♣❛❞❛ ❞❛❆❥✉❞❛✱ ❙❛❧✈❛t❡rr❛ ❞❡ ▼❛❣♦s✱ ❉♦✐s P♦rt♦s✱ ❙❛♥t❛r❡♠✱ ❆❧✈❡❣❛✱ ❛♥❞
❼ Pr❡❝✐♣✐t❛t✐♦♥ ✭❞❛✐❧②✮ ❢♦r ❱✐❧❛ ◆♦❣✉❡✐r❛✱ ▼♦✐♥❤♦❧❛✱ ❈❛♥❤❛✱ ❇❛rr❛❣❡♠ ❞❡ ▼❛❣♦s✱❇❛rr❛❣❡♠ ❞❡ ▼♦♥t❛r❣✐❧✱ ❖t❛✱ ▼❛r✐❛♥♦s✱ ❙❛♥t❛r❡♠ ❊❙❆✱ ❚♦❥❡✐r❛s ❞❡ ❈✐♠❛✱❇❡♠♣♦st❛✱ ❛♥❞ P❡r♥❡s✳
❘❙✻ ❚r♦♦❞♦s✲▼♦✉♥t❛✐♥s ♥♦ ❞❛t❛ ♣r♦❞✉❝ts r❡q✉❡st❡❞✳
❋♦r ♠♦st ♦❢ t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡s ❛ s❡❛s♦♥❛❧❧② r❡s♦❧✈❡❞ ❝❧✐♠❛t♦❧♦❣② ❝♦♠♣✉t❡❞ ❢r♦♠❲❋❉❊■ ✐s t❤❡ r❡❢❡r❡♥❝❡ ❢♦r t❤❡ ❝❧✐♠❛t❡ s✐♠✉❧❛t✐♦♥s✳ ❚❤✐s ❢♦r❝✐♥❣ ❞❛t❛ s❡t ✐s ❜❡❡♥ ❢r❡✲q✉❡♥t❧② ✉s❡❞ ✐♥ t❤❡ ❝♦♥t❡①t ♦❢ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧✐♥❣ ✭❡✳❣✳✱ ●✉❞♠✉♥❞ss♦♥ ❡t ❛❧✳✱ ✷✵✶✶❀❑♦❝❤ ❡t ❛❧✳✱ ✷✵✶✸❀ Pr✉❞❤♦♠♠❡ ❡t ❛❧✳✱ ✷✵✶✹✮✳ ❍♦✇❡✈❡r✱ ❢♦r t❤✐s ❞❛t❛ s❡t✱ ❘✉st ❡t ❛❧✳✭✷✵✶✺✮ ❢♦✉♥❞ t❤❛t ❞✉❡ t♦ t❤❡ ✇❛② ♦❢ ♠❡r❣✐♥❣ t❤❡ ❊❘❆✲■♥t❡r✐♠ r❡❛♥❛❧②s✐s ✇✐t❤ ❛ ❣r✐❞❞❡❞♦❜s❡r✈❛t✐♦♥✲❜❛s❡❞ ❞❛t❛ ♣r♦❞✉❝t ❢r♦♠ ❈❘❯ ✐♠♣❧❛✉s✐❜❧❡ ❞✐✛❡r❡♥❝❡s ✐♥ ❞❛✐❧② t❡♠♣❡r❛t✉r❡s❛❝r♦ss ❜♦✉♥❞❛r✐❡s ♦❢ ❝❛❧❡♥❞❡r ♠♦♥t❤ ♠✐❣❤t ❛r✐s❡ ❢♦r s♦♠❡ r❡❣✐♦♥s✳ ❋♦r ❊✉r♦♣❡✱ ❤♦✇❡✈❡r✱t❤❡s❡ ❞✐✛❡r❡♥❝❡s ❛r❡ ✐♥s✐❣♥✐✜❝❛♥t✳
❋♦r ❜✐❛s ❝♦rr❡❝t✐♦♥ t❤❡ ❢♦❧❧♦✇✐♥❣ ✈❛r✐❛❜❧❡s ♦❢ t❤❡❲❋❉❊■ ❛r❡ ❛✈❛✐❧❛❜❧❡✿ ♠❡❛♥✴♠✐♥✴♠❛①t❡♠♣❡r❛t✉r❡✱ t♦t❛❧ ♣r❡❝✐♣✐t❛t✐♦♥✱ s✉r❢❛❝❡ ❛✐r ♣r❡ss✉r❡✱ ♥❡❛r✲s✉r❢❛❝❡ ✇✐♥❞ s♣❡❡❞✱ ❧♦♥❣✲✴s❤♦rt✇❛✈❡ ✐♥❝✐❞❡♥t r❛❞✐❛t✐♦♥ ❛♥❞ ♥❡❛r✲s✉r❢❛❝❡ s♣❡❝✐✜❝ ❤✉♠✐❞✐t②✳ ❆ ❜✐❛s ❝♦rr❡❝t✐♦♥ ❢♦r♠❡❛♥✴♠✐♥✴♠❛① r❡❧❛t✐✈❡ ❤✉♠✐❞✐t② ✇✐❧❧ ❜❡ ❞♦♥❡ ✐♥ ❧❛t❡r st❛❣❡s✳ ❲❋❉❊■ ❞♦❡s ♥♦t ♣r♦✈✐❞❡✈❡❝t♦r✐❛❧ ✐♥❢♦r♠❛t✐♦♥ ♦❢ t❤❡ ✇✐♥❞ ♥♦r ✐ts ❞✐r❡❝t✐♦♥s✱ t❤✉s ✇✐♥❞ ❞✐r❡❝t✐♦♥ ❝❛♥♥♦t ❜❡ ❝♦r✲r❡❝t❡❞✳ ❚❤✐s ✐s✱ ❤♦✇❡✈❡r✱ ♥♦t ❛ ♣r♦❜❧❡♠ ❢♦r ♠♦st ♦❢ t❤❡ ❝❛s❡s r❡❧❡✈❛♥t t♦ ❇■◆●❖✳ ❲❋❉❊■❝♦♠❡s ♦♥ ❛ ❝♦❛rs❡r r❡s♦❧✉t✐♦♥ t❤❛♥ t❤❡ ❈❖❙▼❖✲❈▲▼ s✐♠✉❧❛t✐♦♥ ✉s❡❞ ❢♦r ❉✷✳✶✳ ✐t ❤❛st❤✉s ❜❡❡♥ ✐♥t❡r♣♦❧❛t❡❞ t♦ t❤❡ ❣r✐❞ ♦❢ t❤❡ ❈❖❙▼❖✲❈▲▼✳
✸✳✷ ❙❡❛s♦♥❛❧ ●❡♥❡r❛❧✐③❡❞ ▲✐♥❡❛r ▼♦❞❡❧ ♠❡t❤♦❞
■♥ t❤✐s ❙❡❝t✐♦♥✱ t❤❡ ❙❡❛s♦♥❛❧ ●❡♥❡r❛❧✐③❡❞ ▲✐♥❡❛r ▼♦❞❡❧ ❜✐❛s ❝♦rr❡❝t✐♦♥ ♠❡t❤♦❞ ✐s ❞❡✲s❝r✐❜❡❞✳ ❚❤❡ ✉♥❞❡r❧②✐♥❣ ✐❞❡❛ ♦❢ t❤❡ ❛♣♣r♦❛❝❤ ✐s ✜rst ♣r❡s❡♥t❡❞ ✭❙❡❝t✳ ✸✳✷✮ ❢♦❧❧♦✇❡❞ ❜②t❤❡ ❝♦♥❝r❡t❡ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ t❤❡ ❛♣♣r♦❛❝❤ ❛t t❤❡ ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s ✐♥ ❙❡❝t✳ ✸✳✷✳✷✳
✸✳✷✳✶ ❯♥❞❡r❧②✐♥❣ ♣r✐♥❝✐♣❧❡ ❛♥❞ ♠♦❞❡❧✐♥❣ ❛♣♣r♦❛❝❤
❚❤❡ ✉♥❞❡r❧②✐♥❣ ✐❞❡❛ ♦❢ t❤❡ ❜✐❛s ❝♦rr❡❝t✐♦♥ ❛♣♣❧✐❡❞ ❤❡r❡ ✐s t❤❡ ❛ss✉♠♣t✐♦♥ t❤❛t t❤❡ ❝❧✐✲♠❛t♦❧♦❣✐❝❛❧ s❡❛s♦♥❛❧ ❝②❝❧❡ ♦❢ ❜♦t❤✱ s✐♠✉❧❛t✐♦♥s ❛♥❞ ♦❜s❡r✈❛t✐♦♥s✱ ✐s ❛ s♠♦♦t❤ ❢✉♥❝t✐♦♥♦❢ t❤❡ ❞❛② ♦❢ t❤❡ ②❡❛r✳ ■❢ t❤❡ s✐♠✉❧❛t❡❞ s❡❛s♦♥❛❧ ❝②❝❧❡ ❞♦❡s ♥♦t ♠❛t❝❤ t❤❡ ♦❜s❡r✈❡❞ ♦♥❡✱
✶✺
✐t ♥❡❡❞s t♦ ❜❡ ❛❞❥✉st❡❞✳ ❚❤❡ s♠♦♦t❤ ❢✉♥❝t✐♦♥s ❛r❡ ♠♦❞❡❧❡❞ ✉s✐♥❣ ❛ ❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r♠♦❞❡❧ ✭●▲▼✱ ▼❝❈✉❧❧❛❣❤ ❛♥❞ ◆❡❧❞❡r✱ ✶✾✽✾✮ ✇✐t❤ ❤❛r♠♦♥✐❝ ❢✉♥❝t✐♦♥ ✭s✐♥❡ ❛♥❞ ❝♦s✐♥❡✮♦❢ t❤❡ ❞❛② ♦❢ t❤❡ ②❡❛r ❛s ♣r❡❞✐❝t♦rs✳ P❡r✐♦❞✐❝ ❢✉♥❝t✐♦♥s✱ s✉❝❤ ❛s t❤❡ s❡❛s♦♥❛❧ ❝②❝❧❡✱ ❝❛♥❜❡ ❛❧✇❛②s ❞❡s❝r✐❜❡❞ ✇✐t❤ ❛ s❡r✐❡s ♦❢ ❤❛r♠♦♥✐❝ ❢✉♥❝t✐♦♥s✭❡✳❣✳✱ Pr✐❡st❧❡②✱ ✶✾✾✷✮❀ t❤❡ ♠♦r❡❢❡❛t✉r❡s t❤❡ ❝②❝❧❡ ❤❛s✱ t❤❡ ❤✐❣❤❡r t❤❡ ♦r❞❡r ♦❢ t❤❡ s❡r✐❡s ❡①♣❛♥s✐♦♥ ♠✉st ❜❡✳ ●❡♥❡r❛❧✐③❡❞❧✐♥❡❛r ♠♦❞❡❧s ❛r❡ ♥♦t r❡str✐❝t❡❞ t♦ ●❛✉ss✐❛♥ r❡s✐❞✉❛❧s ❛s t❤❡ st❛♥❞❛r❞ ❧✐♥❡❛r r❡❣r❡ss✐♦♥✐s✱ ❘❡s✐❞✉❛❧s ❝❛♥ ❜❡ ❢r♦♠ ❛♥② ❞✐str✐❜✉t✐♦♥ ✐♥ t❤❡ ❡①♣♦♥❡♥t✐❛❧ ❢❛♠✐❧② ♦❢ ♣r♦❜❛❜✐❧✐t② ❞✐s✲tr✐❜✉t✐♦♥s ✭▼❝❈✉❧❧❛❣❤ ❛♥❞ ◆❡❧❞❡r✱ ✶✾✽✾✮✱ ❡✳❣✳ ❊①♣♦♥❡♥t✐❛❧✱ ●❛♠♠❛✱ ❇✐♥♦♠✐❛❧✱ P♦✐ss♦♥✳❋♦r ♦✉r ❝❛s❡s ♣❛rt✐❝✉❧❛r❧② ✐♥t❡r❡st✐♥❣ ❞✐str✐❜✉t✐♦♥s ❛r❡ t❤♦s❡ ✇✐t❤ ♣♦s✐t✐✈❡ s✉♣♣♦rt ❢♦r♠♦❞❡❧✐♥❣ ♣r❡❝✐♣✐t❛t✐♦♥ ❛♥❞ ♦t❤❡r ♥♦♥✲♥❡❣❛t✐✈❡ q✉❛♥t✐t✐❡s✳
❖♥❝❡ t❤❡ t✇♦ s❡❛s♦♥❛❧ ❝②❝❧❡s ❤❛✈❡ ❜❡❡♥ ♦❜t❛✐♥❡❞ ✭♠♦❞❡❧✐♥❣ st❡♣✮✱ ❛ ❞✐✛❡r❡♥❝❡ ✭♦rr❛t✐♦ ✐♥ ❝❛s❡ ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥✮ ✐s ♦❜t❛✐♥❡❞ ❛♥❞ t❤✐s ✐s ✉s❡❞ ❢♦r ❛❞❥✉st✐♥❣ t❤❡ s✐♠✉❧❛t❡❞❞❛t❛ ✭❛❞❥✉st♠❡♥t st❡♣✮✳
❚❤❡ ♠♦❞❡❧
❆s ❛ s✐♠✉❧t❛♥❡♦✉s tr❡❛t♠❡♥t ♦❢ ❛❧❧ ❞❛t❛ ✐s ❛❞✈❛♥t❛❣❡♦✉s ♦✈❡r ❛ s❡♣❛r❛t❡ tr❡❛t♠❡♥t ♦❢❞❛t❛ ✐♥ ❞✐✛❡r❡♥t ♠♦♥t❤s✱ t❤❡ s❡❛s♦♥❛❧ ✈❛r✐❛t✐♦♥s ♦❢ t❤❡ ✈❛r✐❛❜❧❡s ❝❛♥ ❜❡ ❝❛♣t✉r❡❞ ❜②✉s✐♥❣ ❤❛r♠♦♥✐❝ ❢✉♥❝t✐♦♥s✱ ❛s ♠❡♥t✐♦♥❡❞ ❛❜♦✈❡✳ ❋♦r t❤❡ ❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r ♠♦❞❡❧✱ s✉❝❤ ❛❞❡s❝r✐♣t✐♦♥ ✐s ❣✐✈❡♥ ✐♥ ❊q✳ ✭✸✳✶✮ ❢♦r t❤❡ ❡①♣❡❝t❛t✐♦♥ ✈❛❧✉❡ µ(t)✳
µ(t) = µ0 +
N∑
n=1
µn1 sin(nω · t) +
N∑
n=1
µn2 cos(nω · t) ✭✸✳✶✮
✇✐t❤ ω = 2π365.25 ✱ t = 1, . . . , 366 ❜❡✐♥❣ t❤❡ t✐♠❡ ✈❛r✐❛❜❧❡ r✉♥♥✐♥❣ ♦✈❡r ❛❧❧ ♣♦ss✐❜❧❡ ❞❛②s
♦❢ t❤❡ ②❡❛r✳ ❋♦r ♣❛r❛♠❡t❡r ❡st✐♠❛t✐♦♥✱ t ✇✐❧❧ ❜❡ ❝❡♥t❡r❡❞ ❛t t❤❡ ♠♦♥t❤s ♦❢ t❤❡ ②❡❛r❀ ❛❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ s❡❛s♦♥❛❧ ❝②❝❧❡ ✐s✱ ❤♦✇❡✈❡r✱ ♣♦ss✐❜❧❡ ❛t ❛ ❞❛✐❧② t✐♠❡ r❡s♦❧✉t✐♦♥✱ t❤✉st = 1, . . . , 366✳ ❚❤❡ ❝❤♦✐❝❡ ♦❢ ❞✐str✐❜✉t✐♦♥ ❢♦r t❤❡ r❡s✐❞✉❛❧s ✭❛♥♦♠❛❧✐❡s✮ ❞♦❡s ✈❛r② ✇✐t❤t❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ♣❛r❛♠❡t❡r ❝♦♥s✐❞❡r❡❞✱ t❤❡ ♠♦❞❡❧ ❢♦r t❤❡ ❡①♣❡❝t❛t✐♦♥ ❣✐✈❡♥ ✐♥ ❊q✳ ✭✸✳✶✮r❡♠❛✐♥s ❜❛s✐❝❛❧❧② t❤❡ s❛♠❡✳
❉✐str✐❜✉t✐♦♥❛❧ ❛ss✉♠♣t✐♦♥s
Pr❡❝✐♣✐t❛t✐♦♥ Pr❡❝✐♣✐t❛t✐♦♥ ✐s ❛ s♦♠❡✇❤❛t ♣❛rt✐❝✉❧❛r q✉❛♥t✐t②✳ ■t s❤♦✇s ❛ ❝♦♥t✐♥✉♦✉s♣r♦❜❛❜✐❧✐t② ❞✐str✐❜✉t✐♦♥ ❢♦r str✐❝t❧② ♣♦s✐t✐✈❡ ✈❛❧✉❡s ❜✉t ❤❛s ❛ ❞✐s❝♦♥t✐♥✉✐t② ❛t ③❡r♦✳ ❋♦r❛ st❛t✐st✐❝❛❧ ❞❡s❝r✐♣t✐♦♥✱ t❤✐s ✐s t②♣✐❝❛❧❧② ❝❛♣t✉r❡❞ ✇✐t❤ ❛ ❝♦♠♣♦✉♥❞ ♠♦❞❡❧ ❝♦♥s✐st✐♥❣♦❢ ❛ ❇✐♥♦♠✐❛❧ ✈❛r✐❛❜❧❡ ❢♦r ❞❡s❝r✐❜✐♥❣ ❞r② ❛♥❞ ✇❡t ❞❛②s ❛♥❞ ❛ str✐❝t❧② ♣♦s✐t✐✈❡ ✈❛r✐❛❜❧❡✭●❛♠♠❛ ♦r ❊①♣♦♥❡♥t✐❛❧✮ ❢♦r t❤❡ q✉❛♥t✐t② ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ♦♥ r❛✐♥② ❞❛②s✳ ❍❡r❡✱ ✇❡ ❛❞❥✉st♦♥❧② t❤❡ ❛♠♦✉♥t ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ♦♥ r❛✐♥② ❞❛②s ❛♥❞ ♥♦t t❤❡ ❞✐str✐❜✉t✐♦♥ ♦❢ ❞r② ❛♥❞ ✇❡t❞❛②s✳ ❚❤✐s ✐s t♦ ❛✈♦✐❞ ✐♥❝♦♥s✐st❡♥❝✐❡s ✐♥ t❤❡ ♣♦st✲♣r♦❝❡ss✐♥❣ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥s✱ s✉❝❤ ❛s♣r❡❝✐♣✐t❛t✐♦♥ ♦♥ ❞❛②s ✇✐t❤ ♥♦ ❝❧♦✉❞s✳
❖t❤❡r ✈❛r✐❛❜❧❡s ❚❛❜❧❡ ✸✳✶ ❣✐✈❡s ❛♥ ♦✈❡r✈✐❡✇ ♦✈❡r ❛❧❧ ✈❛r✐❛❜❧❡s ❛♥❞ t❤❡ ❛ss♦❝✐❛t❡❞♠♦❞❡❧ ❞✐str✐❜✉t✐♦♥s✳ ❚❤❡ ♦r❞❡r ♦❢ t❤❡ ❤❛r♠♦♥✐❝ s❡r✐❡s ❡①♣❛♥s✐♦♥ ✭♠♦❞❡❧ s❡❧❡❝t✐♦♥✮ ❤❛s
✶✻
✈❛r✐❛❜❧❡ ❧♦♥❣ ♥❛♠❡ ❞✐str✐❜✉t✐♦♥
T1 ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ Tmax ❛♥❞ Tmin ❧♦❣✲●❛✉ss✐❛♥T2 s✉♠ ♦❢ Tmax ❛♥❞ Tmin ●❛✉ss✐❛♥
Tmean ♠❡❛♥ s✉r❢❛❝❡ t❡♠♣❡r❛t✉r❡ ●❛✉ss✐❛♥RR ♣r❡❝✐♣✐t❛t✐♦♥ ❣❛♠♠❛v ♥❡❛r✲s✉r❢❛❝❡ ✇✐♥❞ s♣❡❡❞ ❧♦❣✲●❛✉ss✐❛♥P s✉r❢❛❝❡ ❛✐r ♣r❡ss✉r❡ ●❛✉ss✐❛♥
LWdown ❧♦♥❣✇❛✈❡ ✐♥❝✐❞❡♥t r❛❞✐❛t✐♦♥ ❧♦❣✲●❛✉ss✐❛♥SWdown s❤♦rt✇❛✈❡ ✐♥❝✐❞❡♥t r❛❞✐❛t✐♦♥ ❧♦❣✲●❛✉ss✐❛♥Qair ♥❡❛r✲s✉r❢❛❝❡ s♣❡❝✐✜❝ ❤✉♠✐❞✐t② ❧♦❣✲●❛✉ss✐❛♥
❚❛❜❧❡ ✸✳✶✿ ❇✐❛s✲❝♦rr❡❝t❡❞ ✈❛r✐❛❜❧❡s ❛♥❞ ❛ss♦❝✐❛t❡❞ ♠♦❞❡❧ ❞✐str✐❜✉t✐♦♥s✳
❜❡❡♥ ❝❤♦s❡♥ ♦♥ t❤❡ r❡❢❡r❡♥❝❡ ❞❛t❛s❡ts✳ ❍❛r♠♦♥✐❝ s❡r✐❡s t♦ ✺t❤ ♦r❞❡r ❤❛✈❡ ❜❡❡♥ ❝♦♥s✐❞❡r❡❞❛♥❞ s❡❧❡❝t❡❞ ✇✐t❤ t❤❡ ❇❛②❡s✐❛♥ ■♥❢♦r♠❛t✐♦♥ ❈r✐t❡r✐♦♥ ✭❇■❈✮✳ ❚❤❡ ♠♦❞❡❧ t❤✉s ♦❜t❛✐♥❡❞❤❛s ❜❡❡♥ ✉s❡❞ t♦ ❞❡s❝r✐❜❡ t❤❡ ❝❧✐♠❛t❡ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥s ❛♥❞ t❤❡ r❡❢❡r❡♥❝❡ ❞❛t❛✳
▼✐♥✐♠✉♠ ❛♥❞ ♠❛①✐♠✉♠ t❡♠♣❡r❛t✉r❡
P❛rt✐❝✉❧❛r ❝❛r❡ ♥❡❡❞s t♦ ❜❡ t❛❦❡♥ ✇❤❡♥ ❝♦rr❡❝t✐♦♥ ♠✐♥✐♠✉♠ ❛♥❞ ♠❛①✐♠✉♠ t❡♠♣❡r❛t✉r❡t♦ ❛✈♦✐❞ ✐♥❝♦♥s✐st❡♥❝✐❡s s✉❝❤ ❛s Tmax < Tmin✳ ❍❡r❡✱ ❛ ✈❛r✐❛❜❧❡ tr❛♥s❢♦r♠❛t✐♦♥ ❣✐✈❡♥ ✐♥❊q✳ ✭✸✳✷✮ ❡♥s✉r❡s ♣❤②s✐❝❛❧ ❝♦♥s✐st❡♥❝②✳
T1 = Tmax − Tmin ✭✸✳✷✮
T2 = Tmax + Tmin ✭✸✳✸✮
❆❢t❡r ❝♦rr❡❝t✐♥❣ T1 ❛♥❞ T2 ❜❛s❡❞ ♦♥ t❤❡ r❡❢❡r❡♥❝❡✱ t❤❡ ❝♦rr❡❝t❡❞ ✈❛❧✉❡s ❢♦r Tmax ❛♥❞ Tmin
❝❛♥ ❜❡ ❞❡r✐✈❡❞ ❜② ❜❛❝❦✲tr❛♥s❢♦r♠✐♥❣ t❤❡ ✈❛r✐❛❜❧❡s✳
✸✳✷✳✷ ❆t ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s
❋♦r r❡❛s♦♥s ♦❢ ❞❛t❛ ❛✈❛✐❧❛❜✐❧✐t② ❛♥❞ ❢♦r ❛ r♦❜✉st ✜t✱ ✇❡ ✉s❡ ♠♦♥t❤❧② ♠❡❛♥s t♦ ❡st✐♠❛t❡t❤❡ ♠♦❞❡❧ ♣❛r❛♠❡t❡rs ✭❝♦❡✣❝✐❡♥ts ♦❢ t❤❡ ❤❛r♠♦♥✐❝ ❢✉♥❝t✐♦♥s✮✳ ❋♦r s♦♠❡ ❝❛s❡s✱ ❛ ✈❡❝t♦r❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r ♠♦❞❡❧ ✭❱●▲▼✱ ❨❡❡✱ ✷✵✶✺✮ ❤❛s ❜❡❡♥ ✉s❡❞✳ ❊①❡♠♣❧❛r✐❧②✱ ❋✐❣✳ ✸✳✶ s❤♦✇st❤❡ ♠♦♥t❤❧② ♠❡❛♥ ♣r❡❝✐♣✐t❛t✐♦♥ ❢♦r t❤❡ r❡❢❡r❡♥❝❡ st❛t✐♦♥s ❱✐❧❛ ◆♦❣✉❡✐r❛ ❞❡ ❆③❡✐t❛♦✱❧♦❝❛t❡❞ ♦♥ t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡ ❚❛❣✉s✲❘✐✈❡r ✭P♦rt✉❣❛❧✮✳
■♥ t❤❡ ♠♦❞❡❧✐♥❣ st❡♣✱ t❤❡ s❡❛s♦♥❛❧✐t② ♦❢ t❤❡ ♠♦❞❡❧ ♦✉t♣✉t ❛♥❞ t❤❡ r❡s♣❡❝t✐✈❡ r❡❢❡r❡♥❝❡❞❛t❛ ❛r❡ ❞❡r✐✈❡❞ ✉s✐♥❣ t❤❡ ❛♣♣r♦❛❝❤ ❞❡s❝r✐❜❡❞ ❛❜♦✈❡✳ ❋✐❣✉r❡ ✸✳✷ s❤♦✇s ❛♥ ❡①❛♠♣❧❡ ♦❢t❤❡ t✇♦ s❡❛s♦♥❛❧ ❝②❝❧❡s ❢♦r ♣r❡❝✐♣✐t❛t✐♦♥ ❛t t❤❡ st❛t✐♦♥ ❱✐❧❛ ◆♦❣✉❡✐r❛ ❞❡ ❆③❡✐t❛♦ ♦♥ t❤❡❘❡s❡❛r❝❤ ❙✐t❡ ❚❛❣✉s✲❘✐✈❡r ✭P♦rt✉❣❛❧✮✳
❚❤❡ ❛❞❥✉st♠❡♥t st❡♣ ❞❡♣❡♥❞s ♦♥ t❤❡ ✈❛r✐❛❜❧❡ ❝♦♥s✐❞❡r❡❞✿ ❋♦r ●❛✉ss✐❛♥ ❞✐str✐❜✉t✐♦♥st❤❡ ❞✐✛❡r❡♥❝❡ ✭❝❛s❡ ✶✮ ❛♥❞ ❢♦r ♣♦s✐t✐✈❡ ✈❛r✐❛❜❧❡s ✭❡✳❣✳ ●❛♠♠❛ ♦r ❧♦❣✲♥♦r♠❛❧✮ t❤❡ q✉♦t✐❡♥t✭❝❛s❡ ✷✮ ♦❢ t❤❡ ❡st✐♠❛t❡❞ s❡❛s♦♥❛❧ ❝②❝❧❡ ❢♦r t❤❡ r❡❢❡r❡♥❝❡ ❞❛t❛ s❡t r̄(t) ❛♥❞ t❤❡ s✐♠✉❧❛t❡❞
✶✼
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05
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15
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mean p
recip
itation [m
m/d
ay]
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❋✐❣✉r❡ ✸✳✶✿ ▼♦♥t❤❧② ♠❡❛♥ ♦❢ ❞❛✐❧② ♣r❡❝✐♣✐t❛t✐♦♥ s✉♠s ❛t t❤❡ r❡❢❡r❡♥❝❡ st❛t✐♦♥ ❱✐❧❛ ◆♦❣✉❡✐r❛ ❞❡❆③❡✐t❛♦ ✐♥ t❤❡ r❡s❡❛r❝❤ s✐t❡ ❚❛❣✉s✲❘✐✈❡r ✭P♦rt✉❣❛❧✮✳ ❚❤❡ ❞❛t❛ ❝♦✈❡rs t❤❡ ♣❡r✐♦❞ ❢r♦♠ ✶✾✽✵✲✶✵✲✵✶t♦ ✷✵✵✾✲✵✾✲✸✵✳
✶✽
01
23
45
6
month
pre
cip
itation [m
m/d
ay]
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reference
model
❋✐❣✉r❡ ✸✳✷✿ ❙❡❛s♦♥❛❧✐t② ♦❢ t❤❡ ❝❧✐♠❛t❡ s✐♠✉❧❛t✐♦♥ ♦✉t♣✉t ✭❜❧✉❡✮ ❛♥❞ t❤❡ r❡❢❡r❡♥❝❡ ♦❜s❡r✈❛t✐♦♥✭❜❧❛❝❦✮ ❢♦r ♣r❡❝✐♣✐t❛t✐♦♥ ❛t t❤❡ st❛t✐♦♥ ❱✐❧❛ ◆♦❣✉❡✐r❛ ❞❡ ❆③❡✐t❛♦ ✐♥ t❤❡ r❡s❡❛r❝❤ s✐t❡ ❚❛❣✉s✲❘✐✈❡r✭P♦rt✉❣❛❧✮ ✐♥ ❛ ❞❛✐❧② r❡s♦❧✉t✐♦♥ ❞❡r✐✈❡❞ ❜② ❛ ❱●▲▼ tr❛✐♥❡❞ ✇✐t❤ ♠♦♥t❤❧② ♠❡❛♥ ✈❛❧✉❡s✳
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Jan Mär Mai Jul Sep Nov Jan
010
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month
pre
cip
itation [m
m/d
ay]
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bias−corrected data
raw data
❋✐❣✉r❡ ✸✳✸✿ Pr❡❝✐♣✐t❛t✐♦♥ ♦❢ t❤❡ ❝❧✐♠❛t❡ s✐♠✉❧❛t✐♦♥ ❛t t❤❡ st❛t✐♦♥ ❱✐❧❛ ◆♦❣✉❡✐r❛ ❞❡ ❆③❡✐t❛♦ ✐♥t❤❡ r❡s❡❛r❝❤ s✐t❡ ❚❛❣✉s✲❘✐✈❡r ✭P♦rt✉❣❛❧✮ ❢♦r t❤❡ ②❡❛r ✶✾✽✾ ❜❡❢♦r❡ t❤❡ ❜✐❛s ❝♦rr❡❝t✐♦♥ ✭❜❧❛❝❦✮ ❛♥❞❛❢t❡r ✭❜❧✉❡✮✳
❞❛t❛ s❡t x̄(t) ❛r❡ ♦❜t❛✐♥❡❞✱ s❡❡ ❊q✳ ✭✸✳✹✮✳
∆(t) =
{
r̄(t)− x̄(t) ●❛✉ss✐❛♥r̄(t)x̄(t) ♣♦s✐t✐✈❡
✭✸✳✹✮
❋✐♥❛❧❧②✱ t❤❡ ❛❞❥✉st❡❞ ✭❜✐❛s ❝♦rr❡❝t❡❞✮ ✈❛❧✉❡s ❛r❡ ❝❛❧❝✉❧❛t❡❞ ❜② ❡✐t❤❡r ❛❞❞✐♥❣ ✭❝❛s❡ ✶✮♦r ♠✉❧t✐♣❧②✐♥❣ ✭❝❛s❡ ✷✮ t❤❡ t❤✉s ♦❜t❛✐♥❡❞ ✈❛❧✉❡s t♦ t❤❡ ❝❧✐♠❛t❡ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥s✱ s❡❡❊q✳ ✭✸✳✺✮✳
xcorrected(t) =
{
x(t) + ∆(t) ●❛✉ss✐❛♥
x(t) ·∆(t) ♣♦s✐t✐✈❡✭✸✳✺✮
❋✐❣✉r❡ ✸✳✸ ❛♥❞ ❋✐❣✉r❡ ✸✳✹ s✉❣❣❡st t❤❛t t❤❡ ♣r❡❝✐♣✐t❛t✐♦♥ ❞❛t❛s❡t ❛t t❤❡ st❛t✐♦♥ ❱✐❧❛◆♦❣✉❡✐r❛ ❞❡ ❆③❡✐t❛♦ ✐♥ t❤❡ r❡s❡❛r❝❤ s✐t❡ ❚❛❣✉s✲❘✐✈❡r ✭P♦rt✉❣❛❧✮ ✇❛s ❝♦rr❡❝t❡❞ ✐♥ ❣❡♥❡r❛❧t♦✇❛r❞s ❧♦✇❡r ✈❛❧✉❡s✳
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❋✐❣✉r❡ ✸✳✹✿ Pr❡❝✐♣✐t❛t✐♦♥ ♦❢ t❤❡ ❝❧✐♠❛t❡ s✐♠✉❧❛t✐♦♥ ❛t t❤❡ st❛t✐♦♥ ❱✐❧❛ ◆♦❣✉❡✐r❛ ❞❡ ❆③❡✐t❛♦ ✐♥t❤❡ r❡s❡❛r❝❤ s✐t❡ ❚❛❣✉s✲❘✐✈❡r ✭P♦rt✉❣❛❧✮ ❜❡❢♦r❡ t❤❡ ❜✐❛s ❝♦rr❡❝t✐♦♥ ✭①✲❛①✐s✮ ❛♥❞ ❛❢t❡r ✭②✲❛①✐s✮✳
✷✶
✸✳✸ ❈✉♠✉❧❛t✐✈❡ ❉✐str✐❜✉t✐♦♥ ❋✉♥❝t✐♦♥ ❚r❛♥s❢♦r♠ ♠❡t❤♦❞
❲❡ ♣r❡s❡♥t ❤❡r❡ ❛ ♠❡t❤♦❞✱ ♥❛♠❡❧② t❤❡ ❈❉❋✲❚r❛♥s❢♦r♠✱ ✇❤✐❝❤ ❝❛♥ ❜❡ ♣❡r❝❡✐✈❡❞ ❛s ❛♥❡①t❡♥s✐♦♥ ♦❢ t❤❡ ❝❧❛ss✐❝❛❧ q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣ ❛♣♣r♦❛❝❤ ✭P❛♥♦❢s❦② ❛♥❞ ❇r✐❡r✱ ✶✾✻✽✮✳ ❚❤✐s♠❡t❤♦❞ ❤❛s ❜❡❡♥ ❞❡✈❡❧♦♣❡❞ ❜② ✭▼✐❝❤❡❧❛♥❣❡❧✐ ❡t ❛❧✳✱ ✷✵✵✾✮ ❛♥❞ ❛♣♣❧✐❡❞ ✐♥ ♠❛♥② ❝❧✐♠❛t❡✲r❡❧❛t❡❞ st✉❞✐❡s ✭❡✳❣✳ ✭❈♦❧❡tt❡ ❡t ❛❧✳✱ ✷✵✶✷✮✱ ✭❚✐ss❡✉✐❧ ❡t ❛❧✳✱ ✷✵✶✷✮✱ ✭❱✐❣❛✉❞ ❡t ❛❧✳✱ ✷✵✶✸✮✱✭❱r❛❝ ❛♥❞ ❋r✐❡❞❡r✐❝❤s✱ ✷✵✶✺✮✮✳ ■♥ t❤❡ ❢♦❧❧♦✇✐♥❣✱ ✇❡ ✜rst r❡❝❛♣ t❤❡ q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣♠❡t❤♦❞ ✭❙❡❝t✳ ✸✳✸✳✶✮ ❢♦❧❧♦✇❡❞ ❜② ❛ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❈❉❋✲❚r❛♥s❢♦r♠ ♠❡t❤♦❞ ✭❙❡❝t✳✸✳✸✳✷✮ ❛♥❞ s♦♠❡ ❝♦♥❝r❡t❡ ❛♣♣❧✐❝❛t✐♦♥s ♦❢ t❤❡ ❛♣♣r♦❛❝❤ ❛t t❤❡ ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s✭❙❡❝t✳ ✸✳✸✳✸✮✳
✸✳✸✳✶ ◗✉❛♥t✐❧❡✲▼❛♣♣✐♥❣ ▼❡t❤♦❞
▲❡t Fo st❛♥❞ ❢♦r t❤❡ ❈❉❋ ✭❈✉♠✉❧❛t✐✈❡ ❉✐str✐❜✉t✐♦♥ ❋✉♥❝t✐♦♥✮ ♦❢ ❛ ❝❧✐♠❛t❡ r❛♥❞♦♠ ✈❛r✐✲❛❜❧❡ xo ✭t❡♠♣❡r❛t✉r❡✱ ♣r❡❝✐♣✐t❛t✐♦♥✱ ✇✐♥❞✱ ❡t❝✳✮ ♦❜s❡r✈❡❞ ❛t ❛ ❣✐✈❡♥ ✇❡❛t❤❡r st❛t✐♦♥❞✉r✐♥❣ t❤❡ ❤✐st♦r✐❝❛❧ t✐♠❡ ♣❡r✐♦❞✱ ❛♥❞ Fm ❢♦r t❤❡ ❈❉❋ ♦❢ t❤❡ s❛♠❡ ✈❛r✐❛❜❧❡ xm ❢r♦♠ t❤❡♠♦❞❡❧✱ ❢♦r t❤❡ s❛♠❡ t✐♠❡ ♣❡r✐♦❞✳ ❚❤❡ ✐❞❡❛ ♦❢ q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣ ✐s t♦ ❝♦rr❡❝t t❤❡ ❞✐str✐✲❜✉t✐♦♥ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ♠♦❞❡❧❧❡❞ ❝❧✐♠❛t❡ ✈❛r✐❛❜❧❡ t♦ ❛❣r❡❡ ✇✐t❤ t❤❡ ♦❜s❡r✈❡❞ ❞✐str✐❜✉t✐♦♥❢✉♥❝t✐♦♥✿
Fo(xo) = Fm(xm). ✭✸✳✻✮
❚❤❡ ❝♦rr❡❝t❡❞ ✈❛❧✉❡ xbc ❝❛♥ ❜❡ ♦❜t❛✐♥❡❞ ❡♠♣✐r✐❝❛❧❧② ❢r♦♠ ✭s❡❡ ❋✐❣✉r❡ ✸✳✺✮✱
xbc = F−1o [Fm(xm)]. ✭✸✳✼✮
✇❤❡r❡ F−1o ✱ ❞❡✜♥❡❞ ❢r♦♠ ❬✵✱✶❪✱ ✐s t❤❡ ✐♥✈❡rs❡ ❢✉♥❝t✐♦♥ ♦❢ Fo✳
❚❤❡ q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣ ♠❡t❤♦❞ ✐s ♦♥❧② s✉✐t❛❜❧❡ ✇❤❡♥ ♦❜s❡r✈❛t✐♦♥s ❛r❡ ❛✈❛✐❧❛❜❧❡ ❢♦r t❤❡s❛♠❡ t✐♠❡ ♣❡r✐♦❞ ❛s ❢♦r t❤❡ ♠♦❞❡❧ ♦✉t♣✉t ✭❱r❛❝ ❛♥❞ ❋r✐❡❞❡r✐❝❤s✱ ✷✵✶✺✮✳ ❍♦✇❡✈❡r✱ ✐t ♦❢t❡♥❤❛♣♣❡♥s t❤❛t ♦♥❡ ♥❡❡❞s t♦ ❝♦rr❡❝t ♠♦❞❡❧ ♦✉t♣✉t t❤❛t ❝♦✈❡rs ❛ t✐♠❡ ♣❡r✐♦❞ ❧♦♥❣❡r t❤❛♥t❤❛t ♦❢ t❤❡ ♦❜s❡r✈❛t✐♦♥s✳ ❆♥♦t❤❡r ❝❛s❡ ✇❤❡r❡ t❤❡ ❝❧❛ss✐❝❛❧ q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣ ✐s ♥♦t s✉✐t❡❞t♦ ❜✐❛s ❝♦rr❡❝t✐♦♥ ✐s t❤❡ ❝♦rr❡❝t✐♦♥ ♦❢ ♠♦❞❡❧ ❢✉t✉r❡ ♣r❡❞✐❝t✐♦♥s ✭✇❤❡r❡ ♦❜s❡r✈❛t✐♦♥s ❛r❡♦❜✈✐♦✉s❧② ♥♦t ❛✈❛✐❧❛❜❧❡✮✳ ❚❤✐s ♠❡t❤♦❞ ❞♦❡s ♥♦t t❛❦❡ ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ✐♥❢♦r♠❛t✐♦♥ ♦♥ t❤❡❞✐str✐❜✉t✐♦♥ ♦❢ t❤❡ ❢✉t✉r❡ ♠♦❞❡❧❧❡❞ ❞❛t❛s❡t✳ ❚❤❡ ❈❉❋✲❚r❛♥s❢♦r♠ ♠❡t❤♦❞ ✐s ♣r♦♣♦s❡❞ t♦♦✈❡r❝♦♠❡ t❤✐s ♣♦t❡♥t✐❛❧ ✐ss✉❡✳
✸✳✸✳✷ ❈❉❋✲❚r❛♥s❢♦r♠ ▼❡t❤♦❞
❚❤❡ ❈❉❋✲❚r❛♥s❢♦r♠ ❛♣♣r♦❛❝❤ ✭❤❡r❡❛❢t❡r ✧❈❉❋✲t✧✮ ❝❛♥ ❜❡ ♣❡r❝❡✐✈❡❞ ❛s ❛♥ ❡①t❡♥s✐♦♥ ♦❢q✉❛♥t✐❧❡s✲♠❛♣♣✐♥❣✱ ❞✐r❡❝t❧② ❞❡❛❧✐♥❣ ✇✐t❤ ❛♥❞ ♣r♦✈✐❞✐♥❣ ❈❉❋s ✭▼✐❝❤❡❧❛♥❣❡❧✐ ❡t ❛❧✳✱ ✷✵✵✾✮✳
▲❡t Fo,h st❛♥❞ ❢♦r t❤❡ ❈❉❋ ♦❢ ❛ ❝❧✐♠❛t❡ r❛♥❞♦♠ ✈❛r✐❛❜❧❡ ♦❜s❡r✈❡❞ ❛t ❛ ❣✐✈❡♥ ✇❡❛t❤❡rst❛t✐♦♥ ❞✉r✐♥❣ t❤❡ ❤✐st♦r✐❝❛❧ t✐♠❡ ♣❡r✐♦❞ ✭tr❛✐♥✐♥❣ ♣❡r✐♦❞✮ ❛♥❞ Fm,h ❢♦r t❤❡ ❈❉❋ ♦❢ t❤❡
✷✷
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Observation
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❋✐❣✉r❡ ✸✳✺✿ ■❧❧✉str❛t✐♦♥ ♦❢ t❤❡ ◗✉❛♥t✐❧❡✲▼❛♣♣✐♥❣ ▼❡t❤♦❞
✷✸
s❛♠❡ ✈❛r✐❛❜❧❡ ❢r♦♠ t❤❡ ♠♦❞❡❧ ♦✉t♣✉t ❞✉r✐♥❣ t❤❡ s❛♠❡ ♣❡r✐♦❞✳ Fo,f ✭✉♥❦♥♦✇♥✮ ❛♥❞ Fm,f
❛r❡ t❤❡ ❈❉❋s ❡q✉✐✈❛❧❡♥t t♦ Fo,h ❛♥❞ Fm,h ❜✉t ❢♦r ❛ ❢✉t✉r❡ ✭♦r s✐♠♣❧② ❞✐✛❡r❡♥t✮ t✐♠❡♣❡r✐♦❞ ✭s❡❡ ❚❛❜❧❡ ✸✳✷✮✳ ❚❤❡ ♠❛✐♥ ❣♦❛❧ ♦❢ t❤❡ ❈❉❋✲t ✐s t♦ ❛♣♣r♦①✐♠❛t❡ t❤❡ ❈❉❋ ♦❢ t❤❡♦❜s❡r✈❛t✐♦♥s ✐♥ t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞ ✭Fo,f (x)✮ ❜❛s❡❞ ♦♥ ❤✐st♦r✐❝❛❧ ✐♥❢♦r♠❛t✐♦♥ ❛♥❞ t❤❡♥ t♦❛♣♣❧② q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣ ❜❡t✇❡❡♥ Fo,f (x) ❛♥❞ Fm,f (x)✳
❍✐st♦r✐❝❛❧ ♣❡r✐♦❞ ❋✉t✉r❡ ♣❡r✐♦❞
❖❜s❡r✈❛t✐♦♥ Fo,h(x) Fo,f (x) ✭✉♥❦♥♦✇♥✮▼♦❞❡❧ Fm,h(x) Fm,f (x)
❚❛❜❧❡ ✸✳✷✿ ❚❛❜❧❡ s✉♠♠❛r✐③✐♥❣ ❈❉❋ ♥♦t❛t✐♦♥s
❆ss✉♠✐♥❣ t❤❛t ✇❡ ❦♥♦✇ Fm,f ✭✇❤✐❝❤ ❝❛♥ ❜❡ ♠♦❞❡❧❧❡❞ ✈✐❛ ❢✉t✉r❡ ♠♦❞❡❧ ♦✉t♣✉t✮✱ ❛♥❞t❤❛t t❤❡r❡ ❡①✐sts ❛ tr❛♥s❢♦r♠❛t✐♦♥ ❚✿ [0, 1] → [0, 1] s✉❝❤ t❤❛t
T (Fm,h(x)) = Fo,h(x) ✭✸✳✽✮
❚❤❡ ❈❉❚✲t ♠❡t❤♦❞ ✐s ❜❛s❡❞ ♦♥ t❤❡ ❛ss✉♠♣t✐♦♥✱ ✇❤✐❝❤ ✐s ♠❛❞❡ ❜② ♠♦st st❛t✐st✐❝❛❧❜✐❛s ❝♦rr❡❝t✐♦♥ ❛♣♣r♦❛❝❤❡s✱ t❤❛t t❤❡ tr❛♥s❢♦r♠❛t✐♦♥ T ✐s st✐❧❧ ✈❛❧✐❞ ✐♥ t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞
T (Fm,f (x)) = Fo,f (x). ✭✸✳✾✮
❯♥❞❡r t❤✐s ❛ss✉♠♣t✐♦♥✱ ✇❡ ❝❛♥ ❛♣♣r♦①✐♠❛t❡ Fo,f ❜② ❛♣♣❧②✐♥❣ T t♦ Fm,f ✳
❚❤❡ ✜rst st❡♣ ✐s t♦ ♠♦❞❡❧ T ❛♥❞ t❤❡ s✐♠♣❧❡ ✇❛② t♦ ❞♦ s♦ ✐s t♦ r❡♣❧❛❝❡ x ❜② F−1m,h(u)
✐♥ ✭✸✳✽✮✱ ✇❤❡r❡ u ✐s ❛♥② ♣r♦❜❛❜✐❧✐t② ✐♥ [0, 1]✳ ❲❡ t❤❡♥ ♦❜t❛✐♥
T (u) = Fo,h(F−1m,h(u)), ✭✸✳✶✵✮
❝♦rr❡s♣♦♥❞✐♥❣ t♦ t❤❡ s✐♠♣❧❡ ❞❡✜♥✐t✐♦♥ ♦❢ ❚✳ ■♥s❡rt✐♥❣ ✭✸✳✶✵✮ ✐♥ ✭✸✳✽✮ ❧❡❛❞s t♦ ❛ ♠♦❞❡❧❧✐♥❣♦❢ Fm,f ✱
Fo,f = Fo,h(F−1m,h(Fm,f (x))). ✭✸✳✶✶✮
❋r♦♠ ❛ t❡❝❤♥✐❝❛❧✴❛❧❣♦r✐t❤♠✐❝ ♣♦✐♥t ♦❢ ✈✐❡✇✱ t❤❡ ❈❉❋ tr❛♥s❢♦r♠ ❛♣♣r♦❛❝❤ ✐s ❞❡✜♥❡❞✐♥ t❤r❡❡ st❡♣s ❢♦❧❧♦✇✐♥❣ ✭▼✐❝❤❡❧❛♥❣❡❧✐ ❡t ❛❧✳✱ ✷✵✵✾✮ ✿
✶✳ ❚❤❡ ❡st✐♠❛t❡s ♦❢ Fo,h✱ F−1m,h ❛♥❞ Fm,f ✱ r❡s♣❡❝t✐✈❡❧② F̂o,h✱ F̂
−1m,h ❛♥❞ F̂m,f ✱ ❛r❡ ❡♠✲
♣✐r✐❝❛❧❧② ♠♦❞❡❧❧❡❞ r❡s♣❡❝t✐✈❡❧② ❢r♦♠ t❤❡ ❤✐st♦r✐❝❛❧ ♦❜s❡r✈❛t✐♦♥s ❛♥❞ t❤❡ ❤✐st♦r✐❝❛❧❛♥❞ ❢✉t✉r❡ ♠♦❞❡❧ ♦✉t♣✉t ❞❛t❛✳
✷✳ ❚❤❡♥✱ ❜② ❝♦♠❜✐♥✐♥❣ t❤❡♠ ❛❝❝♦r❞✐♥❣ t♦ ❡q✉❛t✐♦♥ ✭✸✳✶✶✮✱ ✇❡ ❞✐s♣♦s❡ ♦❢ F̂0,f ✱ ❛♥❡st✐♠❛t✐♦♥ ♦❢ F0,f ✳ ◆♦t❡ t❤❛t ✐t ✐s ❛❧s♦ ♣♦ss✐❜❧❡ t♦ ✉s❡ ♣❛r❛♠❡tr✐❝ ❈❉❋s✳
✸✳ ❖♥❝❡ F̂m,f ❛♥❞ F̂o,f ❛r❡ ❡st✐♠❛t❡❞✱ q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣ ✐s ❛♣♣❧✐❡❞ ❛s ✐♥ ❙❡❝t✐♦♥ ✸✳✸✳✶
✷✹
❋✐❣✉r❡ ✸✳✻✿ ■❧❧✉str❛t✐♦♥ ♦❢ t❤❡ ❢✉t✉r❡ ♦❜s❡r✈❛t✐♦♥s ❈❉❋ ✭Fo,f ✮ ❡st✐♠❛t✐♦♥
◆♦t❡ t❤❛t✱ ✐♥ t❤❡ ❡q✉❛t✐♦♥ ✭ ✸✳✶✶✮✱ Fo,f ✐s ♦♥❧② ❞❡✜♥❡❞ ❢♦r x ∈ [mh,Mh]✱ ✇❤❡r❡ mh
❛♥❞ Mh ❛r❡ r❡s♣❡❝t✐✈❡❧② t❤❡ ♠✐♥✐♠✉♠ ❛♥❞ t❤❡ ♠❛①✐♠✉♠ ♦❢ t❤❡ ♠♦❞❡❧ ♦✉t♣✉ts ✐♥ t❤❡❤✐st♦r✐❝❛❧ ♣❡r✐♦❞✳ ❖✉ts✐❞❡ [mh,Mh]✱ Fo,f ❣✐✈❡s t❤❡ s❛♠❡ ❝♦♥st❛♥t ✈❛❧✉❡✳ ❆s ✐♥ ✭❉éq✉é✱✷✵✵✼✮ ♦r ✭▼✐❝❤❡❧❛♥❣❡❧✐ ❡t ❛❧✳✱ ✷✵✵✾✮ ❛ ✧❝♦♥st❛♥t ❝♦rr❡❝t✐♦♥✧ ♠❡t❤♦❞ ✐s ❛♣♣❧✐❡❞ ✇❤❡♥❡✈❡rx ✐s ♦✉ts✐❞❡ [mh;Mh] ❡✳❣✳ ✐❢ t❤❡ ♠❛①✐♠✉♠ ✈❛❧✉❡ ♦❢ x ✐♥ t❤❡ r❛♥❣❡ ♦❢ [mh;Mh] ✐s ❝♦rr❡❝t❡❞❜② x0✱ ❛❧❧ x s✉❝❤ ❛s x > Mf ✐s ❝♦rr❡❝t❡❞ ❜② x0✳ ■t ✐s ✐♠♣♦rt❛♥t t♦ ♠❡♥t✐♦♥❡❞ t❤❛t t❤❡♣♦rt✐♦♥ ♦❢ ❞❛t❛ ❢♦r ✇❤✐❝❤ t❤❡ ✧❝♦♥st❛♥t ❝♦rr❡❝t✐♦♥✧ ♠❡t❤♦❞ ✐s ❛♣♣❧✐❡❞ ✐s ✈❡r② s♠❛❧❧✳
✸✳✸✳✸ ❆♣♣❧✐❝❛t✐♦♥ ♦❢ ❈❉❋✲t ❛t ❇■◆●❖ r❡s❡❛r❝❤ s✐t❡s
❲❆❚❈❍ ❢♦r❝✐♥❣ ❞❛t❛ ❊❘❆✲■♥t❡r✐♠ ✭❲❋❉❊■✮ ❛r❡ ✉s❡❞ ❛s r❡❢❡r❡♥❝❡ ❞❛t❛ ❢♦r ❛❧❧ r❡s❡❛r❝❤s✐t❡s✳ ❚❤❡ ❛✈❛✐❧❛❜❧❡ ✈❛r✐❛❜❧❡s ✐♥ ❲❋❉❊■ ❢♦r ❜✐❛s ❝♦rr❡❝t✐♦♥ ❛r❡✿ t❡♠♣❡r❛t✉r❡✱ t♦t❛❧♣r❡❝✐♣✐t❛t✐♦♥✱ s✉r❢❛❝❡ ❛✐r ♣r❡ss✉r❡✱ ♥❡❛r✲s✉r❢❛❝❡ ✇✐♥❞ s♣❡❡❞✱ ❧♦♥❣✴s❤♦rt✇❛✈❡ ✐♥❝✐❞❡♥t r❛✲❞✐❛t✐♦♥ ❛♥❞ ♥❡❛r✲s✉r❢❛❝❡ s♣❡❝✐✜❝ ❤✉♠✐❞✐t②✳ ❚♦ t❛❦❡ ❝❛r❡ ♦❢ t❤❡ s❡❛s♦♥❛❧✐t②✱ t❤❡ ❈❉❋✲t ✐s❛♣♣❧✐❡❞ s❡♣❛r❛t❡❧② ❢♦r ❡❛❝❤ ❝❛❧❡♥❞❡r ♠♦♥t❤✳ ❚❤❡ ❝❛❧✐❜r❛t✐♦♥ ♣❡r✐♦❞ ✐s s❡t t♦ ✶✾✽✵✲✷✵✶✸✳
❙♣❡❝✐❛❧ ❛tt❡♥t✐♦♥ ✐s ❣✐✈❡♥ t♦ ♣r❡❝✐♣✐t❛t✐♦♥ s✐♥❝❡ ✐t s❤♦✇s ❛ ❝♦♥t✐♥✉♦✉s ♣r♦❜❛❜✐❧✐t② ❞✐s✲tr✐❜✉t✐♦♥ ❢♦r str✐❝t❧② ♣♦s✐t✐✈❡ ✈❛❧✉❡s ❜✉t ❤❛s ❛ ❞✐s❝♦♥t✐♥✉✐t② ❛t ③❡r♦✳ ❚❤❡ ❈❉❋✲t ✐s ❛♣♣❧✐❡❞❢♦r ❞❛✐❧② ♣r❡❝✐♣✐t❛t✐♦♥ ❛♠♦✉♥ts ❣r❡❛t❡r t❤❛♥ ❛ ✜①❡❞ t❤r❡s❤♦❧❞✳ ❚❤❡ ❝❤♦s❡♥ t❤r❡s❤♦❧❞ ✐s✵✳✶♠♠ ❢♦r ❲❋❉❊■ ❛♥❞ ❢♦r t❤❡ ♠♦❞❡❧✱ t❤❡ t❤r❡s❤♦❧❞ ✐s ❛❞❥✉st❡❞ s♦ t❤❛t t❤❡ ❢r❡q✉❡♥❝② ♦❢✇❡t ❞❛②s ✐s t❤❡ s❛♠❡ ❛s ✐♥ t❤❡ ❲❋❉❊■✳
✷✺
❋✐❣✉r❡s ✸✳✼ ❛♥❞ ✸✳✽ s❤♦✇ s♦♠❡ r❡s✉❧ts ♦❜t❛✐♥❡❞ ❢♦r ♣r❡❝✐♣✐t❛t✐♦♥ ❛t t❤❡ ❣r✐❞ ♣♦✐♥t♦❢ ❝♦♦r❞✐♥❛t❡s ✭❧♦♥❣✐t✉❞❡❂✼✳✹✻ ❛♥❞ ❧❛t✐t✉❞❡❂✺✶✳✶✶✮✳ ■♥ ✜❣✉r❡ ✸✳✼✱ ❛s ❡①♣❡❝t❡❞✱ ❛ ❣♦♦❞❛❣r❡❡♠❡♥t ❝❛♥ ❜❡ ♦❜s❡r✈❡❞ ❜❡t✇❡❡♥ t❤❡ r❡❢❡r❡♥❝❡ ❞❛t❛ q✉❛♥t✐❧❡s ❛♥❞ t❤❡ q✉❛♥t✐❧❡s ♦❢t❤❡ ♠♦❞❡❧ ❛❢t❡r ❜✐❛s ❝♦rr❡❝t✐♦♥✳ ❆❧t❤♦✉❣❤ ❈❉❋✲t ✐s ❜❛s❡❞ ♦♥ ❝✉♠✉❧❛t✐✈❡ ❞✐str✐❜✉t✐♦♥❢✉♥❝t✐♦♥✱ ✐t ✐s ❛❜❧❡ t♦ ❝♦rr❡❝t ❛❧s♦ t❤❡ ♠❡❛♥ ❛♥❞ t❤❡ ✈❛r✐❛♥❝❡✳ ■♥❞❡❡❞✱ ✐♥ ❋✐❣✉r❡ ✸✳✽ ✇❡❝♦♠♣❛r❡ t❤❡ ♠♦♥t❤❧② ♠❡❛♥ ✭❧❡❢t✮ ❛♥❞ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ ✭r✐❣❤t✮ ♦❢ ❞❛✐❧② ♣r❡❝✐♣✐t❛t✐♦♥❛♥❞ t❤❡r❡ ✐s ❛ ❣♦♦❞ ❛❣r❡❡♠❡♥t ❜❡t✇❡❡♥ t❤❡ r❡❢❡r❡♥❝❡ ❛♥❞ t❤❡ ♠♦❞❡❧ ❛❢t❡r ❈❉❋✲t ❜✐❛s❝♦rr❡❝t✐♦♥✳
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
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●●● ●
●●
● ●●
●
●
●
0 10 20 30 40 50
010
20
30
40
50
WFDEI
CO
SM
O−
CLM
lon= 7.46 lat= 51.11
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
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●
●
●
●
●
●
●
●
●
0 10 20 30 40 50
010
20
30
40
50
WFDEI
CO
SM
O−
CLM
●
●
Model without correction
Model with CDFt correction
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●
●● ●
●●
● ●
●
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●
0 10 20 30 40
010
20
30
40
WFDEI
CO
SM
O−
CLM
lon= 7.46 lat= 51.11
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
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●
●
●
●
●
●
●
●
0 10 20 30 40
010
20
30
40
WFDEI
CO
SM
O−
CLM
●
●
Model without correction
Model with CDFt correction
❋✐❣✉r❡ ✸✳✼✿ ◗✉❛♥t✐❧❡✲q✉❛♥t✐❧❡ ♣❧♦t ♦❢ ❲❋❉❊■ ❞❛✐❧② ♣r❡❝✐♣✐t❛t✐♦♥ ✭♠♠✴❞❛②✮ ❛♥❞ ❈❖❙▼❖✲❈▲▼❞❛✐❧② ♣r❡❝✐♣✐t❛t✐♦♥ ✭♠♠✴❞❛②✮ ✇✐t❤♦✉t ❛♥❞ ✇✐t❤ ❈❉❋✲t ❜✐❛s ❝♦rr❡❝t✐♦♥ ❛t ❧♦❝❛t✐♦♥ ❞❡✜♥❡❞ ❜②❧♦♥❣✐t✉❞❡❂✼✳✹✻ ❛♥❞ ❧❛t✐t✉❞❡❂✺✶✳✶✶✳ ❚❤❡ ❧❡❢t ♣❧♦t ❝♦rr❡s♣♦♥❞s t♦ ❏❛♥✉❛r② ❛♥❞ t❤❡ r✐❣❤t ♣❧♦t t♦t❤❡ ❆✉❣✉st
✷✻
lon= 7.46 lat= 51.11
Mean o
f pre
cip
itation [m
m/d
ay]
23
45
67
8
●
●
●
●
●
●●
●
●
● ●
●
J F M A M J J A S O N D
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
WFDEI
COSMO−CLM without correction
COSMO−CLM with CDFt correction
lon= 7.46 lat= 51.11
Std
of pre
cip
itation [m
m/d
ay]
24
68
10
J F M A M J J A S O N D
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
WFDEI
COSMO−CLM without correction
COSMO−CLM with CDFt correction
❋✐❣✉r❡ ✸✳✽✿ ▼♦♥t❤❧② ♠❡❛♥ ✭❧❡❢t✮ ❛♥❞ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ ✭r✐❣❤t✮ ♦❢ ❞❛✐❧② ♣r❡❝✐♣✐t❛t✐♦♥ ❛t ❧♦❝❛✲t✐♦♥ ❞❡✜♥❡❞ ❜② ❧♦♥❣✐t✉❞❡❂✼✳✹✻ ❛♥❞ ❧❛t✐t✉❞❡❂✺✶✳✶✶✳ ❚❤❡ ♠❡❛♥ ❛♥❞ t❤❡ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ ❛r❡❝❛❧❝✉❧❛t❡❞ ♦♥❧② ❢♦r ✇❡t ❞❛②s
lon= 7.46 lat= 51.11
Mean o
f pre
cip
itation [m
m/h
]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
●
●
●
●
●
● ● ● ●●
●●
J F M A M J J A S O N D
●
● ●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
Observation
Model without correction
Model with CDFt correction
lon= 7.46 lat= 51.11
Std
of pre
cip
itation [m
m/h
]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
J F M A M J J A S O N D
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
Observation
Model without correction
Model with CDFt correction
❋✐❣✉r❡ ✸✳✾✿ ▼♦♥t❤❧② ♠❡❛♥ ✭❧❡❢t✮ ❛♥❞ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ ✭r✐❣❤t✮ ♦❢ ✸ ❤♦✉r❧② ♣r❡❝✐♣✐t❛t✐♦♥ ❛t❧♦❝❛t✐♦♥ ❞❡✜♥❡❞ ❜② ❧♦♥❣✐t✉❞❡❂✼✳✹✻ ❛♥❞ ❧❛t✐t✉❞❡❂✺✶✳✶✶✳
✷✼
❈❤❛♣t❡r ✹
❉❊❈❖ ✕ ❆ ❇■◆●❖ ♣❧✉❣✲✐♥ ❢♦r ❋r❡❱❛
✹✳✶ ❋r❡❱❛ ✕ ❋r❡✐❡ ❯♥✐✈❡rs✐tät ❇❡r❧✐♥ ❡✈❛❧✉❛t✐♦♥ s②st❡♠
❋r❡✈❛ ✐s t❤❡ ❋r❡✐❡ ❯♥✐✈❡rs✐tät ❇❡r❧✐♥ ❊✈❛❧✉❛t✐♦♥ ❋r❛♠❡✇♦r❦ ❢♦r ❊❛rt❤ ❙②st❡♠ ❙❝✐❡♥❝❡✳❚❤❡ ❢✉❧❧② ♦♣❡r❛t✐♦♥❛❧ ❤②❜r✐❞ ❢❡❛t✉r❡s ❛ ❍P❈ s❤❡❧❧ ❛❝❝❡ss ❛♥❞ ❛♥ ✉s❡r ❢r✐❡♥❞❧② ✇❡❜✲✐♥t❡r❢❛❝❡✳ ■t ❡♠♣❧♦②s ♦♥❡ ❝♦♠♠♦♥ s②st❡♠ ✇✐t❤ ❛ ✈❛r✐❡t② ♦❢ ✈❡r✐✜❝❛t✐♦♥ t♦♦❧s ❛♥❞ ✈❛❧✐❞❛✲t✐♦♥ ❞❛t❛ ❢r♦♠ ❞✐✛❡r❡♥t ♣r♦❥❡❝ts ✐♥✲ ❛♥❞ ♦✉ts✐❞❡ ♦❢ t❤❡ ❋❯❇✳ ❚❤❡ ❡✈❛❧✉❛t✐♦♥ s②st❡♠ ✐s❧♦❝❛t❡❞ ❛t t❤❡ ❋❯❇✱ t❤❡ ❉❲❉ ❛♥❞ ●❡r♠❛♥ ❈❧✐♠❛t❡ ❈♦♠♣✉t✐♥❣ ❈❡♥tr❡ ✭❉❑❘❩✮✱ ❡s♣❡✲❝✐❛❧❧② t❤✐s ❤❛s ❞✐r❡❝t ❛❝❝❡ss t♦ t❤❡ ❜✉❧❦ ♦❢ ✐ts ❊❙●❋ ♥♦❞❡ ✐♥❝❧✉❞✐♥❣ ♠✐❧❧✐♦♥s ♦❢ ❝❧✐♠❛t❡♠♦❞❡❧ ❞❛t❛ s❡ts✱ ❡✳❣✳ ❢r♦♠ ❈▼■P✺ ❛♥❞ ❈❖❘❉❊❳✳ ❚❤❡ ❞❛t❛❜❛s❡ ✐s ♦r❣❛♥✐③❡❞ ❜② t❤❡✐♥t❡r♥❛t✐♦♥❛❧ ❈▼❖❘ st❛♥❞❛r❞ ✉s✐♥❣ t❤❡ ♠❡t❛ ✐♥❢♦r♠❛t✐♦♥ ♦❢ t❤❡ s❡❧❢✲❞❡s❝r✐❜✐♥❣ ♠♦❞❡❧✱r❡❛♥❛❧②s✐s ❛♥❞ ♦❜s❡r✈❛t✐♦♥❛❧ ❞❛t❛ s❡ts✳ ❆♣❛❝❤❡ ❙♦❧r ✐s ✉s❡❞ ❢♦r ✐♥❞❡①✐♥❣ t❤❡ ❞✐✛❡r❡♥t ❞❛t❛♣r♦❥❡❝ts ✐♥t♦ ♦♥❡ ❝♦♠♠♦♥ s❡❛r❝❤ ❡♥✈✐r♦♥♠❡♥t✳ ❚❤✐s ✐♠♣❧❡♠❡♥t❡❞ ♠❡t❛ ❞❛t❛ s②st❡♠ ✇✐t❤✐ts ❛❞✈❛♥❝❡❞ ❜✉t ❡❛s② t♦ ❤❛♥❞❧❡ s❡❛r❝❤ t♦♦❧ s✉♣♣♦rts ✉s❡rs✱ ❞❡✈❡❧♦♣❡rs ❛♥❞ t❤❡✐r t♦♦❧st♦ r❡tr✐❡✈❡ t❤❡ r❡q✉✐r❡❞ ✐♥❢♦r♠❛t✐♦♥✳ ❆ ❣❡♥❡r✐❝ ❛♣♣❧✐❝❛t✐♦♥ ♣r♦❣r❛♠♠✐♥❣ ✐♥t❡r❢❛❝❡ ✭❆P■✮❛❧❧♦✇s s❝✐❡♥t✐✜❝ ❞❡✈❡❧♦♣❡rs t♦ ❝♦♥♥❡❝t t❤❡✐r ❛♥❛❧②s✐s t♦♦❧s ✇✐t❤ t❤❡ ❡✈❛❧✉❛t✐♦♥ s②st❡♠✐♥❞❡♣❡♥❞❡♥t❧② ♦❢ t❤❡ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡ ✉s❡❞✳ ❯s❡rs ♦❢ t❤❡ ❡✈❛❧✉❛t✐♦♥ t❡❝❤♥✐q✉❡s❜❡♥❡✜t ❢r♦♠ t❤❡ ❝♦♠♠♦♥ ✐♥t❡r❢❛❝❡ ♦❢ t❤❡ ❡✈❛❧✉❛t✐♦♥ s②st❡♠ ✇✐t❤♦✉t ❛♥② ♥❡❡❞ t♦ ✉♥❞❡r✲st❛♥❞ t❤❡ ❞✐✛❡r❡♥t s❝r✐♣t✐♥❣ ❧❛♥❣✉❛❣❡s✳ ❋❛❝✐❧✐t❛t✐♥❣ t❤❡ ♣r♦✈✐s✐♦♥ ❛♥❞ ✉s❛❣❡ ♦❢ t♦♦❧s ❛♥❞❝❧✐♠❛t❡ ❞❛t❛ ✐♥❝r❡❛s❡s ❛✉t♦♠❛t✐❝❛❧❧② t❤❡ ♥✉♠❜❡r ♦❢ s❝✐❡♥t✐sts ✇♦r❦✐♥❣ ✇✐t❤ t❤❡ ❞❛t❛ s❡ts❛♥❞ ✐❞❡♥t✐❢② ❞✐s❝r❡♣❛♥❝✐❡s✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ❤✐st♦r② ❛♥❞ ❝♦♥✜❣✉r❛t✐♦♥ s✉❜✲s②st❡♠ st♦r❡s❡✈❡r② ❛♥❛❧②s✐s ♣❡r❢♦r♠❡❞ ✇✐t❤ t❤❡ ❡✈❛❧✉❛t✐♦♥ s②st❡♠ ✐♥ ❛ ▼②❙◗▲ ❞❛t❛❜❛s❡✳ ❈♦♥✜❣✉✲r❛t✐♦♥s ❛♥❞ r❡s✉❧ts ♦❢ t❤❡ t♦♦❧s ❝❛♥ ❜❡ s❤❛r❡❞ ❛♠♦♥❣ s❝✐❡♥t✐sts ✈✐❛ s❤❡❧❧ ♦r ✇❡❜✲s②st❡♠✳❚❤❡r❡❢♦r❡✱ ♣❧✉❣❣❡❞✲✐♥ t♦♦❧s ❣❛✐♥ ❛✉t♦♠❛t✐❝❛❧❧② ❢r♦♠ tr❛♥s♣❛r❡♥❝② ❛♥❞ r❡♣r♦❞✉❝✐❜✐❧✐t②✳❋✉rt❤❡r♠♦r❡✱ ✇❤❡♥ ❝♦♥✜❣✉r❛t✐♦♥s ♠❛t❝❤ ✇❤✐❧❡ st❛rt✐♥❣ ❛ ❡✈❛❧✉❛t✐♦♥ t♦♦❧✱ t❤❡ s②st❡♠s✉❣❣❡sts t♦ ✉s❡ r❡s✉❧ts ❛❧r❡❛❞② ♣r♦❞✉❝❡❞ ❜② ♦t❤❡r ✉s❡rs✕s❛✈✐♥❣ ❈P❯ t✐♠❡✱ ■✴❖ ❛♥❞ ❞✐s❦s♣❛❝❡✳ ✇❡❜s✐t❡✿ ❢r❡✈❛✳♠❡t✳❢✉✲❜❡r❧✐♥✳❞❡ ✈✐s✐t♦r✲❧♦❣✐♥✿ ❝❧✐❝❦ ♦♥ ✧●✉❡st✧✳ ❆ ❞❡t❛✐❧❧❡❞ ❞❡✲s❝r✐♣t✐♦♥ ✐s ❝✉rr❡♥t❧② ❜❡✐♥❣ ♣r❡♣❛r❡❞ ❢♦r ●❡♦s❝✐❡♥t✐✜❝ ▼♦❞❡❧ ❉❡✈❡❧♦♣♠❡♥t ✭❑❛❞♦✇ ❡t ❛❧✳✱✐♥ ♣r❡♣❛r❛t✐♦♥✮✳
✷✽
✹✳✷ ❉♦❝✉♠❡♥t❛t✐♦♥ ♦❢ ❉❊❈❖
✹✳✷✳✶ ■♥tr♦❞✉❝t✐♦♥
❚❤❡ ❇■◆●❖✲❉❊❈❖ ❋r❡❱❛ ♣❧✉❣✲✐♥ ♣r♦❞✉❝❡s ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❛♥❞ ❝❧✐♠❛t♦❧♦❣✐❝❛❧ ✐♥♣✉t ❞❛t❛❢♦r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s ✇✐t❤✐♥ t❤❡ ❇■◆●❖ ♣r♦❥❡❝t✳ ❋♦r ❛ ❧✐st ♦❢ ♠♦❞❡❧s s❡❡ ❚❛❜✳ ✹✳✶ ✐♥❙❡❝t✳ ✹✳✷✳✷✳ ❚❤❡ ♣❧✉❣✲✐♥ ✐s ♣❛rt ♦❢ ❛♥ ❣❡♥❡r❛❧ ❡✈❛❧✉❛t✐♦♥ s②st❡♠ ✭❙❡❝t✳ ✹✳✶✮❀ ❛ s❦❡t❝❤ ♦❢t❤✐s s②st❡♠ ✇✐t❤ t❤❡ ❇■◆●❖✲❉❊❈❖ ♣❧✉❣✲✐♥ ❤✐❣❤❧✐❣❤t❡❞ ✐s ❣✐✈❡♥ ✐♥ ❋✐❣✳ ✹✳✶✳ ❋r❡❱❛ ✐s
❋✐❣✉r❡ ✹✳✶✿ ❙❦❡t❝❤ ♦❢ t❤❡ ❋r❡❱❛ ❡✈❛❧✉❛t✐♦♥ s②st❡♠ ✇✐t❤ t❤❡ ❇■◆●❖✲❉❊❈❖ ♣❧✉❣✐♥ ❤✐❣❤❧✐❣❤t❡❞✳
❛ ❢r❛♠❡✇♦r❦ ❤♦st✐♥❣ s❡✈❡r❛❧ ♣❧✉❣✲✐♥s ✭❛♣♣❧✐❝❛t✐♦♥s✮ ✇❤✐❝❤ ❤❛✈❡ ❛❧❧ ❛❝❝❡ss t♦ ❛ ❝♦♠♠♦♥❞❛t❛ ♣♦♦❧✳ ❉❛t❛ ✐♥ t❤✐s ♣♦♦❧ ✐s st❛♥❞❛r❞✐③❡❞ s✉❝❤ t❤❛t ♣❧✉❣✲✐♥s ❝❛♥ ✐♥st❛♥t❧② ❛❝❝❡ss♥❡✇ ❞❛t❛ ✇❤✐❝❤ ❝♦♠❡s ✐♥t♦ t❤✐s ♣♦♦❧✳ ❚❤❡ ❝❧✐♠❛t❡ ❞❛t❛ ♣r♦❞✉❝❡❞ ❢♦r ❇■◆●❖ ✇✐❧❧ ❜❡♣❛rt ♦❢ t❤✐s ♣♦♦❧✳ ❚♦ ✉s❡ t❤❡ ❢r❛♠❡✇♦r❦✱ ✉s❡rs ♠✉st r❡❣✐st❡r ✈✐❛ t❤❡ ❋r❡❱❛ ✇❡❜✲♣❛❣❡❤tt♣s✿✴✴❢r❡✈❛✳♠❡t✳❢✉✲❜❡r❧✐♥✳❞❡✴ ❛♥❞ ❛❝❝❡ss ✐s ❣r❛♥t❡❞ ❜② t❤❡ ❋r❡❱❛ t❡❛♠✳ ❚❤❡ t❡❛♠ ❤❛s❝✉rr❡♥t❧② ❛ ❧✐st ♦❢ ❇■◆●❖ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧❡rs ♣r♦✈✐❞❡❞ ❜② ❲P✸✳
❘❡❣❛r❞❧❡ss ♦❢ t❤❡ ❝❤♦s❡♥ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞❛t❛ s❡t t♦ ❜❡ ♣r♦❝❡ss❡❞✱ t❤❡ ♣❧✉❣✲✐♥ ♣r❡♣❛r❡s❛ s♣❡❝✐✜❝ ❞♦✇♥❧♦❛❞❛❜❧❡ st❛♥❞❛r❞ ♦✉t♣✉t ❛❝❝♦r❞✐♥❣ t♦ t❤❡ s❡❧❡❝t❡❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧ ❛♥❞❘❡s❡❛r❝❤ ❙✐t❡ r❡s♣❡❝t✐✈❡❧② ✭❚❛❜✳ ✹✳✸✮✳ ❇❡s✐❞❡s ♣r❡♣❛r✐♥❣ t❤❡ ♦r✐❣✐♥❛❧ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞❛t❛❢♦r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✱ t❤❡ ♣❧✉❣✲✐♥ ❤❛s ❛♥ ♦♣t✐♦♥ t♦ ❜✐❛s✲❝♦rr❡❝t t❤❡ ❞❛t❛ ❜❛s❡❞ ♦♥❞✐✛❡r❡♥t ♠❡t❤♦❞s ❜❡❢♦r❡❤❛♥❞✱ s❡❡ ❈❤❛♣✳ ✸ ✳
❚❤✐s s❡❝t✐♦♥ ✐s str✉❝t✉r❡❞ ❛s ❢♦❧❧♦✇s✿ ❙❡❝t✐♦♥ ✹✳✷✳✷ ❞❡s❝r✐❜❡s t❤❡ ♣r❡♣r♦❝❡ss✐♥❣✱ ❙❡❝✲t✐♦♥s ✹✳✷✳✸ ❛♥❞ ✹✳✷✳✹ ❣✐✈❡ ❛♥ ♦✈❡r✈✐❡✇ ♦✈❡r t❤❡ ✐♥♣✉t ❛♥❞ t❤❡ ♦✉t♣✉t ♦❢ t❤❡ ❇■◆●❖✲❉❊❈❖
✷✾
♣❧✉❣✲✐♥✱ r❡s♣❡❝t✐✈❡❧②✳
✹✳✷✳✷ Pr❡♣r♦❝❡ss✐♥❣
❚❤❡ ♣r❡♣r♦❝❡ss✐♥❣ ❝♦♥s✐sts ❜❛s✐❝❛❧❧② ♦❢ ❛ s♣❛t✐❛❧ s❡❧❡❝t✐♦♥ ♦❢ t❤❡ r❡❣✐♦♥✴st❛t✐♦♥s✱ ❛s ✇❡❧❧ ❛s❛ t❡♠♣♦r❛❧ s❡❧❡❝t✐♦♥ ♦❢ ❞❛t❡s ♣❧✉s ❛ ❝♦♥✈❡rs✐♦♥ ♦❢ ✈❛r✐❛❜❧❡s ❛♥❞ t❤❡✐r ❛ss♦❝✐❛t❡❞ ✉♥✐ts✳ ❚♦❛✈♦✐❞ ✉♥♥❡❝❡ss❛r② ❣r✐❞ r❡♠❛♣♣✐♥❣✱ ✐♥ t❤❡ ✜rst ✈❡rs✐♦♥ ♦❢ t❤❡ ♣❧✉❣✲✐♥ t❤❡ s♣❛t✐❛❧ s❡❧❡❝t✐♦♥✐s ❛♣♣❧✐❡❞ ♦♥ t❤❡ ♥❛t✐✈❡ ❣r✐❞ ♦❢ t❤❡ ❝❤♦s❡♥ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥♣✉t ❞❛t❛✳ ❋♦r st❛t✐♦♥ ❞❛t❛✱ ❛♥❡❛r❡st ♥❡✐❣❤❜♦r r❡♠❛♣♣✐♥❣ ✭s❡❡ ❝❞♦ ✲r❡♠❛♣♥♥ ✐♥ t❤❡ ❈❉❖ ❯s❡r✬s ●✉✐❞❡ ✭❙❝❤✉❧③✇❡✐❞❛✱✷✵✶✺✮✮ ✐s ❛♣♣❧✐❡❞ t♦ ❣❡t t❤❡ ♥❡❛r❡st ❣r✐❞ ❝❡❧❧ ♦❢ ❛ ❣✐✈❡♥ ❧♦♥❣✐t✉❞❡✴❧❛t✐t✉❞❡ ❧♦❝❛t✐♦♥✳ ❋♦rt❤❡ r❡❣✐♦♥ s❡❧❡❝t✐♦♥✱ ❛ ❜♦① ✇✐❧❧ ❜❡ s❡❧❡❝t❡❞ ✭❝❞♦ ✲s❡❧❧♦♥❧❛t❜♦①✮ r❡❣❛r❞✐♥❣ t♦ ❛ ❞❡✜♥❡❞❧♦♥❣✐t✉❞❡✴❧❛t✐t✉❞❡ r❡❝t❛♥❣❧❡✳ ❚❤✐s ❞❡✜♥✐t✐♦♥ ♦❢ r❡❝t❛♥❣❧❡ ✐s ❜❛s❡❞ ♦♥ t❤❡ r❡♣❧✐❡s t♦ t❤❡❤②❞r♦❧♦❣✐❝❛❧✲♠♦❞❡❧✲❜❛s❡❞ q✉❡st✐♦♥♥❛✐r❡s✱ s❡♥t ❛r♦✉♥❞ ❜② ❇■◆●❖ ❲P✸✳ ❘❡s✉❧ts ♦❢ t❤❡s❡q✉❡st✐♦♥♥❛✐r❡s ❛r❡ ❣✐✈❡♥ ✐♥ ❚❛❜✳ ✹✳✶✳ ◆♦t❡✱ t❤❛t ❞✉❡ t♦ t❤❡ ✉s❡ ♦❢ ♥❛t✐✈❡ ❣r✐❞✱ t❤❡✜♥❛❧ s❡❧❡❝t❡❞ ❣r✐❞ ❜♦✉♥❞❛r② ✐s ❧❛r❣❡r ❛♥❞ ❞♦❡s ♥♦t ❡①❛❝t❧② ♠❛t❝❤ t❤❡ ❞❡✜♥❡❞ r❡❝t❛♥❣❧❡✳◆❡✈❡rt❤❡❧❡ss✱ ❛❧❧ ❣r✐❞ ❝❡❧❧ ❝❡♥t❡rs ♦❢ t❤❡ s❡❧❡❝t❡❞ ♥❛t✐✈❡ ❣r✐❞ ❛r❡ ❞❡✜♥✐t✐✈❡❧② ✐♥s✐❞❡ t❤❡❞❡✜♥❡❞ r❡❝t❛♥❣❧❡ r❛♥❣❡ ❜② ✉s❡rs✳ ❲✐t❤ ✜♥❡r ❣r✐❞s ✐♥ ❧❛t❡r ♣r♦❥❡❝t st❛❣❡s✱ t❤✐s ❡✛❡❝t❜❡❝♦♠❡s ♠♦r❡ ❛♥❞ ♠♦r❡ ♥❡❣❧✐❣✐❜❧❡✳
❚❛❜❧❡ ✹✳✶✿ ◆❛♠✐♥❣ ❝♦♥✈❡♥t✐♦♥ ♦❢ ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s ❛♥❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s ✇❤✐❝❤ ❛r❡✉s❡❞ ✐♥ t❤❡ ❇■◆●❖✲❉❊❈❖ ♣❧✉❣✲✐♥✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ❞❡✜♥❡❞ ❧♦♥✴❧❛t r❡❝t❛♥❣❧❡ ❜❛s❡❞ ♦♥ t❤❡ ✉s❡r✲q✉❡st✐♦♥♥❛✐r❡ ✐s s❤♦✇♥✳ ◆♦t❡✱ ✐♥ ❝❛s❡ ✇❡ ❞✐❞ ♥♦t ❣❡t ❢❡❡❞❜❛❝❦ r❡❧❛t❡❞ t♦ t❤❡ r❡❣✐♦♥ ❜♦✉♥❞❛r✐❡s✱✇❡ ❞❡✜♥❡❞ ❛ r❡❝t❛♥❣❧❡ ♠❛t❝❤✐♥❣ t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡✳
★ ❈♦✉♥tr② ❘❡s❡❛r❝❤ ❙✐t❡ ❍②❞r♦❧✳ ▼♦❞❡❧ ❧♦♥✴❧❛t r❡❝t❛♥❣❧❡
✶ ◆❖❘ ❇❡r❣❡♥ ❊◆❑■ ✺✳✶✵◦❊ ✲ ✺✳✼✻◦❊
✻✵✳✶✸◦◆ ✲ ✻✵✳✻✹◦◆
✷ ◆❖❘ ❇❡r❣❡♥ ❍❇❱ ✺✳✶✵◦❊ ✲ ✺✳✼✻◦❊
✻✵✳✶✸◦◆ ✲ ✻✵✳✻✹◦◆
✸ ◆❊❉ ❱❡❧✉✇❡ ❆❩❯❘❊ ✸✳✵✸✾✻✶✺◦❊ ✲ ✼✳✺✻✾✶✾✾◦❊
✺✵✳✺✽✵✶✼✺◦◆ ✲ ✺✸✳✼✸✼✾✷✷◦◆
✹ ●❊❘ ❲✉♣♣❡r ◆❆❙■▼ ✻✳✾✶✹◦❊ ✲ ✼✳✻✷✵◦❊
✺✵✳✾✾✺◦◆ ✲ ✺✶✳✸✼✵◦◆
✺ ●❊❘ ❲✉♣♣❡r ❚❆▲❙■▼ ✻✳✾✶✹◦❊ ✲ ✼✳✻✷✵◦❊
✺✵✳✾✾✺◦◆ ✲ ✺✶✳✸✼✵◦◆
✻ ❊❙P ❇❛❞❛❧♦♥❛ ■♥❢♦✇♦r❦s✲■❈▼ ✶✳✾✸✺✵✵✵◦❊ ✲ ✷✳✹✵✶✽✼✺◦❊
✹✶✳✷✹✵✵◦◆ ✲ ✹✶✳✻✵✹✹✻◦◆
✼ ❊❙P ❇❛❞❛❧♦♥❛ ▼♦❤✐❞ ✵✳✵✻◦❊ ✲ ✸✳✻✵◦❊
✹✵✳✶◦◆ ✲ ✹✸✳✶◦◆
✸✵
❚❛❜❧❡ ✹✳✷ ❝♦♥t✐♥✉❡❞
✽ P❖❘ ❚❛❣✉s✲❘✐✈❡r ❈❊✲◗❯❆▲✲❲✷ ◆❆ ✭st❛t✐♦♥ ❞❛t❛✮
✾ P❖❘ ❚❛❣✉s✲❘✐✈❡r ❊❈❖✲❙❊▲❋❊ ✾✳✻◦❲ ✲ ✽✳✻◦❲
✸✽✳✹◦◆ ✲ ✸✾✳✸◦◆
✶✵ P❖❘ ❚❛❣✉s✲❘✐✈❡r ❋❡✢♦✇✲❇❆▲❙❊◗ ◆❆ ✭st❛t✐♦♥ ❞❛t❛✮
✶✶ P❖❘ ❚❛❣✉s✲❘✐✈❡r ❍❊❈❍▼❙ ✾✳✸✵◦❲ ✲ ✾✳✵✺◦❲
✸✽✳✼✺✵✵◦◆ ✲ ✸✽✳✾✽✸✸◦◆
✶✷ P❖❘ ❚❛❣✉s✲❘✐✈❡r ◗❯❆▲✲✷❑ ◆❆ ✭st❛t✐♦♥ ❞❛t❛✮
✶✸ P❖❘ ❚❛❣✉s✲❘✐✈❡r ❙❈❍■❙▼ ✾✳✻◦❲ ✲ ✽✳✻◦❲
✸✽✳✹◦◆ ✲ ✸✾✳✸◦◆
✶✹ ❈❨P ❚r♦♦❞♦s✲ ❲❘❋✲❍②❞r♦ ✸✷✳✵◦❲ ✲ ✸✺✳✵◦❲
▼♦✉♥t❛✐♥s ✸✹✳✵◦◆ ✲ ✸✻✳✵◦◆
✹✳✷✳✸ ■♥♣✉t ♣❛r❛♠❡t❡rs
❯s✐♥❣ t❤❡ ✜rst ♦♣t✐♦♥ ♦❢ t❤❡ ♣❧✉❣✲✐♥ ❧❡ts t❤❡ ✉s❡r ❝❤♦♦s❡ ❛♠♦♥❣ t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡s ❛♥❞ t❤❡❛ss♦❝✐❛t❡❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s ❝♦♠❜✐♥❛t✐♦♥ ✭❘❡s❡❛r❝❤ s✐t❡ ❛♥❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧✮✳❚❤❡ ♦♣t✐♦♥ ❉❛t❡ r❛♥❣❡ s♣❡❝✐✜❡s t❤❡ t✐♠❡ ♣❡r✐♦❞ t♦ ❜❡ ♣r♦❝❡ss❡❞✳ ❚❤❡ ♣❛r❛♠❡t❡r ❇✐❛s❝♦rr❡❝t✐♦♥ ♦♣t✐♦♥❛❧❧② ❧❡❛❞s t♦ ❛ s✉❜s❡q✉❡♥t ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❛ ❜✐❛s ❝♦rr❡❝t✐♦♥ s❝❤❡♠❡✭❙❡❝t✳ ✸ t♦ t❤❡ s✐♠✉❧❛t❡❞ ❞❛t❛❀ ❝❤♦♦s❡ ◆♦♥❡ ❢♦r ♥♦ ❜✐❛s ❝♦rr❡❝t✐♦♥ ❛♥❞ ♦✉t♣✉t ♦❢ t❤❡♥❛t✐✈❡✱ ✉♥❝♦rr❡❝t❡❞ ❞❛t❛ ✐♥st❡❛❞✳ ❇✐❛s ❝♦rr❡❝t✐♦♥ ✐s ❛♣♣❧✐❡❞ ✇✐t❤ r❡❢❡r❡♥❝❡ t♦ st❛t✐♦♥❞❛t❛ ✐♥ ❝❛s❡ t❤❡s❡ ❞❛t❛ ✇❛s ♠❛❞❡ ❛❝❝❡ss✐❜❧❡ ❢♦r ✉s ❛♥❞ ✇✐t❤ r❡❢❡r❡♥❝❡ t♦ t❤❡ ❲❆❚❈❍❋♦r❝✐♥❣ ❉❛t❛ ❊❘❆✲■♥t❡r✐♠ ✭❲❋❉❊■✮✭❲❡❡❞♦♥ ❡t ❛❧✳✱ ✷✵✶✹✮ ♦t❤❡r✇✐s❡✳
❚❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥♣✉t ❞❛t❛ t♦ ❜❡ ❝❤♦s❡♥ ❢♦r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧ ❝❛♥ ❜❡ ✉♥✐q✉❡❧②❛❞❞r❡ss❡❞ ❜② s♣❡❝✐❢②✐♥❣ s❡✈❡♥ ♣❛r❛♠❡t❡rs✳ ❚❤❡s❡ ♣❛r❛♠❡t❡rs r❡s✉❧t ❢r♦♠ t❤❡ st❛♥❞❛r❞✲✐③❡❞ st♦r❛❣❡ ♦❢ ❝❧✐♠❛t❡ ♠♦❞❡❧ ❞❛t❛ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ❈▼❖❘ ❝♦♥✈❡♥t✐♦♥ ❛❧s♦ ✉s❡❞ ✐♥ t❤❡❈♦✉♣❧❡❞ ▼♦❞❡❧ ■♥t❡r✲❝♦♠♣❛r✐s♦♥ Pr♦❥❡❝t ✺ ✭❈▼■P✺✱ ❚❛②❧♦r ❡t ❛❧✳✱ ✷✵✶✷✮✳ ❋♦r t❤❡ ❞❡❧✐✈✲❡r❛❜❧❡ ❉✷✳✶ t❤❡s❡ ❛r❡ s❡t ❜② ❞❡❢❛✉❧t✳ ❋♦r ❝♦♠♣❧❡t❡♥❡ss✱ t❤❡s❡ ♦♣t✐♦♥s ❛r❡ ❉❛t❛♣r♦❥❡❝t✱❉❛t❛♣r♦❞✉❝t✱ ■♥st✐t✉t❡ ❛♥❞ ▼♦❞❡❧ ♣r♦✈✐❞✐♥❣ ✐♥♣✉t ❞❛t❛✳ ❋✉rt❤❡r✱ t❤❡ ❊①♣❡r✐✲♠❡♥t✱ ❊♥s❡♠❜❧❡ ♠❡♠❜❡r ❛♥❞ ❚✐♠❡ ❢r❡q✉❡♥❝② ♦❢ ♣r♦✈✐❞❡❞ ✐♥♣✉t ❞❛t❛ ♠✉st ❜❡s♣❡❝✐✜❡❞✳ ▼❛♥② ♦❢ t❤❡s❡ ♣❛r❛♠❡t❡rs ✇✐❧❧ ♠❛❦❡ s❡♥s❡ ❛t ❛ ❧❛t❡r st❛❣❡ ♦❢ ❇■◆●❖✳
❲✐t❤ t❤❡ ❢♦❧❧♦✇✐♥❣ ♣❛r❛♠❡t❡rs ✈❛r✐♦✉s t❡❝❤♥✐❝❛❧ ♦♣t✐♦♥s ❝❛♥ ❜❡ s❡t✿ ❆ s♣❡❝✐✜❝ ♦✉t♣✉t✭❖✉t♣✉t❞✐r✮ ❛♥❞ ❝❛❝❤❡ ❞✐r❡❝t♦r② ✭❈❛❝❤❡❞✐r✮ ❝❛♥ ❜❡ ❞❡✜♥❡❞✱ ♣❧✉s t❤❡ ❖✉t♣✉t t②♣❡✳❇② s❡❧❡❝t✐♥❣ t❤❡ ♦♣t✐♦♥ ❇❛s✐❝ ♦♥❧② ♦♥❡ ❝♦♠♣r❡ss❡❞ ③✐♣✲✜❧❡ ❝♦♥t❛✐♥✐♥❣ t❤❡ ❤②❞r♦❧♦❣✐❝❛❧✲♠♦❞❡❧✲s♣❡❝✐✜❝✲❢♦r♠❛tt❡❞ ❞❛t❛ ✜❧❡s ✇✐❧❧ ❜❡ ♣r♦❞✉❝❡❞✱ ✇❤✐❧❡ ❆❞❞✐t✐♦♥❛❧ ✇✐❧❧ r❡s✉❧t ✐♥ ❛♥❛❞❞✐t✐♦♥❛❧ ◆❡t❈❉❋✲✜❧❡ ❝♦♥t❛✐♥✐♥❣ ❛❧❧ ✈❛r✐❛❜❧❡s✱ t✐♠❡ st❡♣s ❛♥❞ ❧♦❝❛t✐♦♥s✳ ❚❤❡ s✉❜s❡q✉❡♥t♦♣❡r❛t♦r ❈❛❝❤❡❝❧❡❛r ❛❧❧♦✇s t❤❡ ❝❛❝❤❡ ❞✐r❡❝t♦r② t♦ ❜❡ ❝❧❡❛r❡❞ ❛♥❞ t❤❡ ✐♥t❡r♠❡❞✐❛t❡ ❞❛t❛✉s❡❞ ❢♦r ♣r♦❝❡ss✐♥❣ t♦ ❜❡ ❞❡❧❡t❡❞ ♦r ♥♦t✱ ✐♥ ❝❛s❡ ♦♥❡ ✇❛♥ts t♦ ❣✉❛r❞ t❤❡s❡ ❞❛t❛✳ ■♥◆t❛s❦t❤❡ ♥✉♠❜❡r ♦❢ ♣❛r❛❧❧❡❧✲♣r♦❝❡ss✐♥❣ t❛s❦ ❝❛♥ ❜❡ s❡❧❡❝t❡❞✱ t♦ ♦♣t✐♠✐③❡ t❤❡ ✉s❛❣❡ ♦❢ ❝♦♠♣✉t❡r
✸✶
r❡s♦✉r❝❡s✳ ❙❡tt✐♥❣ t❤❡ ♦♣t✐♦♥ ❉r②r✉♥ t♦ ❚r✉❡ ❣✐✈❡s ♦♥❧② ❛ ❧✐st ♦❢ t❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞❛t❛❝❤♦s❡♥✳ ❋✐♥❛❧❧②✱ ❛ ❝❛♣t✐♦♥ ❝❛♥ ❜❡ ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤❡ r❡s✉❧ts ♣r♦❞✉❝❡❞ ❜② t❤✐s r✉♥✳ ❚❤❡❧❛st ♣❛r❛♠❡t❡r ♦♣t✐♦♥ ❯♥✐q✉❡ ♦✉t♣✉t ✐❞ ✇✐❧❧ ♣r❡✈❡♥t ②♦✉ ❢r♦♠ ♦✈❡r✇r✐t✐♥❣ ❛♥ ❡①✐st✐♥❣r❡s✉❧t✳ ❆ ❢✉❧❧ ❧✐st ♦❢ ❛❧❧ ❛✈❛✐❧❛❜❧❡ ♣❛r❛♠❡t❡rs ❛♥❞ t❤❡✐r ❞❡s❝r✐♣t✐♦♥s ❝❛♥ ❜❡ ❢♦✉♥❞ ✐♥❚❛❜✳ ✹✳✷
❚❛❜❧❡ ✹✳✷✿ ■♥♣✉t ♣❛r❛♠❡t❡rs ❢♦r t❤❡ ❇■◆●❖✲❉❊❈❖ ♣❧✉❣✲✐♥✳
❘❡s❡❛r❝❤ s✐t❡ ❛♥❞❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧
❈♦♠❜✐♥❛t✐♦♥ ♦❢ ❘❡s❡❛r❝❤ ❙✐t❡ ❛♥❞ ❍②❞r♦❧♦❣✐❝❛❧ ▼♦❞❡❧ ❢♦r✇❤✐❝❤ ②♦✉ ✇❛♥t t♦ ♣r♦❞✉❝❡ t❤❡ ✐♥♣✉t ❞❛t❛✳
♠❛♥❞❛t♦r②
❉❛t❡ r❛♥❣❡ ❚✐♠❡ ♣❡r✐♦❞ ❢♦r ✇❤✐❝❤ ②♦✉ ✇❛♥t t♦ ♣r♦❝❡ss t❤❡ ❞❛t❛✭❝♦♠♠❛✲s❡♣❛r❛t❡❞ ❢♦r♠❛t✿ ❨❨❨❨✲▼▼✲❉❉✱❨❨❨❨✲▼▼✲❉❉✮✳
♠❛♥❞❛t♦r②
❇✐❛s ❝♦rr❡❝t✐♦♥ ❇✐❛s✲❝♦rr❡❝t✐♦♥ ♠❡t❤♦❞✳
♠❛♥❞❛t♦r②
❉❛t❛♣r♦❥❡❝t ♣r♦✈✐❞✐♥❣✐♥♣✉t ❞❛t❛
❚❤❡ ❞❛t❛ ♣r♦❥❡❝t ♣r♦✈✐❞✐♥❣ t❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞❛t❛✱ ❡✳❣✳❜✐♥❣♦✳
♠❛♥❞❛t♦r②
❉❛t❛♣r♦❞✉❝t ♣r♦✈✐❞✐♥❣✐♥♣✉t ❞❛t❛
❚❤❡ ❞❛t❛ ♣r♦❞✉❝t ♣r♦✈✐❞✐♥❣ t❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥♣✉t❞❛t❛✱ ❡✳❣✳ ❡✉r✲✶✶✳
♠❛♥❞❛t♦r②
■♥st✐t✉t❡ ♣r♦✈✐❞✐♥❣✐♥♣✉t ❞❛t❛
❚❤❡ ✐♥st✐t✉t❡ ♣r♦✈✐❞✐♥❣ t❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥♣✉t ❞❛t❛✱ ❡✳❣✳❝❧♠❝♦♠✳
♠❛♥❞❛t♦r②
▼♦❞❡❧ ♣r♦✈✐❞✐♥❣✐♥♣✉t ❞❛t❛
❚❤❡ ♠♦❞❡❧ ♣r♦✈✐❞✐♥❣ t❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥♣✉t ❞❛t❛✱ ❡✳❣✳❡❝♠✇❢✲❡r❛✐♥t✲❝❧♠❝♦♠✲❝❝❧♠✹✲✽✲✶✼✲✈✶✳
♠❛♥❞❛t♦r②
❊①♣❡r✐♠❡♥t ♦❢♣r♦✈✐❞❡❞ ✐♥♣✉t ❞❛t❛
❚❤❡ ❡①♣❡r✐♠❡♥t ♥❛♠❡ ♦❢ t❤❡ ♣r♦✈✐❞❡❞ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥✲♣✉t ❞❛t❛✱ ❡✳❣✳ ❡✈❛❧✉❛t✐♦♥✳
♠❛♥❞❛t♦r②
❊♥s❡♠❜❧❡ ♠❡♠❜❡r ♦❢♣r♦✈✐❞❡❞ ✐♥♣✉t ❞❛t❛
❚❤❡ ❡♥s❡♠❜❧❡ ♠❡♠❜❡r ♦❢ t❤❡ ♣r♦✈✐❞❡❞ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥✲♣✉t ❞❛t❛✱ ❡✳❣✳ r✶✐✶♣✶✳
♠❛♥❞❛t♦r②
❚✐♠❡ ❢r❡q✉❡♥❝② ♦❢♣r♦✈✐❞❡❞ ✐♥♣✉t ❞❛t❛
❚❤❡ t✐♠❡ ❢r❡q✉❡♥❝② ♦❢ t❤❡ ♣r♦✈✐❞❡❞ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥♣✉t❞❛t❛✱ ❡✳❣✳ ❞❛②✳
♠❛♥❞❛t♦r②
❖✉t♣✉t❞✐r ❖✉t♣✉t ❞✐r❡❝t♦r②
✸✷
❚❛❜❧❡ ✹✳✷ ❝♦♥t✐♥✉❡❞
♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ✴♥❡t✴s❝r❛t❝❤✴✉s❡r✴❡✈❛❧✉❛t✐♦♥❴s②st❡♠✴♦✉t♣✉t✴❜✐♥❣♦❴❞❡❝♦✴t✐♠❡st❡♠♣
❈❛❝❤❡❞✐r ❈❛❝❤❡ ❞✐r❡❝t♦r②
♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ✴♥❡t✴s❝r❛t❝❤✴✉s❡r✴❡✈❛❧✉❛t✐♦♥❴s②st❡♠✴❝❛❝❤❡✴❜✐♥❣♦❴❞❡❝♦✴t✐♠❡st❡♠♣
❖✉t♣✉t t②♣❡ ❚②♣❡ ♦❢ ♦✉♣✉t✳ ❇❛s✐❝✿ ❖♥❡ ❝♦♠♣r❡ss❡❞ ③✐♣✲✜❧❡ ✭st♦r❡❞✐♥ ❖✉t♣✉t❞✐r✴❩■P✮ ❝♦♥t❛✐♥✐♥❣ t❤❡ ❤②❞r♦❧♦❣✐❝❛❧✲♠♦❞❡❧✲s♣❡❝✐✜❡❞✲❢♦r♠❛tt❡❞ ❞❛t❛ ✜❧❡s✳ ❆❞❞✐t✐♦♥❛❧✿ ❆❞❞✐t✐♦♥❛❧❧②✱♦♥❡ ◆❡t❈❉❋✲✜❧❡ ✭st♦r❡❞ ✐♥ ❖✉t♣✉t❞✐r✴◆❊❚❈❉❋✮ ❝♦♥✲t❛✐♥✐♥❣ ❛❧❧ ✈❛r✐❛❜❧❡s✱ t✐♠❡ st❡♣s ❛♥❞ ❧♦❝❛t✐♦♥s✳
♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ❇❛s✐❝
❈❛❝❤❡❝❧❡❛r ❖♣t✐♦♥ t♦ ❝❧❡❛r t❤❡ ❝❛❝❤❡ ❞✐r❡❝t♦r②✳
♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ❚r✉❡
◆t❛s❦ ◆✉♠❜❡r ♦❢ ♣❛r❛❧❧❡❧✲♣r♦❝❡ss✐♥❣ t❛s❦s✳
♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ✻
❉r②r✉♥ ❙❡t ✧❚r✉❡✧ ❢♦r ❥✉st s❤♦✇✐♥❣ t❤❡ ❧✐st ♦❢ ❢♦✉♥❞ ✜❧❡s ♦❢ ②♦✉r❝❤♦s❡♥ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞❛t❛✳ ❙❡t ✧❋❛❧s❡✧ t♦ ♣r♦❝❡ss ❞❛t❛✳
♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ❋❛❧s❡
❈❛♣t✐♦♥ ❆♥ ❛❞❞✐t✐♦♥❛❧ ❝❛♣t✐♦♥ t♦ ❜❡ ❞✐s♣❧❛②❡❞ ✇✐t❤ t❤❡ r❡s✉❧ts✳
♦♣t✐♦♥❛❧
❯♥✐q✉❡ ♦✉t♣✉t ✐❞ ■❢ tr✉❡ ❛♣♣❡♥❞ t❤❡ ❢r❡✈❛ r✉♥ ✐❞ t♦ ❡✈❡r② ♦✉t♣✉t ❢♦❧❞❡r✳
♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ❚r✉❡
✹✳✷✳✹ ❖✉t♣✉t
❚❤❡ r❡s✉❧t✐♥❣ ❞❛t❛ ✜❧❡s ❛r❡ st♦r❡❞ ✐♥ t❤❡ ❝❤♦s❡♥ ❖✉t♣✉t❞✐r ❛♥❞ ❝❛♥ ❜❡ ❛❝❝❡ss❡❞ ❡✐t❤❡r❞✐r❡❝t❧② ✈✐❛ t❤❡ ✇❡❜ ❞♦✇♥❧♦❛❞ ❢r♦♠ t❤❡ ❋r❡❱❛ s②st❡♠ ♦r ❜② ✉s✐♥❣ s❡❝✉r❡ ❝♦♣② ✭s❝♣✮♦r s❡❝✉r❡ s❤❡❧❧ ✭ss❤✮✶✳ ❚❤❡ ❞♦✇♥❧♦❛❞❛❜❧❡ ❝♦♠♣r❡ss❡❞ ③✐♣✲✜❧❡ ✇❤✐❝❤ ❝♦♥t❛✐♥s t❤❡ ❞❛t❛✜❧❡s ❢♦r♠❛tt❡❞ ❛s s♣❡❝✐✜❡❞ ❢♦r t❤❡ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧ ✐s st♦r❡❞ ✐♥ t❤❡ ❖✉t♣✉t❞✐r✴❩■P❞✐r❡❝t♦r②✳ ❆♥ ❛❞❞✐t✐♦♥❛❧❧② ♣r♦❞✉❝❡❞ ◆❡t❈❉❋ ✜❧❡s ✭✐❢ ❖✉t♣✉t t②♣❡ ✐s s❡t ❆❞❞✐t✐♦♥❛❧✮❛r❡ ❧♦❝❛t❡❞ ✐♥ t❤❡ ❖✉t♣✉t❞✐r✴◆❊❚❈❉❋ ❞✐r❡❝t♦r②✳ ◆♦t❡ t❤❛t✱ ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ❝❤♦s❡♥r❡s❡❛r❝❤ s✐t❡ ❛♥❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧✱ t❤❡ ✜❧❡s ✐♥ t❤❡ t✇♦ ❞✐r❡❝t♦r✐❡s ❝♦✉❧❞ ❜❡ t❤❡ s❛♠❡✳❙♦♠❡ ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t t❤❡ ♦✉t♣✉t ❝❛♥ ❜❡ ❢♦✉♥❞ ✐♥ ❚❛❜✳ ✹✳✸✳ ❚❤❡ s♣❡❝✐✜❝ ♦✉t♣✉t ❝♦♥t❡♥t❛♥❞ ❢♦r♠❛t ✐s ❜❛s❡❞ ♦♥ t❤❡ q✉❡st✐♦♥♥❛✐r❡ s❡♥❞ ♦✉t ❜② ❲P✸✳ ■♥ ❝❛s❡ ✇❡ ❞✐❞ ♥♦t ❣❡t ❛♥②❢❡❡❞❜❛❝❦ ❛ st❛♥❞❛r❞ ♦✉t♣✉t ✭◆❡t❈❉❋ ✜❧❡✮ ✇✐❧❧ ❜❡ ♣r♦✈✐❞❡❞✳
✶P❧❡❛s❡ ❝♦♥t❛❝t t❤❡ ❞❡✈❡❧♦♣❡rs ✐❢ ②♦✉ ❧✐❦❡ t♦ ✉s❡ s❝♣ ❛♥❞ ss❤✳
✸✸
❚❛❜❧❡ ✹✳✸✿ ❋✐❧❡ ❢♦r♠❛ts✱ ✈❛r✐❛❜❧❡s ✇✐t❤ ✉♥✐ts ❛♥❞ t❤❡✐r ❞❡s❝r✐♣t✐♦♥ ❣✐✈❡♥ ❢♦r ❡❛❝❤ ❘❡s❡❛r❝❤ ❙✐t❡❛♥❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧ ❝♦♠❜✐♥❛t✐♦♥✳
★ ❚②♣❡ ❋♦r♠❛t ❱❛r✐❛❜❧❡ ❬✉♥✐t❪ ❱❛r✐❛❜❧❡ ❉❡s❝r✐♣t✐♦♥
✶ ❣r✐❞ ♥❝ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮
❝✉r✈✐❧✐♥❡❛r t❛s ❬◦❈❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
✉❛s ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
✈❛s ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥
r❧❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥
❤✉ss ❬✶❪ ◆❡❛r✲❙✉r❢❛❝❡ ❙♣❡❝✐✜❝ ❍✉♠✐❞✐t②
✷ ❣r✐❞ ♥❝ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞✴❧✐q✉✐❞✮
❝✉r✈✐❧✐♥❡❛r t❛s♠✐♥ ❬◦❈❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
t❛s♠❛① ❬◦❈❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
✸ ❣r✐❞ ♥❝ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮
❝✉r✈✐❧✐♥❡❛r t❛s ❬◦❈❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
♣s ❬P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡
❤✉rs ❬✪❪ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②
s❢❝❲✐♥❞ ❬♠✴s❪ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞ ❙♣❡❡❞
rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥
r❧❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥
✹ ❣r✐❞ ♥❝ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮
❝✉r✈✐❧✐♥❡❛r t❛s ❬❑❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
♣s ❬P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡
✉❛s ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
✈❛s ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥
r❧❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥
❤✉ss ❬✶❪ ◆❡❛r✲❙✉r❢❛❝❡ ❙♣❡❝✐✜❝ ❍✉♠✐❞✐t②
✺ ❣r✐❞ ♥❝ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮
❝✉r✈✐❧✐♥❡❛r t❛s ❬◦❈❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
✉❛s ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
✈❛s ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
♣s ❬P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡
✸✹
❚❛❜❧❡ ✹✳✸ ❝♦♥t✐♥✉❡❞
rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥
r❧❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥
❤✉ss ❬✶❪ ◆❡❛r✲❙✉r❢❛❝❡ ❙♣❡❝✐✜❝ ❍✉♠✐❞✐t②
✻ ❣r✐❞ ♥❝✹ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮
❝✉r✈✐❧✐♥❡❛r
✼ ❣r✐❞ ♥❝✹ ✉❛s ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
❝✉r✈✐❧✐♥❡❛r ✈❛s ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
t❛s ❬◦❈❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥
❤✉rs ❬✪❪ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②
❝❧t ❬✪❪ ❚♦t❛❧ ❈❧♦✉❞ ❋r❛❝t✐♦♥
✽ st❛t✐♦♥ ❝s✈ Pr❡❝ ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮
❚♠✐♥ ❬◦❈❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
❚♠❛① ❬◦❈❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
❘❍♠✐♥ ❬✪❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②
❘❍♠❛① ❬✪❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②
✈✈ ❬♠✴s❪ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞ ❙♣❡❡❞
P ❬❦P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡
❘s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥
✾ ❣r✐❞ ♥❝ st♠♣ ❬❑❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
❝✉r✈✐❧✐♥❡❛r ✉✇✐♥❞ ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
✈✇✐♥❞ ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
♣r♠s❧ ❬P❛❪ ❙❡❛ ▲❡✈❡❧ Pr❡ss✉r❡
❞s✇r❢ ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥
❞❧✇r❢ ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥
s♣❢❤ ❬✶❪ ◆❡❛r✲❙✉r❢❛❝❡ ❙♣❡❝✐✜❝ ❍✉♠✐❞✐t②
✶✵ st❛t✐♦♥ ❝s✈ Pr❡❝ ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮
❚♠✐♥ ❬◦❈❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
❚♠❛① ❬◦❈❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
❘❍♠✐♥ ❬✪❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②
❘❍♠❛① ❬✪❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②
✈✈ ❬♠✴s❪ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞ ❙♣❡❡❞
✸✺
❚❛❜❧❡ ✹✳✸ ❝♦♥t✐♥✉❡❞
P ❬❦P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡
❘s ❬❦P❛❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥
✶✶ ❣r✐❞ ❝s✈ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮
❝✉r✈✐❧✐♥❡❛r t❛s ❬◦❈❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
♣s❧ ❬P❛❪ ❙❡❛ ▲❡✈❡❧ Pr❡ss✉r❡
❤✉rs ❬✪❪ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②
s❢❝❲✐♥❞ ❬❦♠✴❤❪ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞ ❙♣❡❡❞
rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥
r❧❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥
✶✷ st❛t✐♦♥ ❝s✈ Pr❡❝ ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮
❚♠✐♥ ❬◦❈❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
❚♠❛① ❬◦❈❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
❘❍♠✐♥ ❬✪❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②
❘❍♠❛① ❬✪❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②
✈✈ ❬♠✴s❪ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞ ❙♣❡❡❞
P ❬❦P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡
❘s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥
✶✸ ❣r✐❞ ♥❝ ✉✇✐♥❞ ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
❝✉r✈✐❧✐♥❡❛r ✈✇✐♥❞ ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
♣r♠s❧ ❬P❛❪ ❙❡❛ ▲❡✈❡❧ Pr❡ss✉r❡
✶✹ ❣r✐❞ ♥❝ t❛s ❬❑❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡
❝✉r✈✐❧✐♥❡❛r ✉❛s ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
✈❛s ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞
♣s ❬P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡
rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥
r❧❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥
❤✉ss ❬✶❪ ◆❡❛r✲❙✉r❢❛❝❡ ❙♣❡❝✐✜❝ ❍✉♠✐❞✐t②
✸✻
❈❤❛♣t❡r ✺
❙✉♠♠❛r②
❚❤✐s ❞♦❝✉♠❡♥t ❞❡s❝r✐❜❡s t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❛ ✇❡❜ ❜❛s❡❞ ❛♣♣❧✐❝❛t✐♦♥ ❢♦r t❤❡ ❡①tr❛❝t✐♦♥❛♥❞ ❝♦♥✈❡rs✐♦♥ ♦❢ ❝❧✐♠❛t❡ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥s✳ ❈❧✐♠❛t❡ ♠♦❞❡❧ ❞❛t❛ ✐s ❡①tr❛❝t❡❞ ❢r♦♠ ❛❝❡♥tr❛❧ ❞❛t❛ ♣♦♦❧✱ ♣♦st✲♣r♦❝❡ss❡❞ ✭❜✐❛s✲❝♦rr❡❝t❡❞✱ r❡❣r✐❞❞❡❞✮ ❛♥❞ ❝♦♥✈❡rt❡❞ t♦ ❛ s❡t ♦❢♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞r✐✈✐♥❣ ❞❛t❛ ❞✐r❡❝t❧② ✉s❛❜❧❡ ❢♦r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✳ ❚❤✐s ❛♣♣❧✐❝❛t✐♦♥❤❛s ❜❡❡♥ r❡❛❧✐③❡❞ ❛s ❛ ♣❧✉❣✲✐♥ t♦ t❤❡ ❋r❡✐❡ ❯♥✐✈❡rs✐tät ❇❡r❧✐♥ ❊✈❛❧✉❛t✐♦♥ ❋r❛♠❡✇♦r❦
❢♦r ❊❛rt❤ ❙②st❡♠ ❙❝✐❡♥❝❡ ✭❋r❡❱❛✮ ✇❤✐❝❤ ❝❛♥ ❤♦❧❞ ✈❛r✐♦✉s t②♣❡s ♦❢ ❡✈❛❧✉❛t✐♦♥ ✇♦r❦✢♦✇s❤❛✈✐♥❣ ❛❝❝❡ss t♦ ❛♥ ✐♥❞❡①❡❞ ❞❛t❛ ♣♦♦❧✳ ❲♦r❦✢♦✇s ❝❛♥ ❜❡ ❛❝❝❡ss❡❞ ✈✐❛ ❛ ✇❡❜✲♣❧❛t❢♦r♠ ♦rt❤❡ ❝♦♠♠❛♥❞ ❧✐♥❡ ✐♥t❡r❢❛❝❡✳ ❚❤❡ ❇■◆●❖✲❉❊❈❖ ♣❧✉❣✲✐♥ ❤❛s ❜❡❡♥ s♣❡❝✐✜❝❛❧❧② ❞❡s✐❣♥❡❞❢♦r t❤❡ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s ❛t t❤❡ s✐① ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s ❜✉t ❝❛♥ ✐♥ ♣r✐♥❝✐♣❧❡ ❜❡❡①t❡♥❞❡❞ t♦ ♦t❤❡r ♠♦❞❡❧s✳ ❆ ♠❛❥♦r ❛❞✈❛♥t❛❣❡ ✐s t❤❡ ♦♥✲❞❡♠❛♥❞ ♣♦st✲♣r♦❝❡ss✐♥❣ ❛♥❞❝♦♥✈❡rs✐♦♥ ♦❢ t❤❡ ❞r✐✈✐♥❣ ❞❛t❛ ❢r♦♠ ❛ st❛♥❞❛r❞✐③❡❞ ❝❧✐♠❛t❡ ♠♦❞❡❧ ❞❛t❛ s♦✉r❝❡✳ ■♥st❡❛❞♦❢ st♦r✐♥❣ ❛♥❞ ❦❡❡♣✐♥❣ t❤❡ ✈❡r② s❛♠❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞r✐✈✐♥❣ ✐♥❢♦r♠❛t✐♦♥ ✐♥ ❞✐✛❡r❡♥t❢♦r♠❛ts✱ t❤❡ s②st❡♠ ❤♦❧❞s t❤❡ ❝♦♥✈❡rs✐♦♥ r♦✉t✐♥❡s ❛♥❞ ❣❡♥❡r❛t❡s t❤❡ ❞❛t❛ ♦♥ ❞❡♠❛♥❞✳❚❤✐s ✐s st♦r❛❣❡ ❡✣❝✐❡♥t ❛♥❞ ❡♥s✉r❡s r❡♣r♦❞✉❝✐❜❧❡ ❛♥❞ tr❛♥s♣❛r❡♥t r❡s✉❧ts✳
✸✼
❇✐❜❧✐♦❣r❛♣❤②
◆✐❦♦❧✐♥❛ ❇❛♥✱ ❏✉❡r❣ ❙❝❤♠✐❞❧✐✱ ❛♥❞ ❈❤r✐st♦♣❤ ❙❝❤är✳ ❍❡❛✈② ♣r❡❝✐♣✐t❛t✐♦♥ ✐♥ ❛ ❝❤❛♥❣✐♥❣❝❧✐♠❛t❡✿ ❉♦❡s s❤♦rt✲t❡r♠ s✉♠♠❡r ♣r❡❝✐♣✐t❛t✐♦♥ ✐♥❝r❡❛s❡ ❢❛st❡r❄ ●❡♦♣❤②s✐❝❛❧ ❘❡s❡❛r❝❤
▲❡tt❡rs✱ ✹✷✭✹✮✿✶✶✻✺✕✶✶✼✷✱ ✷✵✶✺✳
❊r✇❛♥ ❇r✐ss♦♥✱ ▼❛tt❤✐❛s ❉❡♠✉③❡r❡✱ ❛♥❞ ◆✐❝♦❧❡ P▼ ✈❛♥ ▲✐♣③✐❣✳ ▼♦❞❡❧❧✐♥❣ str❛t❡❣✐❡s❢♦r ♣❡r❢♦r♠✐♥❣ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ ❝❧✐♠❛t❡ s✐♠✉❧❛t✐♦♥s✳ ▼❡t❡♦r♦❧♦❣✐s❝❤❡ ❩❡✐ts❝❤r✐❢t✱✷✵✶✺✳
❆✉❣✉st✐♥ ❈♦❧❡tt❡✱ ❘♦❜❡rt ❱❛✉t❛r❞✱ ❛♥❞ ▼ ❱r❛❝✳ ❘❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ❞♦✇♥s❝❛❧✐♥❣ ✇✐t❤ ♣r✐♦rst❛t✐st✐❝❛❧ ❝♦rr❡❝t✐♦♥ ♦❢ t❤❡ ❣❧♦❜❛❧ ❝❧✐♠❛t❡ ❢♦r❝✐♥❣✳ ●❡♦♣❤②s✐❝❛❧ ❘❡s❡❛r❝❤ ▲❡tt❡rs✱ ✸✾✭✶✸✮✱ ✷✵✶✷✳
❉✳ P✳ ❉❡❡ ❡t ❛❧✳ ❚❤❡ ❊❘❆✲✐♥t❡r✐♠ r❡❛♥❛❧②s✐s✿ ❝♦♥✜❣✉r❛t✐♦♥ ❛♥❞ ♣❡r❢♦r♠❛♥❝❡ ♦❢ t❤❡ ❞❛t❛❛ss✐♠✐❧❛t✐♦♥ s②st❡♠✳ ◗✳ ❏✳ ❘✳ ▼❡t❡♦r✳ ❙♦❝✳✱ ✶✸✼✭✻✺✻✮✿✺✺✸✕✺✾✼✱ ✷✵✶✶✳ ■❙❙◆ ✶✹✼✼✲✽✼✵❳✳❞♦✐✿ ✶✵✳✶✵✵✷✴q❥✳✽✷✽✳
▼✐❝❤❡❧ ❉éq✉é✳ ❋r❡q✉❡♥❝② ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ❛♥❞ t❡♠♣❡r❛t✉r❡ ❡①tr❡♠❡s ♦✈❡r ❢r❛♥❝❡ ✐♥ ❛♥❛♥t❤r♦♣♦❣❡♥✐❝ s❝❡♥❛r✐♦✿ ♠♦❞❡❧ r❡s✉❧ts ❛♥❞ st❛t✐st✐❝❛❧ ❝♦rr❡❝t✐♦♥ ❛❝❝♦r❞✐♥❣ t♦ ♦❜s❡r✈❡❞✈❛❧✉❡s✳ ●❧♦❜❛❧ ❛♥❞ P❧❛♥❡t❛r② ❈❤❛♥❣❡✱ ✺✼✭✶✮✿✶✻✕✷✻✱ ✷✵✵✼✳
▲✳ ●✉❞♠✉♥❞ss♦♥✱ ▲✳ ▼✳ ❚❛❧❧❛❦s❡♥✱ ❑✳ ❙t❛❤❧✱ ❛♥❞ ❆✳ ❑✳ ❋❧❡✐❣✳ ▲♦✇✲❢r❡q✉❡♥❝② ✈❛r✐❛❜✐❧✐t②♦❢ ❡✉r♦♣❡❛♥ r✉♥♦✛✳ ❍②❞r♦❧✳ ❊❛rt❤ ❙②st❡♠ ❙❝✐✳✱ ✶✺✭✾✮✿✷✽✺✸✕✷✽✻✾✱ ✷✵✶✶✳
❯✳ ❍❡✐❦❦✐❧ä✳✱ ❆✳ ❙❛♥❞✈✐❦✳✱ ❛♥❞ ❆✳ ❙♦rt❡❜❡r❣✳ ❉②♥❛♠✐❝❛❧ ❞♦✇♥s❝❛❧✐♥❣ ♦❢ ❊❘❆✲✹✵ ✐♥❝♦♠♣❧❡① t❡rr❛✐♥ ✉s✐♥❣ t❤❡ ✇r❢ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧✳ ❈❧✐♠✳ ❉②♥✳✱ ✸✼✭✼✲✽✮✿✶✺✺✶✕✶✺✻✹✱✷✵✶✶✳
❈✳ ❑❛❞♦✇✱ ❙✳ ■❧❧✐♥❣✱ ❖✳ ❑✉♥st✱ ❚✳ ❙❝❤❛rt♥❡r✱ ■✳ ❑✐r❝❤♥❡r✱ ❍✳❲✳ ❘✉st✱ ❯✳ ❈✉❜❛s❝❤✱ ❛♥❞❯ ❯❧❜r✐❝❤✳ ❋r❡✈❛ ✲ ❢r❡✐❡ ✉♥✐✈ ❡✈❛❧✉❛t✐♦♥ ❢r❛♠❡✇♦r❦ ❢♦r s❝✐❡♥t✐✜❝ ✐♥❢r❛str✉❝t✉r❡s ✐♥ ❡❛rt❤s②st❡♠ ♠♦❞❡❧✐♥❣✳ ●❡♦s❝✐❡♥t✐❢✳ ▼♦❞❡❧ ❉❡✈❡❧♦♣✳✱ ✐♥ ♣r❡♣❛r❛t✐♦♥✳
❊❧✐③❛❜❡t❤ ❏ ❑❡♥❞♦♥✱ ◆✐❣❡❧ ▼ ❘♦❜❡rts✱ ❍❛②❧❡② ❏ ❋♦✇❧❡r✱ ▼❛❧❝♦❧♠ ❏ ❘♦❜❡rts✱ ❙t❡✈❡♥ ❈❈❤❛♥✱ ❛♥❞ ❈❛t❤❡r✐♥❡ ❆ ❙❡♥✐♦r✳ ❍❡❛✈✐❡r s✉♠♠❡r ❞♦✇♥♣♦✉rs ✇✐t❤ ❝❧✐♠❛t❡ ❝❤❛♥❣❡ r❡✲✈❡❛❧❡❞ ❜② ✇❡❛t❤❡r ❢♦r❡❝❛st r❡s♦❧✉t✐♦♥ ♠♦❞❡❧✳ ◆❛t✉r❡ ❈❧✐♠❛t❡ ❈❤❛♥❣❡✱ ✹✭✼✮✿✺✼✵✕✺✼✻✱✷✵✶✹✳
✸✽
❍✳ ❑♦❝❤✱ ❙✳ ▲✐❡rs❝❤✱ ❛♥❞ ❋✳ ❍❛tt❡r♠❛♥♥✳ ■♥t❡❣r❛t✐♥❣ ✇❛t❡r r❡s♦✉r❝❡s ♠❛♥❛❣❡♠❡♥t ✐♥❡❝♦✲❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧❧✐♥❣✳ ■♥t❡❣r❛t✐✈❡ ❲❛t❡r ❘❡s♦✉r❝❡ ▼❛♥❛❣❡♠❡♥t ✐♥ ❛ ❈❤❛♥❣✐♥❣
❲♦r❧❞✿ ▲❡ss♦♥s ▲❡❛r♥t ❛♥❞ ■♥♥♦✈❛t✐✈❡ P❡rs♣❡❝t✐✈❡s✱ ♣❛❣❡ ✶✸✱ ✷✵✶✸✳
❏♦❝❤❡♠ ▼❛r♦t③❦❡✱ ❲♦❧❢❣❛♥❣ ❆ ▼ü❧❧❡r✱ ❋r❡❥❛ ❙❊ ❱❛♠❜♦r❣✱ P❛✉❧ ❇❡❝❦❡r✱ ❯❧r✐❝❤ ❈✉❜❛s❝❤✱❍❡♥❞r✐❦ ❋❡❧❞♠❛♥♥✱ ❋r❛♥❦ ❑❛s♣❛r✱ ❈❤r✐st♦♣❤ ❑♦tt♠❡✐❡r✱ ❈❛♠✐❧❧❡ ▼❛r✐♥✐✱ ■✉❧✐✐❛P♦❧❦♦✈❛✱ ❡t ❛❧✳ ▼✐❦❧✐♣✲❛ ♥❛t✐♦♥❛❧ r❡s❡❛r❝❤ ♣r♦❥❡❝t ♦♥ ❞❡❝❛❞❛❧ ❝❧✐♠❛t❡ ♣r❡❞✐❝t✐♦♥✳ ❇✉❧✲❧❡t✐♥ ♦❢ t❤❡ ❆♠❡r✐❝❛♥ ▼❡t❡♦r♦❧♦❣✐❝❛❧ ❙♦❝✐❡t②✱ ✭✷✵✶✻✮✱ ✷✵✶✻✳
P✳ ▼❝❈✉❧❧❛❣❤ ❛♥❞ ❏✳ ◆❡❧❞❡r✳ ●❡♥❡r❛❧✐③❡❞ ▲✐♥❡❛r ▼♦❞❡❧s✳ ❈❘❈ Pr❡ss✱ ❇♦❝❛ ❘❛t♦♥✱ ❋❧❛✱✷ ❡❞✐t✐♦♥✱ ✶✾✽✾✳
❊❞♠✉♥❞ P ▼❡r❡❞✐t❤✱ ❱❧❛❞✐♠✐r ❆ ❙❡♠❡♥♦✈✱ ❉♦✉❣❧❛s ▼❛r❛✉♥✱ ❲♦♥s✉♥ P❛r❦✱ ❛♥❞ ❆❧❡①❛♥✲❞❡r ❱ ❈❤❡r♥♦❦✉❧s❦②✳ ❈r✉❝✐❛❧ r♦❧❡ ♦❢ ❜❧❛❝❦ s❡❛ ✇❛r♠✐♥❣ ✐♥ ❛♠♣❧✐❢②✐♥❣ t❤❡ ✷✵✶✷ ❦r②♠s❦♣r❡❝✐♣✐t❛t✐♦♥ ❡①tr❡♠❡✳ ◆❛t✉r❡ ●❡♦s❝✐❡♥❝❡✱ ✷✵✶✺✳
P✲❆ ▼✐❝❤❡❧❛♥❣❡❧✐✱ ▼❛tt❤✐❡✉ ❱r❛❝✱ ❛♥❞ ❍ ▲♦✉❦♦s✳ Pr♦❜❛❜✐❧✐st✐❝ ❞♦✇♥s❝❛❧✐♥❣ ❛♣♣r♦❛❝❤❡s✿❆♣♣❧✐❝❛t✐♦♥ t♦ ✇✐♥❞ ❝✉♠✉❧❛t✐✈❡ ❞✐str✐❜✉t✐♦♥ ❢✉♥❝t✐♦♥s✳ ●❡♦♣❤②s✐❝❛❧ ❘❡s❡❛r❝❤ ▲❡tt❡rs✱✸✻✭✶✶✮✱ ✷✵✵✾✳
❲♦❧❢❣❛♥❣ ❆ ▼✉❡❧❧❡r✱ ❏♦❤❛♥♥❛ ❇❛❡❤r✱ ❍❡❧♠✉t❤ ❍❛❛❦✱ ❏♦❤❛♥♥ ❍ ❏✉♥❣❝❧❛✉s✱ ❏ür❣❡♥❑rö❣❡r✱ ❉❛♥✐❡❧❛ ▼❛t❡✐✱ ❉✐r❦ ◆♦t③✱ ❍♦❧❣❡r P♦❤❧♠❛♥♥✱ ❏❙ ❙t♦r❝❤✱ ❛♥❞ ❏♦❝❤❡♠ ▼❛r♦t③❦❡✳❋♦r❡❝❛st s❦✐❧❧ ♦❢ ♠✉❧t✐✲②❡❛r s❡❛s♦♥❛❧ ♠❡❛♥s ✐♥ t❤❡ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥ s②st❡♠ ♦❢ t❤❡ ♠❛①♣❧❛♥❝❦ ✐♥st✐t✉t❡ ❢♦r ♠❡t❡♦r♦❧♦❣②✳ ●❡♦♣❤②s✐❝❛❧ ❘❡s❡❛r❝❤ ▲❡tt❡rs✱ ✸✾✭✷✷✮✱ ✷✵✶✷✳
❍❛♥s ❆ P❛♥♦❢s❦② ❛♥❞ ●❧❡♥♥ ❲✐❧s♦♥ ❇r✐❡r✳ ❙♦♠❡ ❛♣♣❧✐❝❛t✐♦♥s ♦❢ st❛t✐st✐❝s t♦ ♠❡t❡♦r♦❧♦❣②✳❯♥✐✈❡rs✐t② P❛r❦ ✿ P❡♥♥✳ ❙t❛t❡ ❯♥✐✈❡rs✐t②✱ ❈♦❧❧❡❣❡ ♦❢ ❊❛rt❤ ❛♥❞ ▼✐♥❡r❛❧ ❙❝✐❡♥❝❡s✱ ✶✾✻✽✳
❍♦❧❣❡r P♦❤❧♠❛♥♥✱ ❲♦❧❢❣❛♥❣ ❆ ▼✉❡❧❧❡r✱ ❑ ❑✉❧❦❛r♥✐✱ ▼ ❑❛♠❡s✇❛rr❛♦✱ ❉❛♥✐❡❧❛ ▼❛t❡✐✱❋❙❊ ❱❛♠❜♦r❣✱ ❈ ❑❛❞♦✇✱ ❙ ■❧❧✐♥❣✱ ❛♥❞ ❏♦❝❤❡♠ ▼❛r♦t③❦❡✳ ■♠♣r♦✈❡❞ ❢♦r❡❝❛st s❦✐❧❧ ✐♥t❤❡ tr♦♣✐❝s ✐♥ t❤❡ ♥❡✇ ♠✐❦❧✐♣ ❞❡❝❛❞❛❧ ❝❧✐♠❛t❡ ♣r❡❞✐❝t✐♦♥s✳ ●❡♦♣❤②s✐❝❛❧ ❘❡s❡❛r❝❤ ▲❡tt❡rs✱✹✵✭✷✶✮✿✺✼✾✽✕✺✽✵✷✱ ✷✵✶✸✳
❆♥❞r❡❛s ❋ Pr❡✐♥✱ ❲♦❧❢❣❛♥❣ ▲❛♥❣❤❛♥s✱ ●✐♦r❣✐❛ ❋♦ss❡r✱ ❆♥❞r❡✇ ❋❡rr♦♥❡✱ ◆✐❦♦❧✐♥❛ ❇❛♥✱❑❧❛✉s ●♦❡r❣❡♥✱ ▼✐❝❤❛❡❧ ❑❡❧❧❡r✱ ▼❡r❥❛ ❚ö❧❧❡✱ ❖❧✐✈❡r ●✉t❥❛❤r✱ ❋r❛✉❦❡ ❋❡s❡r✱ ❡t ❛❧✳ ❆ r❡✲✈✐❡✇ ♦♥ r❡❣✐♦♥❛❧ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ ❝❧✐♠❛t❡ ♠♦❞❡❧✐♥❣✿ ❉❡♠♦♥str❛t✐♦♥s✱ ♣r♦s♣❡❝ts✱❛♥❞ ❝❤❛❧❧❡♥❣❡s✳ ❘❡✈✐❡✇s ♦❢ ❣❡♦♣❤②s✐❝s✱ ✺✸✭✷✮✿✸✷✸✕✸✻✶✱ ✷✵✶✺✳
▼✳ ❇✳ Pr✐❡st❧❡②✳ ❙♣❡❝tr❛❧ ❆♥❛❧②s✐s ❛♥❞ ❚✐♠❡ ❙❡r✐❡s✳ ❆❝❛❞❡♠✐❝ Pr❡ss✱ ▲♦♥❞♦♥✱ ✶✾✾✷✳
❈✳ Pr✉❞❤♦♠♠❡✱ ■✳ ●✐✉♥t♦❧✐✱ ❊✳ ▲✳ ❘♦❜✐♥s♦♥✱ ❉✳ ❈❧❛r❦ ❇✱ ◆✳ ❲✳ ❆r♥❡❧❧✱ ❘✳ ❉❛♥❦❡rs✱❇✳ ▼✳ ❋❡❦❡t❡✱ ❲✳ ❋r❛♥ss❡♥✱ ❉✳ ●❡rt❡♥✱ ❙✳ ◆✳ ●♦s❧✐♥❣✱ ❡t ❛❧✳ ❍②❞r♦❧♦❣✐❝❛❧ ❞r♦✉❣❤ts✐♥ t❤❡ ✷✶st ❝❡♥t✉r②✱ ❤♦ts♣♦ts ❛♥❞ ✉♥❝❡rt❛✐♥t✐❡s ❢r♦♠ ❛ ❣❧♦❜❛❧ ♠✉❧t✐♠♦❞❡❧ ❡♥s❡♠❜❧❡❡①♣❡r✐♠❡♥t✳ Pr♦❝✳ ◆❛t✳ ❆❝❛❞✳ ❙❝✐✳✱ ✶✶✶✭✾✮✿✸✷✻✷✕✸✷✻✼✱ ✷✵✶✹✳
❇✳ ❘♦❝❦❡❧✱ ❆✳ ❲✐❧❧✱ ❛♥❞ ❆✳ ❍❡♥s❡✳ ❚❤❡ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧ ❈❖❙▼❖✲❈▲▼ ✭❈❈▲▼✮✳▼❡t❡♦r♦❧✳ ❩✳✱ ✶✼✭✹✮✿✸✹✼✕✸✹✽✱ ✷✵✵✽✳
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❍✳ ❲✳ ❘✉st✱ ❚✳ ❑r✉s❝❤❦❡✱ ❆✳ ❉♦❜❧❡r✱ ▼✳ ❋✐s❝❤❡r✱ ❛♥❞ ❯✳ ❯❧❜r✐❝❤✳ ❉✐s❝♦♥t✐♥✉♦✉s ❞❛✐❧②t❡♠♣❡r❛t✉r❡s ✐♥ t❤❡ ✇❛t❝❤ ❢♦r❝✐♥❣ ❞❛t❛s❡ts✳ ❏✳ ❍②❞r♦♠❡t❡♦r✳✱ ✶✻✭✶✮✿✹✻✺✕✹✼✷✱ ✷✵✶✺✳
❯✳ ❙❝❤✉❧③✇❡✐❞❛✳ ❈❧✐♠❛t❡ ❉❛t❛ ❖♣❡r❛t♦rs✿ ❈❉❖ ❯s❡r✬s ●✉✐❞❡✳ ▼P■ ❢♦r ▼❡t❡♦r♦❧♦❣②✱ ❖❝✲t♦❜❡r ✷✵✶✺✳ ❯❘▲ ❤tt♣s✿✴✴❝♦❞❡✳③♠❛✇✳❞❡✴♣r♦❥❡❝ts✴❝❞♦✴❡♠❜❡❞❞❡❞✴❝❞♦✳♣❞❢✳ ❱❡rs✐♦♥✶✳✼✳✵✳
❉♦✉❣ ▼ ❙♠✐t❤✱ ❙t❡♣❤❡♥ ❈✉s❛❝❦✱ ❆♥❞r❡✇ ❲ ❈♦❧♠❛♥✱ ❈❤r✐s ❑ ❋♦❧❧❛♥❞✱ ●❧❡♥ ❘ ❍❛rr✐s✱❛♥❞ ❏❛♠❡s ▼ ▼✉r♣❤②✳ ■♠♣r♦✈❡❞ s✉r❢❛❝❡ t❡♠♣❡r❛t✉r❡ ♣r❡❞✐❝t✐♦♥ ❢♦r t❤❡ ❝♦♠✐♥❣ ❞❡❝❛❞❡❢r♦♠ ❛ ❣❧♦❜❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧✳ s❝✐❡♥❝❡✱ ✸✶✼✭✺✽✸✾✮✿✼✾✻✕✼✾✾✱ ✷✵✵✼✳
❑✳ ❊✳ ❚❛②❧♦r✱ ❘✳ ❏✳ ❙t♦✉✛❡r✱ ❛♥❞ ●✳ ❆✳ ▼❡❡❤❧✳ ❆♥ ♦✈❡r✈✐❡✇ ♦❢ ❈▼■P✺ ❛♥❞ t❤❡ ❡①♣❡r✐♠❡♥t❞❡s✐❣♥✳ ❇✉❧❧✳ ❆♠❡r✳ ▼❡t❡♦r✳ ❙♦❝✳✱ ✾✸✭✹✮✿✹✽✺✕✹✾✽✱ ✷✵✶✷✳
❈❧é♠❡♥t ❚✐ss❡✉✐❧✱ ▼ ❱r❛❝✱ ● ●r❡♥♦✉✐❧❧❡t✱ ❆❏ ❲❛❞❡✱ ▼ ●❡✈r❡②✱ ❚❤✐❡rr② ❖❜❡r❞♦r✛✱ ❏✲❇ ●r♦❞✇♦❤❧✱ ❛♥❞ ❙ ▲❡❦✳ ❙tr❡♥❣t❤❡♥✐♥❣ t❤❡ ❧✐♥❦ ❜❡t✇❡❡♥ ❝❧✐♠❛t❡✱ ❤②❞r♦❧♦❣✐❝❛❧ ❛♥❞s♣❡❝✐❡s ❞✐str✐❜✉t✐♦♥ ♠♦❞❡❧✐♥❣ t♦ ❛ss❡ss t❤❡ ✐♠♣❛❝ts ♦❢ ❝❧✐♠❛t❡ ❝❤❛♥❣❡ ♦♥ ❢r❡s❤✇❛t❡r❜✐♦❞✐✈❡rs✐t②✳ ❙❝✐❡♥❝❡ ♦❢ t❤❡ t♦t❛❧ ❡♥✈✐r♦♥♠❡♥t✱ ✹✷✹✿✶✾✸✕✷✵✶✱ ✷✵✶✷✳
❈✳ ❚♦r♠❛✱ ❋✳ ●✐♦r❣✐✱ ❛♥❞ ❊✳ ❈♦♣♣♦❧❛✳ ❆❞❞❡❞ ✈❛❧✉❡ ♦❢ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧✐♥❣ ♦✈❡r❛r❡❛s ❝❤❛r❛❝t❡r✐③❡❞ ❜② ❝♦♠♣❧❡① t❡rr❛✐♥✖♣r❡❝✐♣✐t❛t✐♦♥ ♦✈❡r t❤❡ ❆❧♣s✳ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳✿❆t♠♦s♣❤❡r❡s✱ ✶✷✵✭✾✮✿✸✾✺✼✕✸✾✼✷✱ ✷✵✶✺✳ ✷✵✶✹❏❉✵✷✷✼✽✶✳
◆ ❱✐❣❛✉❞✱ ▼ ❱r❛❝✱ ❛♥❞ ❨ ❈❛❜❛❧❧❡r♦✳ Pr♦❜❛❜✐❧✐st✐❝ ❞♦✇♥s❝❛❧✐♥❣ ♦❢ ❣❝♠ s❝❡♥❛r✐♦s ♦✈❡rs♦✉t❤❡r♥ ✐♥❞✐❛✳ ■♥t❡r♥❛t✐♦♥❛❧ ❏♦✉r♥❛❧ ♦❢ ❈❧✐♠❛t♦❧♦❣②✱ ✸✸✭✺✮✿✶✷✹✽✕✶✷✻✸✱ ✷✵✶✸✳
▼❛t❤✐❡✉ ❱r❛❝ ❛♥❞ P❡tr❛ ❋r✐❡❞❡r✐❝❤s✳ ▼✉❧t✐✈❛r✐❛t❡✲✐♥t❡r✈❛r✐❛❜❧❡✱ s♣❛t✐❛❧✱ ❛♥❞ t❡♠♣♦r❛❧✲❜✐❛s ❝♦rr❡❝t✐♦♥✳ ❏♦✉r♥❛❧ ♦❢ ❈❧✐♠❛t❡✱ ✷✽✭✶✮✿✷✶✽✕✷✸✼✱ ✷✵✶✺✳
●✳ P✳ ❲❡❡❞♦♥✱ ●✳ ❇❛❧s❛♠♦✱ ◆✳ ❇❡❧❧♦✉✐♥✱ ❙✳ ●♦♠❡s✱ ▼✳ ❏✳ ❇❡st✱ ❛♥❞ P✳ ❱✐t❡r❜♦✳ ❚❤❡✇❢❞❡✐ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❢♦r❝✐♥❣ ❞❛t❛ s❡t✿ ❲❛t❝❤ ❢♦r❝✐♥❣ ❞❛t❛ ♠❡t❤♦❞♦❧♦❣② ❛♣♣❧✐❡❞ t♦❡r❛✲✐♥t❡r✐♠ r❡❛♥❛❧②s✐s ❞❛t❛✳ ❲❛t❡r ❘❡s♦✉r✳ ❘❡s✳✱ ✺✵✭✾✮✿✼✺✵✺✕✼✺✶✹✱ ✷✵✶✹✳
❚✳ ❲✳ ❨❡❡✳ ❱❡❝t♦r ❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r ❛♥❞ ❛❞❞✐t✐✈❡ ♠♦❞❡❧s✳ ❙♣r✐♥❣❡r✱ ✷✵✶✺✳
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