Finding needles in haystacks: symbolic resonance analysis of event-related potentials unveils different processing demands.

Abstract

Previous ERP studies have found an N400-P600 pattern in sentences in which the number of arguments does not match the number of arguments that the verb can take. In the present study, we elaborate on this question by investigating whether the case of the mismatching object argument in German (accusative/direct object versus dative/indirect object) affects processing differently. In general, both types of mismatches elicited a biphasic N400-P600 response in the ERP. However, traditional voltage average analysis was unable to reveal differences between the two mismatching conditions, that is, between a mismatching accusative versus dative. Therefore, we employed a recently developed method on ERP data analysis, the symbolic resonance analysis (SRA), where EEG epochs are symbolically encoded in sequences of three symbols depending on a given parameter, the encoding threshold. We found a larger proportion of threshold crossing events with negative polarity in the N400 time window for a mismatching dative argument compared to a mismatching accusative argument. By contrast, the proportion of threshold crossing events with positive polarity was smaller for dative in the P600 time window. We argue that this difference is due to the phenomenon of "free dative" in German. This result also shows that the SRA provides a useful tool for revealing ERP differences that cannot be discovered using the traditional voltage average analysis.

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Research Report
Finding needles in haystacks: Symbolic resonance analysis of
event-related potentials unveils different processing demands
Stefan Frischa,b,T, Peter beim Grabenb,c
aMax-Planck-Institute of Human Cognitive and Brain Sciences, Leipzig, Germany
bInstitute of Linguistics, University of Potsdam, Germany
cInstitute of Physics, University of Potsdam, Germany
Accepted 1 March 2005
Available online 8 April 2005
Abstract
Previous ERP studies have found an N400–P600 pattern in sentences in which the number of arguments does not match the number of
arguments that the verb can take. In the present study, we elaborate on this question by investigating whether the case of the mismatching
object argument in German (accusative/direct object versus dative/indirect object) affects processing differently. In general, both types of
mismatches elicited a biphasic N400–P600 response in the ERP. However, traditional voltage average analysis was unable to reveal
differences between the two mismatching conditions, that is, between a mismatching accusative versus dative. Therefore, we employed a
recently developed method on ERP data analysis, the symbolic resonance analysis (SRA), where EEG epochs are symbolically encoded in
sequences of three symbols depending on a given parameter, the encoding threshold. We found a larger proportion of threshold crossing
events with negative polarity in the N400 time window for a mismatching dative argument compared to a mismatching accusative argument.
By contrast, the proportion of threshold crossing events with positive polarity was smaller for dative in the P600 time window. We argue that
this difference is due to the phenomenon of bfree dativeQ in German. This result also shows that the SRA provides a useful tool for revealing
ERP differences that cannot be discovered using the traditional voltage average analysis.
D 2005 Elsevier B.V. All rights reserved.
Theme: Neural basis of behavior
Topic: Cognition
Keywords: Event-related brain potential; Language processing; Argument structure; Symbolic dynamic; Stochastic resonance
1. Introduction
Much has been written on the many different types of
linguistic information that have to be brought together when
we understand a sentence. Generally, it is undisputed that the
verbanditsargumentsconstitutethebcoreQofasentence[32].
Thus,mappingtheargumentsinasentencetotheverbslotsis
the crucial point in deriving a coherent sentential interpreta-
tion,thatis,foransweringthequestionofwhoisdoingwhatto
whom as for example in a sentence such as (1).
(1). Peter visited Mary at night.
We immediately understand that the sentence tells us
something about a visiting event and that this event has two
participants, namely Peter and Mary. Moreover, we also do
not hesitate to conclude that Peter is doing the visiting (i.e.,
that he is the agent), whereas Mary is the one being visited
(i.e., that she is the patient). In other words, we would not
doubt that it is Peter who visits Mary and not vice versa. But
our feeling that this interpretation is derived fast and
effortlessly should not obscure the fact that much informa-
tion processing has to be performed by our brains in order to
achieve it. Accordingly, this central issue has led to many
studies in both psycholinguistics (see [15], for an overview)
as well as aphasiology (see [17], for an overview). In order
0926-6410/$ - see front matter D 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.cogbrainres.2005.03.004
T Corresponding author. Max-Planck Institute of Human Cognitive and
Brain Sciences, P.O. Box 500 355, D-04303 Leipzig, Germany. Fax: +49
341 99 40 113.
E-mail address: frisch@cbs.mpg.de (S. Frisch).
Cognitive Brain Research 24 (2005) 476–491
www.elsevier.com/locate/cogbrainres

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to characterize this type of information more closely, we will
consider a sentence such as (2), which can immediately be
judged to be unacceptable in English.
(2). *Peter snored Mary at night.
Since the surface structure of (2) is identical to (1), the
reason for the unacceptability must lie in different properties
of the verb to snore in (2) compared to the verb to visit in
(1). More specifically, a verb such as to visit can take a
subject argument (Peter) and an object argument (Mary),
whereas an object is not possible in a verb such as to snore,
but only a subject (Peter). Interestingly, this difference can
be described not only syntactically (i.e., with respect to
sentence structure), but also in terms of semantics (i.e., with
respect to meaning/interpretation), in that the event
expressed by the verb in (1) has two participants (one
doing the visiting and one being visited), whereas the
snoring event in (2) has only one participant (one doing the
snoring). Obviously, our language processing routines have
to determine whether the number of arguments in a sentence
matches with the number of arguments a verb can take, and
a mismatch (such as in (2)) induces both syntactic as well as
semantic problems in processing. It is therefore not
unexpected that electrophysiological patterns in response
to a mismatch such as in (2) seem to reflect this twofold
nature of the violation. Event-related brain potential (ERP)
studies in both English [29] and German [11,15] sentences
in which an argument could not be integrated into the verb’s
argument structure have been reported to elicit a biphasic
N400–P600 response. Friederici and Frisch [11] have
presented sentences with a subject (SUB) and a direct
object (OBJ), but with an intransitive verb (i.e., only
allowing for a subject, but no object) such as in (3).
(3). *Paulweig,dassderChemikerdenPhysikeremigrierte...
Paul knows that [the chemist]SUB [the physicist]OBJ
emigrated.
On the mismatching verb, they found an N400 followed
by a P600 compared to a condition with a transitive verb.
Similar to Osterhout et al. [29], they interpreted the N400
for these types of violation as an indicator of the semantic
anomaly induced by a thematic role mismatch, i.e., by the
fact that there are more arguments that need a thematic role
than there are roles provided by the verb. The P600 was
seen to indicate the fact that a transitive structure is built up
which is however not licensed by the lexicon information of
the (intransitive) verb (cf. [10,15]).
A numerical correspondence between the arguments in a
sentence and the argument structure information specified in
the verb’s lexical entry, however, does not suffice to
determine who is doing what to whom. What is necessary
in addition is that the different thematic roles of the verb are
correctly assigned to the different arguments in the sentence.
In a sentence such as (1), it is important to know that the
verb provides two roles (agent and patient) and that there
are two candidates to receive those roles (Peter and Mary),
but this alone does not tell us that Peter is doing the visiting
and Mary is being visited and not vice versa. The arguments
have to be systematically assigned (mapped) to the
respective syntactic constituents. Thereby, the respective
thematic bhierarchizationQ of the arguments has to be
preserved, that is, the fact that verb arguments are
distinguishable on thematic dimensions such as control
[30] (with the agent Peter in (1) having more control over
the visiting event than the patient Mary). There are
important cues in the linguistic input that allow us to
determine the correct assignment effortlessly, at least in
most cases. These cues are not the same for all languages,
and German and English provide good examples for
languages with differing cues. In an English (declarative)
sentence such as (1), the linear order of the arguments is
crucial: Peter is (linearly, in a left-to-right sequence) the first
argument in the clause and therefore the higher argument
(with more agentive properties) compared to the second
argument Mary that is thematically lower. In German, by
contrast, case morphology is the crucial cue for hierarchiz-
ing arguments (cf. [7,13]), as it is in many other languages
with a relatively free word order. In a sentence such as (3),
the subject indeed precedes the object, but in (4), the first
argument bears accusative (ACC) case (direct object),
whereas the second argument is marked with the subject
case nominative (NOM).
(4). Den Dichter hat der Arzt zuerst besucht.
[the poet]ACC has [the doctor]NOM first visited.
Assigning the thematic roles in (4) on the basis of linear
order would lead to a completely different (and wrong)
interpretation of the sentence. That case information of
arguments in German is used immediately for syntactic
analysis as well as thematic interpretation (i.e., hierarchiza-
tion) can also be traced neurophysiologically [7,13,14]. For
example, it can be shown that constructions with two
identically case marked arguments induce a biphasic pattern
of an N400 (reflecting thematic interpretation problems) and
a subsequent P600 (reflecting ill-formedness) compared to
sentences in which the arguments can be hierarchized on the
basis of different case markings [13,14].
With respect to ditransitive constructions, that is,
sentences with two object arguments, English also
strictly relies on argument order. In (5a), it is clear that
the tickets are given and the brother must be the recipient of
the tickets. Swapping the argument noun phrases (NPs)
would result in a semantic anomaly, see (5b).
(5a). Mary gave her brother the tickets.
(5b). ??Mary gave the tickets her brother.
In German, by contrast, this is again different, as it is
again the case marking of the arguments (rather than their
linear order) which determines their grammatical function:
A dative (DAT) marked NP is the indirect object, whereas
an accusative NP is the direct object. This is independent of
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the linear sequence of the two since (6a) and (6b) have the
same meaning.
(6a). Der Junge hat dem Freund das Buch gegeben.
[the boy]NOM has [the friend]DAT [the book]ACC
given.
dthe boy has given the book to his friendT.
(6b). Der Junge hat das Buch dem Freund gegeben.
[the boy]NOM has [the book]ACC [the friend]DAT
given.
dthe boy has given the book to his friendT.
With respect to the earlier studies testing constructions
with a surplus argument [11,15], there is – at first sight – no
reason not to expect a biphasic N400–P600 effect for a
transitive verb that occurs in a sentence with three argu-
ments such as (7).
(7). *Der Junge hat dem Freund das Buch gekannt.
[the boy]NOM has [the friend]DAT [the book]ACC
known.
However, although the argument bdem FreundQ in (7)
cannot be integrated into the argument structure of a verb
such as kennen (to know), the question arises whether the
resulting processing problems might differ from those
induced by the verb in (3). Such an assumption could be
derived from the fact that the mismatching NP bears dative
(indirect object) case and that dative case in German can be
used in order to expand the argument structure of a
transitive (nominative–accusative) verb, see (8).
(8). Anna hat ihrem Bruder das Motorrad repariert.
Anna has [her brother]DAT [the motorcycle]ACC
repaired.
dAnna has repaired the motorcycle for her brotherT.
The verb reparieren (to repair) itself has only two
arguments (a repairer and something being repaired),
according to the criterion of semantic necessity [33]. Adding
a so-called benefactive dative serves to indicate someone
who profits from (or is harmed by) the event expressed by
the verb. Adding an argument expressing a beneficent is
possible in many languages, although it is achieved by
different syntactic means. In English, for example, such a
beneficent is not realized as an indirect object, but by means
of a prepositional phrase (PP) with bforQ (see (8)). In
German, by contrast, it is realized as an indirect object with
dative case, which behaves syntactically exactly like a btrueQ
(i.e., semantically necessary, cf. [33]) dative argument of a
ditransitive verb such as dem Freund in (6a) and (6b) and is
therefore syntactically indistinguishable from the latter.1
There is some controversy concerning the exact conditions
which have to be met so that a benefactive dative in German
can be added (such as in (8)) or whether such a procedure
results in an unacceptable construction (such as in (7))
[34,37]. It has been argued, for example, that a benefactive
dative is not possible if such a status of the dative argument
was not intended by the agent [37], as it is normally not the
case with experiencer verbs. Furthermore, it was proposed
that (8) is not possible when the benefactive dative is not
physically affected [34]. Although none of these accounts
gives an exhaustive characterization, they converge in the
view that the benefactive dative has to fulfill restrictions by
the verb that are by and large semantic in nature (cf.
[34,36,37]). By contrast, there is no such possibility of
adding an accusative object in German sentences with
transitive verbs that mark their object irregularly with dative
case, such as in (9).
(9). *Anna hat ihrem Bruder die Hausaufgaben geholfen.
Anna has [her brother]DAT [the homework]ACC
helped.
This principal possibility – however limited – for adding
a dative–but not an accusative–argument to a transitive
relation might affect the ERP patterns for an extra-dative
compared to an extra-accusative differently. With respect to
the present study, therefore, the following questions arise:
First, is the biphasic N400–P600 pattern as found for
argument structure violations in intransitive (Frisch et al.,
2004) and transitive structures (Friederici and Frisch, 2000)
also found in ditransitives such as (7) or (9)? Second, do the
linguistic differences between adding a dative and adding an
accusative affect the N400–P600 differently for an incorrect
dative compared to an incorrect accusative?
2. The present study
From the fact that adding a dative argument in German is
only semantically restricted whereas adding an accusative is
both syntactically and semantically impossible, one might
expect different electrophysiological responses for sentences
with a mismatching dative (inducing mainly semantic
processing problems) compared to sentences in which an
accusative marked argument cannot be integrated (inducing
both semantic and syntactic processing problems). Although
sentences with a mismatching argument have been consis-
tently found to elicit biphasic N400–P600 patterns in ERPs
[11,15], these patterns might be different depending on the
type of argument, that is, if the mismatching argument bears
accusative or dative case. Therefore, we presented sentences
with a surplus accusative as well as with a surplus dative
object and compared the ERP responses on the verb to those
1It has been argued that, in German, there is a similar way to add a
beneficent by means of a PP as in English and that this PP is equivalent to a
benefactive dative [19]. This was taken as evidence that benefactive dative
in German is an adjunct rather than an argument. However, it can be shown
that Anna hat das Motorrad fu ¨r ihren Bruder repariert (Anna has repaired
the motorcycle for her brother) is not a paraphrase of Sentence 8 [9].
Furthermore, the fact that benefactives are affected by all syntactic
restrictions (for example, recipient passive, topicalization, etc.) in exactly
the same way as brealQ argument datives can be taken as a criterion to give
them argument status [9].
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elicited by correct sentences. Seeing that traditional voltage
average analysis was only able to replicate the generally
expected ERP pattern, but not the fine-grained differences
between the two mismatching conditions, a newly devel-
oped analysis procedure, the symbolic resonance analysis
[4], was employed.
3. Materials and methods
3.1. Subjects
Sixteen monolingual native speakers of German (mean
age 23 years, six female), all students from the University of
Leipzig, participated in the experiment. They were all right-
handed according to Oldfield [27] and had normal or
corrected-to-normal vision. They were naRve with respect to
the aims of the study and were paid for their participation.
3.2. Materials
All sentences were created out of 40 sets of three NPs and
a sentence final PP. Each of these sets had four different
verbs, two ditransitive ones that completed the sentence
correctly, a transitive verb that marked its sole object in the
accusative,andonewhosesoleobjecthadtobeardativecase.
The second ditransitive verb was used to create another 80
sentences in order to balance the number of correct and
incorrect conditions. Sentences in this latter condition were
treated as fillers and were not analyzed any further as the
verbs in this condition were not matched with respect to
lexicalparameters.Bycontrast,suchamatchingwasdonefor
the three groups of critical verbs that were kept similar in
logarithmic lemma frequency as determined on the basis of
theCELEXdatabase(cf.[1]).Themeanforcorrectverbswas
1.19, for the verbs not subcategorizing a dative 1.28, and for
the verbs that could not take an accusative 1.10. An ANOVA
performed for these frequencies revealed an F b 1 and no
differences in direct single comparisons [correct vs. dative:
F b 1; correct vs. accusative: F b 1; dative vs. accusative:
F(1,78) = 1.62, P = 0.21].
Seeing that German declarative sentences have an
unmarked order with respect to the object arguments (with
the dative object preceding the accusative object, see (5a)
and (5b)), we were faced with the possible confound that the
distance between the mismatching argument and the critical
verb was different for the dative and the accusative object.
We therefore decided to use welcher/which-questions where
the which-constituent is always in the same position (i.e., at
the beginning of the subclause) irrespective of its case.
Furthermore, we varied the argument in the which-position
systematically between direct/accusative and indirect/dative
object, as exemplified in (10a) and (10b).
(10). Jochen weig,
Jochen knows
(a) [welchen Betrag]ACC [der Bl7ser]NOM [dem
Geiger]DAT neulich VERB-te
[which amount]ACC [the trumpeter]NOM [the violinist]
DAT recently VERB-ed
(b) [welchem Geiger]DAT [der Bl7ser]NOM [den
Betrag]ACC neulich VERB-te
[which violinist]DAT [the trumpeter]NOM [the amount]
ACC recently VERB-ed
bei jener Reise nach Paris.
during that visit to Paris.
Examples for the VERB-position for each of the three
critical conditions are provided in (11), (12), and (13):
(11). COR: correct (ditransitive) verb: borgte (lent).
(12). DAT: verb which cannot take a dative argument:
verbrauchte (consumed).
(13). ACC: verb which cannot take an accusative argument:
half (helped).
After the verb, a complex (and therefore preferably
extraposed) prepositional phrase (PP) such as bduring that
visit to ParisQ in (10) was added in order to avoid
confounding sentence final wrap-up effects (cf. [11,28]).
3.3. Procedure
There were 80 sentences in each of the three critical
conditions (40 with the dative argument in which-position
and 40 with the accusative argument in which-position). All
sentences were presented in randomized order in the center
of a computer monitor as words or phrases, respectively. All
three NPs and the second PP were presented for 500 ms, the
first PP for 550 ms. All other items were presented word-by-
word for 400 ms. The ISI was 100 ms. 800 ms after the
sentence final PP, the subjects were asked to judge the
acceptability of the sentence within a 2500-ms interval by
pressing a button. 1000 ms after their response, the next trial
began.
The EEG was recorded by means of 59 Ag/AgCl
electrodes with a sampling rate of 250 Hz and was
referenced to the left mastoid (re-referenced to linked
mastoids off-line). In order to control for eye movement
artifacts, a horizontal electro-oculogram (EOG) was moni-
tored from electrodes at the outer canthus of each eye and a
vertical EOG from two electrodes located above and below
the subject’s right eye. Electrode impedances were kept
below 5 kV. EEG and EOG channels were recorded
continuously with a band pass filter from DC to 30 Hz
with a digitization rate of 250 Hz.
3.4. EEG data analysis
EEG data were high pass filtered with a cutoff frequency
of 0.4 Hz in order to compensate for drifts. Only correctly
performed trials without ocular or amplifier saturation
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artifacts entered the EEG data analysis (83% of all trials,
evenly distributed across conditions).
3.4.1. Voltage average data
ERPs were averaged in a 1300-ms time window (relative
to the onset of the critical verb) and aligned to a 200-ms pre-
stimulus baseline. ERPs were additionally filtered with a 10-
Hz low pass filter for presentation purposes only.
3.4.2. Symbolic resonance analysis
3.4.2.1. General idea.
research suggest that only polarity and latency of a voltage
deflection are to be taken into consideration even at the level
of single EEG trials. This has, of course, some tradition in
ERP analysis: by counting the number of EEG epochs
which have a positive or negative voltage value at a certain
instance of time, one obtains the polarity histogram
reflecting the intertrial coherence of the ERP [8]. Lehmann
[22] suggested to consider only positive and negative
maximal field values. The common overlap of their time
ranges across trials yields again a measure of the intertrial
coherence. However, these coarse-graining techniques were
lacking a theoretical foundation that has recently been
provided by beim Graben et al. [6] (cf. [3,5,16]) in the
framework of symbolic dynamics [18,23]. In this branch of
nonlinear science, measured or predicted time series of
dynamical systems are mapped onto sequences of very few
symbols by partitioning the range of values that is assumed
by the data. In the case of ERP data, for example, one can
take the pre-stimulus baseline as a threshold and assign the
symbols b+Q or b?Q to each sample point if the measured
EEG in a single trial is above or below the baseline at this
time point, respectively, thus obtaining a sequence of b+Q
and b?Q.2After collecting all the sequences corresponding
to one experimental condition in an ensemble, the number
of b+Q or b?Q symbols across all trials yields the polarity
histogram [8]. beim Graben et al. [6] have shown that these
polarity histograms can be formally captured by probability
measures of cylinder sets, which are subsets drawn from an
ensemble of sequences having a common building block,
which is called a word. beim Graben et al. [6] have further
argued that ERP components are characterized by large
cylinder sets corresponding to a particular word. The
likelihood of these cylinders is then assessed by generalized
polarity histograms, the word statistics [5,16], and by
information theoretic measures such as the Shannon entropy
or measures of complexity [2,31], which serve as indicators
of the intertrial coherence [24].
In particular, Lehmann’s idea to encode the maxima and
minima of the EEG time series has led us to developing the
The naming conventions of ERP
symbolic resonance analysis (SRA) of ERP data [4]. In the
approach pursued in the present paper, three symbols
instead of two are assigned to the EEG data at each sample
point by introducing two thresholds which partition the
range of voltage values of the EEG into three intervals. This
results in the following encoding rule (cf. [4]):
(14). One symbol (b0Q) is assigned to all sample points
below the lower threshold, the second one (b1Q) for the
sample points above the lower and below the upper
threshold, and the third (b2Q) for all data points above the
upper threshold.
The distance between both thresholds can be varied, but
the absolute value, abbreviated h, of both thresholds must be
the same (i.e., both thresholds are equidistant from the
baseline and only different in their signs).3
An EEG epoch is thereby mapped onto a sequence of
b0Qs, b1Qs, and b2Qs. For instance, b10122Q means that the
signal was between the thresholds at times t = 1 and t = 3,
below the lower threshold at t = 2, and above the upper
threshold at t = 4 and t = 5. Since time is represented by
discrete sampling points, for a sample rate of, e.g., 250 Hz,
t = 1 corresponds to 4 ms, t = 2 to 8 ms, and so on. It is
clear that the symbolic representation of the EEG epoch
depends on the chosen threshold. If h is too small, the
intermediary symbol b1Q will not occur often since the
signal is oscillating between its maxima and minima. If, on
the other hand, h is too large, that is, larger than the
maximum of the absolute value of the upper and lower
boundaries of the signal, the symbols b0Q and b2Q will
never occur, and one observes only sequences of b1Qs.
Let us assume that the absolute value h of the threshold is
slightly larger than the amplitude of the ERP content of the
signal, which results from the ensemble average of the
baseline aligned EEG epochs. Employing the encoding rule
(14) at the signal yields a sequence of only b1Qs since the
thresholds ?h and +h will not be exceeded by the signal at
all.
However, because a single epoch of the raw EEG is
regarded in the traditional voltage averaging analysis as the
sum of the underlying nonstationary ERP wave and some
noise, rule (14) applied to the raw EEG yields b2Qs
whenever the noise drives the signal across the upper
threshold +h near the maxima of the ERP, and b0Qs if the
2Note that the particular symbols assigned to the measurements are
completely arbitrary. So one might also use b0Q instead of b?Q and b1Q
instead of b+Q, or baQ instead of b?Q and bbQ instead of b+Q, or any other
representation.
3As one of the referees suggested, one could compute the standard
deviation of the signal in the pre-stimulus time window and express the
threshold in standard deviation units. We actually attempted this during the
development of the SRA. Compared to the use of absolute voltages, this
approach has one serious disadvantage: the standard deviation is obtained
for each single EEG time series, and the standard deviations of different
trials could thus differ significantly. As a consequence, using standard
deviation units, one would abandon any information about the amplitude of
the ERP. As we will point out below, the critical encoding threshold
represents this important information. Thus, absolute voltage thresholds
make the SRA results more compatible with the averaged ERPs than
standard deviation thresholds would do.
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sum of the ERP and the noise is smaller than the lower
threshold ?h, which is the case around the minima of the
ERP. Thus, the local maxima and minima of the ERP are
encoded by b2Qs and b0Qs, respectively. This is illustrated
in Fig. 1, where we display in Fig. 1(A) a nonstationary
ERP-like test signal (a Bessel function) having a local
maximum at t = 0 with amplitude 1 and two local minima
around t = ?4 and t = +4. Adding noise to this
subthreshold signal (Fig. 1(B)) makes threshold crossing
events probable, resulting in the symbol b2Q around t = 0
and the symbol b0Q around t = ?4 and t = +4.
As we have already mentioned, while the background
EEG superimposed with the ERP is commonly regarded as
being detrimental noise in the customary ERP analysis that
has to be eliminated by averaging, our three-symbol
encoding rule (14) utilizes it constructively to drive the
subthreshold ERP signal across the encoding thresholds.
By encoding each EEG epoch for a fixed threshold, we
obtain a set of sequences, which can be arranged as an array
of the symbols b0Q, b1Q, and b2Q. Table 1 displays such a
possible array, where the time is given by the columns while
the rows denote the trial index.
The next step of the SRA is determining the word
statistics (i.e., the polarity histogram). We restrict ourselves
to the statistics of the three symbols across trials. The word
statistics count the relative frequencies of b0Qs, b1Qs, and
b2Qs depending on time. Considering Table 1 again, we
observe that at t = 1, the frequency of b0Qs is P0= 0.25, the
frequency of b1Qs is P1= 0.50 and the frequency of b2Qs is
P2= 0.25. At t = 2, we have P0= 0.50, P1= 0, P2= 0.50,
and so on. Table 2 shows the resulting symbol distributions.
Let us assume that there is a local maximum in the ERP
at t = 4 with no effects at other times for this example. beim
Graben and Kurths [4] presented an algorithm to transform
the distribution of three symbols to a distribution of only
two symbols, b0Q and b2Qs, where b0Q denotes a local
minimum in the ERP, while b2Q denotes a local maximum.4
This transformation, which is inspired by the theory of spin
lattice models in statistical mechanics [35] works in the
following way: The differences of the symbol frequencies
M0= P0? P1and M2= P2? P1are regarded as competing
bmagnetic fieldsQ (so-called mean-fields) which act at the
symbol distribution across the columns of Table 1 trying to
flip the bundecidedQ symbol b1Q either into a b0Q, if M0z 0 N
M2(i.e., there are more b0Qs than b2Qs, which thereby win the
competition), or into a b2Q, if M0b 0 V M2(when there are
more b2Qs than b0Qs). We present the magnetic field strengths
for the example from Table 1 in Table 3.
By looking at the mean-fields in Table 3, we can now
decide how the b1Qs of Table 1 must be flipped into b0Qs or
b2Qs, according to the spin-flip transformation. At t = 1 we
have M2V M0b 0, where the transform is still undefined.
We close this gap by saying that, if M2V M0b 0 or M2z
M0N 0, the b1Qs should be equally converted into the same
number of b0Qs and b2Qs, i.e., one half of the b1Qs becomes
b0Qs while the other half becomes b2Qs. Thus, at t = 1, we
obtain column one of Table 4 where the b1Q in the first row
of Table 1 is converted into b0Q and the b1Q in row 3 is
flippedinto ab2Q.Theparticularsymbolthathastobeflipped
was chosen randomly. At t = 2 we see that M2z M0N 0, the
second case where the b1Qs are equally converted into b0Qs
and b2Qs. However, in our example, there is no b1Q to which
the transformation applies so that nothing happens. At t = 3
and also at t = 5, we encounter the same situation as at t = 1.
However, at t = 4, there is a real winner of the competition,
namely, b2Q, where M0b 0 V M2. Here, all b1Qs are flipped
into b2Qs. The mean-field transformation might remind the
reader of the game bReversiQ, where single-colored chips
have to be flipped when they are trapped by chips of the
converse color. We will therefore call this transformation the
Reversi transformation (see Table 4).
4Our presentation of the mean-field transformation here deviates a bit
from that given by beim Graben and Kurths [4] in order to make the idea
more clear.
Fig. 1. (A) An ERP like test signal (the zero-order Bessel function of the
first kind) with a positive voltage deflection at t = 0. (B) The test signal
superimposed with Gaussian white noise of variance 0.64 and encoding
thresholds yielding a symbolic dynamics with b0Q, b1Q, and b2Q.
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After employing the Reversi transformation, we obtain
an array of only b0Qs and b2Qs (cf. [4]) where b0Q denotes
bnegative polarityQ and b2Q denotes bpositive polarityQ with
respect to the chosen threshold. From this recoded array, we
determine again the word statistics that are shown in Table 5
for the present example.
The symbols b0Q and b2Q are obviously uniformly
distributed for t = 1, 2, 3, 5 but not at t = 4, where the
distribution is highly degenerated. As we have pointed out
above, in our example model, an ERP deflection was
assumed at t = 4, thus the spin-flip transformation enhances
threshold crossing events in the positive and negative
direction in a strongly nonlinear way, while suppressing
random fluctuations around thebaselinewhich leads either to
a large number of b1Qs in the original three-symbol encoding
for large thresholds, or to an almost uniform distribution of
b0Qs and b2Qs for small thresholds. Both cases are mapped by
the Reversi transformation onto a uniform distribution of
b0Qs and b2Q.
From the word statistics, we then derive the running
cylinder entropies [6] that are presented in Table 6 for the
example data.
Entropy is a measure of uncertainty of a given
probability distribution. It reaches its maximum value 1.0
for uniformly distributed events and it assumes its minimum
0.0 if there is only one certain event with probability 1.0 (cf.
[31]). Entropies of symbol distributions measure the amount
of order in the system at one instance of time and thereby its
intertrial coherence. Since ERP components are reflected by
highly degenerated word statistics, the corresponding
cylinder entropies generally decrease within the time range
of an ERP. It was therefore tempting to relate the amplitude
of an entropy drop to the signal-to-noise ratio (SNR) of the
EEG data. This has been accomplished by beim Graben [3],
who found that the time-averaged entropy is inversely
proportional to the SNR incremented by a constant. Applied
to our example from Table 6, we state that the SNR of the
signal is zero at t = 1, 2, 3, 5 and high at t = 4.
So far, we have described the SRA for a fixed encoding
threshold that is approximately as large as the amplitude of a
voltage ERP. But how can the appropriate threshold be
found? The answer is, by trial-and-error. We therefore
employ the abovementioned algorithm over a range of
reasonably chosen threshold parameters. After computing
the SNR within some interesting time window, we plot these
results against the encoding threshold. We have seen that if
the threshold is too small, we observe mainly b0Qs and b2Qs in
the original three-symbol encoding, which are mapped onto
a uniform distribution of b0Qs and b2Qs by the Reversi
transformation, as was the case at t = 2 in our example. This
distribution has maximal entropy and therefore a low SNR.
On the other hand, if the threshold is too large, prohibiting
any threshold crossing events, we observe almost all b1Qs in
the three-symbol encoding, which are again mapped onto a
uniform distribution of b0Qs and b2Qs by the Reversi
transformation. This was the case at t = 1, t = 3, and t = 5
in our example. As a result, we have a low SNR here as well.
However, an ERP component gives rise to a maximum of the
SNR at a critical threshold h*, indicating most probable
threshold crossing events in the positive or negative
direction, or, technically speaking, an aperiodic stochastic
resonance effect [4,25,26].
The critical threshold, h*, where this resonance takes
place, depends, of course, on the time window where the
SNR is computed. This time window can be heuristically
determined by the latency of the averaged voltage ERP.
Slight variations of the onset and the end of the window yield
only slight differences between the resonance curves; the
dependency is therefore rather robust against arbitrary
changes of the analysis parameters. Moreover, one has to
observe that the determination of h* compensates for the
alleged loss of information entailed by the symbolic coarse-
graining. The critical threshold contains all information
about the btrueQ amplitude of the ERP. In contrast to the
voltage-averaged ERP, where amplitude and coherence
information are mixed up into one dimension, the symbolic
resonance analysis pulls both kinds of information apart into
two different dimensions: amplitude is represented by the
critical encoding threshold, whereas intertrial coherence is
contained in the time-dependent word statistics or cylinder
entropy. The SRA is also robust against outliers in the EEG,
whereas the amplitudes of the voltage-averaged ERP are
Table 3
Magnetic mean-fields obtained from the word statistics of Table 2
Prob\t
12345
M0
M2
?0.25
?0.25
0.50
0.50
?0.25
?0.25
?0.25
0.50
?0.25
?0.25
Table 1
Example of a three-symbol ERP dynamics
Epoch\t
12345
1
2
3
4
1
0
1
2
0
2
0
2
1
2
0
1
2
1
2
2
2
1
0
1
Rows denote EEG trials, columns denote sample points.
Table 2
Word statistics of the model data from Table 1
Prob\t
12345
P0
P1
P2
0.25
0.50
0.25
0.50
0
0.50
0.25
0.50
0.25
0
0.25
0.75
0.25
0.50
0.25
Table 4
Mean-field transformed symbolic dynamics from Table 1
Epoch\t
12345
1
2
3
4
0
0
2
2
0
2
0
2
2
2
0
0
2
2
2
2
2
0
0
2
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very susceptible to them. Consider two cases: First, a
possible outlier is consistent with an ERP effect, i.e., the
outlier has the same polarity as the ERP. By means of the
coarse-graining, the outlier will be represented by the very
same symbol (either b0Q or b2Q) as the ERP, but will
contribute only one trial to the word statistics. On the other
hand, in the averaging paradigm, an outlier is weighted by its
numerical value in the ERP average, which might cause a
large deviation. In the second case, when the outlier is not
consistent with the ERP component, the ERP average is
diminished by its numerical extent. Conversely, one incon-
sistent outlier-trial is treated by the Reversi transformation of
the SRA either as being undecided (b1Q) or as a loser in the
competition of the mean-fields. Thus, the coarse-graining of
the SRA combined with the multiple-threshold analysis does
not involve any renunciation of information, but is very
robust against statistical outliers on the other hand.
3.4.2.2. Symbolic resonance analysis of the present EEG
data.
The EEG data were epoched in a time window
beginning 200 ms before and ending 1300 ms after the onset
ofthecritical verb.EachEEGepochhadbeenfirstlyencoded
in sequences of the three symbols b0Q, b1Q, and b2Q according
totheencodingrule((14)),afteraligningtheirbaselinestothe
time average of the 200-ms pre-stimulus interval. The
encoding thresholds h were tuned from 0.5 AV up to 9.8
AVin steps of 0.1 AV. Afterwards, the symbolic sequences of
all subjects per threshold and per condition were swept up to
thegrandepochensembles (GEE,cf.Table1)fromwhichthe
relative frequencies of the symbols in each time slice have
been determined (cf. Table 2). These three-symbol distribu-
tionsweresubjectedtotheReversitransformation,leadingto
a distribution of two symbols b0Q and b2Q, whose relative
frequenciesyieldthetransformedwordstatistics(cf.Table5).
Fig. 2 illustrates the effect of the Reversi transformation
by showing the original three-symbol distribution for the
mismatching dative ERPs at electrode PZ in Fig. 2(A) for the
encoding threshold h = 4.8 AV. The N400 is reflected by the
largest frequency of b0Qs around 400 ms after stimulus onset,
while the P600 is indicated by the largest frequency of b2Qs
around 750 ms. By contrast, Fig. 2(B) shows the two-word
statistics resulting from the Reversi transformation. In the
400-ms window, the between-threshold symbols b1Q are
completely reverted into b0Qs due to the impact of the mean-
fields. Hence, the N400 corresponds to a highly degenerated
word statistics of almost constant amplitude over the
characteristic time window. Correspondingly, the between-
threshold symbols b1Q are flipped into the symbol b2Q in the
P600 time range. When the b1Qs predominate the three-
symbol distributions, such as before 400 ms or after 1000
ms, the resulting two-symbol distributions are uniform. Note
that both the symbolic encoding rule ((14)) and the Reversi
transformation act instantaneously and independently at
each sampling point in time across all measured epochs.
This assures that the word statistics of different ERP
components are independent from one another. This might
not be the case for other symbolic encoding procedures,
such as the median threshold encoding (cf. [6]).
Table 5
Word statistics of the mean-field transformed example data
Prob\t
12345
P0V
P2V
0.50
0.50
0.50
0.50
0.50
0.50
0
1
0.50
0.50
Table 6
Running cylinder entropies of the mean-field transformed example data
t
12345
H(t) 1.01.01.0 0.01.0
Fig. 2. (A) Relative frequencies of the symbols b0Q (solid), b1Q (dotted), and
b2Q (dashed) in the coarse of time of the grand ensemble EEG of the
mismatching dative condition for encoding threshold h = 4.8 AV at
electrode PZ. (B) Relative frequencies of the symbols b0Q (solid), and b2Q
(dashed) after the spin-flipping Reversi transformation applied to the same
data. N400 and P600 are indicated by arrows.
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In order to achieve the aim of the symbolic resonance
analysis, we have to compute the estimator of the signal-to-
noise ratio (SNR) [4] depending on the noise strength of the
EEG. Since the noise itself is not accessible in single EEG
epochs, we have systematically varied the encoding thresh-
olds. The first step towards determining the SNR is
computing the running cylinder entropies of the mean-field
filtered two-symbol statistics for each condition, respec-
tively. Fig. 3 displays the cylinder entropies of the dative
condition for three different encoding thresholds: h = 2.0
AV, h = 4.8 AV, and h = 6.0 AV.
Fig. 3 illustrates the resonance effect of the three-symbol
encoding combined with the Reversi transformation. For
thresholds that are too small (h = 2.0 AV, dotted line) or too
large (h = 6.0 AV, dashed line), the ERP appears either as
noise or remains subthreshold, both leading to uniform
distributions of the spin-flipped three-symbol encoding, thus
having large entropy.
Finally, we average the cylinder entropies over the same
time windows that were used for the ANOVA of the
voltage-averaged ERPs, i.e., 300 to 600 ms for the N400,
and 700 to 1000 ms for the P600. This yields the SNR
estimators that are shown in Fig. 4.
Fig. 4 reveals particular differences in the ERP between
conditions. All conditions lead to a bell-shaped resonance
curve indicating the presence of a signal that is not simply
noise recorded during the experiment. On contrast, both
experimental conditions (accusative: dashed, dative: dotted)
possess resonance curves with larger amplitude than the
control condition (solid). The amplitude of the resonance
indicates the intertrial coherence of the ERP, while its
abscissa is a direct measure of the amplitude of the ERP
signal. Fig. 4(A) shows that the ERP effect elicited by the
mismatching dative has a much larger SNR and thus a
larger intertrial coherence than the ERP that is related to
the mismatching accusative in the N400 time window. On
the other hand, Fig. 4(B) discloses a contrary effect where
the mismatching accusative leads to a higher SNR maxi-
mum than the mismatching dative case in the P600 time
window.
Since we are interested in differences between con-
ditions, we introduce the concept of the optimal threshold,
meaning those threshold values which maximize the SNR
difference of two conditions. While the optimal thresholds
for the accusative condition compared to the correct
condition and for the dative condition with respect to the
correct condition are both around 4.0 AV in the N400
window (Fig. 4(A)), the optimal threshold for the dative
condition compared to the accusative condition is just 4.8
AV, the value we have used in our illustrations. In the
P600 time window, we obtain an optimal threshold of
Fig. 3. Running cylinder entropies of the grand ensemble EEG of the
mismatching dative condition for three different encoding thresholds h = 2
AV (dotted), h = 4.8 AV (solid), and h = 6.0 AV (dashed) at electrode PZ.
Fig. 4. (A) Resonance curves (signal-to-noise ratio against encoding
thresholds) for the ERP data of three conditions obtained by averaging the
cylinder entropy in the time window from 300 to 600 ms for the N400 ERP.
Conditions: correct (solid), accusative (dashed), and dative (dotted). (B)
Resonance curves (signal-to-noise ratio against encoding thresholds) for the
ERP data of three conditions obtained by averaging the cylinder entropy in
the time window from 700–1000 ms for the P600. Conditions: correct
(solid), accusative (dashed), and dative (dotted).
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5.3 AV at PZ between the dative condition and the
accusative condition.
3.5. Statistical analysis
The statistical analyses of the voltage average data were
computed in an ANOVA with repeated measures on the
basis of the original data. Analyses were computed
separately over the midline and the lateral electrode sites.
The design consisted of a condition factor Violation
(VIOL) with the three levels correct (COR) vs. mismatching
dative (DAT) vs. mismatching accusative (ACC) and a
topographical factor Electrode (ELEC) for the midline
analysis and a factor Region of Interest (ROI) for the
analysis of the lateral sites, respectively. The factor ELEC
had three levels, namely, the midline electrodes FZ vs. CZ
vs. PZ. The factor ROI had six levels, namely, the following
lateral ROIs: left-anterior (electrodes F3, F5, FC3, FC5),
right-anterior (electrodes F4, F6, FC4, FC6), left-central
(electrodes C3, C5, CP3, CP5), right-central (electrodes C4,
C6, CP4, CP6), left-posterior (electrodes P3, P5, PO3,
PO7), and right-posterior (electrodes P4, P6, PO4, PO8).
When computing post hoc single comparisons between
the three levels of the factor Violation, the probability
level was adjusted according to the modified Bonferroni
procedure (cf. [21]). To protect against excessive type 1
errors, resulting from violations of sphericity, the correction
proposed by Huynh and Feldt [20] was applied when
evaluating effects with more than one degree of freedom in
the numerator. In these cases, we report the original degrees
of freedom and the corrected probability level.
The symbolic resonance data were statistically evaluated
using the same ANOVA design as for the voltage average
data. In order to do this, we determined the optimal
thresholds for both time windows for each single electrode
of the arrays displayed in Figs. 5–7. In order to allow for
employing an ANOVA statistics for the symbolic resonance
analysis as well, we decomposed the Reversi transformed
GEE of two symbols into the single subject ensembles.
Then, we could compute the relative frequencies of b0Qs and
Fig. 5. Averaged ERPs from the onset of the critical item (verb, onset marked by vertical line at 0 ms) up to 1200 ms thereafter for all 16 subjects at a subset of
nine electrodes. Negativity is plotted upwards.
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b2Qs for each subject separately and computed ANOVAs
with exactly the same design as for the voltage-averaged
ERPs (see above). In order to reduce the impact of singular
resonance events and also of the selected reference electro-
des for which the optimal thresholds have been computed,
we averaged the symbol statistics over a threshold window
ranging from the smallest optimal threshold determined for
one reference channel to the largest optimal threshold
determined for another reference.
4. Results
4.1. Behavioral data
Although the acceptability judgments served only as a
control task in order to make sure that subjects judged the
sentences in the way we expected them to do, we report the
mean accuracies (in %) and mean response latencies (in ms)
for the correctly performed trials.
Subjects made 6.9% errors in the correct condition
(COR), 9.9% in the condition with a mismatching dative
(DAT), and 9.2% in the condition with a mismatching
accusative (ACC). There was no main effect of Violation
[F(2,30) = 1.02, P = 0.35] and none of the single
comparisons was significant [DAT vs. COR: F(1,15) =
1.11, P = 0.31; ACC vs. COR: F(1,15) = 1.20, P = 0.29;
DAT vs. ACC: F b 1].
Mean response latencies were 507 ms in condition COR,
523 ms in DAT, and 535 ms in ACC. Again, there was no
main effect of Violation [F(2,30) = 1.08, P = 0.35] and
none of the single comparisons was significant [DAT vs.
COR: F b 1; ACC vs. COR: F(1,15) = 1.52, P = 0.24; DAT
vs. ACC: F b 1]. Results show that subjects did not have
problems in processing the sentences and that they were
able to tell correct from incorrect sentences in the way we
expected them to do.
4.2. Voltage-averaged ERP data
4.2.1. Descriptive results
Fig. 5 depicts the voltage-averaged ERPs at the critical
word (verb, onset at 0 ms) in all three critical conditions for
all 16 subjects at a subset of 9 electrodes. As can be clearly
Fig. 6. Distribution of b0Qs (relative frequency of trials with negative polarity) in each of the three critical conditions averaged over 16 subjects and over
threshold range (I) (4.0 to 4.8 AV) from the onset of the critical item (verb, onset marked by vertical line) up to 1200 ms thereafter.
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seen from the figure, both violation conditions show a
negativity peaking at around 400 ms (N400) and a positivity
peaking at around 750 ms (P600) compared to the correct
condition. However, the patterns in the two violations are
very much alike and seem to differ neither in the N400 nor
the P600 time window.
4.2.2. Statistical results
4.2.2.1. Negativity time window (300 to 600 ms).
midline sites, we found a main effect of Violation
[F(2,30) = 14.23, P b 0.01], due to more negative going
waveforms in both DAT [F(1,15) = 28.32, P b 0.01] and
ACC [F(1,15) = 14.90, P b 0.01] compared to the correct
condition. However, there was no difference between the two
violation conditions (F b 1). An interaction Violation ?
Electrode[F(4,60)=11.10,P b 0.01]wasduetosignificant
main effects of Violation at electrodes CZ [F(2,30) = 18.38,
P b 0.01] and PZ [F(2,30) = 22.60, P b 0.01], but only a
marginal one at FZ [F(2,30) = 2.92, P = 0.07]. Sentences in the
DAT condition were more negative going compared to correct
sentences at FZ [F(1,15) = 6.88, P b 0.05], CZ [F(1,15) =
33.64, P b 0.01], and PZ [F(1,15) = 41.84, P b 0.01]. ACC
Over
sentences differed from correct ones at CZ [F(1,15) = 21.24,
P b 0.01] and PZ [F(1,15) = 22.22, P b 0.01], but not at FZ
[F(1,15) = 2.81, P = 0.11]. However, the comparison between
the two violation conditions did not reveal any significant
differences at FZ (F b 1), CZ (F b 1), or PZ [F(1,15) = 2.08,
P = 0.26].
Over lateral sites, we found a main effect of Violation
[F(2,30) = 13.72, P b 0.01], which was due to a negativity
for both DAT [F(1,15) = 25.43, P b 0.01] and ACC
[F(1,15) = 11.80, P b 0.01] compared to COR. However,
there was no difference between the two violation con-
ditions [F(1,15) = 2.28, P = 0.23]. Furthermore, we found
an interaction Violation ? ROI [F(10,150) = 9.78, P b
0.01] which was due to main effects of Violation in the
right-anterior [F(2,30) = 7.38, P b 0.01], the left-central
[F(2,30) = 6.41, P b 0.01], the right-central [F(2,30) =
27.44, P b 0.01], the left-posterior [F(2,30) = 14.59, P b
0.01], and the right-posterior [F(2,30) = 33.49, P b 0.01].
Mismatching datives induced negativities compared to
correct sentences in each of these ROIs, as did the
mismatching accusatives [right-anterior: DAT: F(1,15) =
15.43, P b 0.01, ACC: F(1,15) = 5.85, P b 0.05; left-
central: DAT: F(1,15) = 10.96, P b 0.01, ACC: F(1,15) =
Fig. 7. Distribution of b2Qs (relative frequency of trials with positive polarity) in each of the three critical conditions averaged over 16 subjects and over
threshold range (II) (3.9 to 5.3 AV) from the onset of the critical item (verb, onset marked by vertical line) up to 1200 ms thereafter.
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4.83, P = 0.07; right-central: DAT: F(1,15) = 45.89, P b
0.01, ACC: F(1,15) = 32.56, P b 0.01; left-posterior: DAT:
F(1,15) = 22.14, P b 0.01, ACC: F(1,15) = 15.29, P b 0.01;
right-posterior: DAT: F(1,15) = 58.04, P b 0.01, ACC:
F(1,15) = 46.64, P b 0.01]. However, both violation
conditions did not differ from each other in any of these
ROIs (all P N 0.21).
4.2.2.2. Positivity time window (700 to 1000 ms).
midline sites, we found a main effect of Violation
[F(2,30) = 6.36, P b 0.01] due to positivities in both the
DAT [F(1,15) = 7.42, P b 0.05] and the ACC condition
[F(1,15) = 9.77, P b 0.05] compared to the correct
condition. Similar to the N400 time window, the two
violation conditions did not differ from one another (F b 1).
Resolving an interaction Violation ? Electrode
[F(4,60) = 5.04, P b 0.05] revealed main effects of
Violation at CZ [F(2,30) = 5.19, P b 0.05] and PZ only
[F(2,30) = 10.46, P b 0.01], but not at FZ [F(2,30) = 1.60,
P = 0.22]. Both violation conditions differed from the
correct condition at CZ [DAT vs. COR: F(1,15) = 7.36, P b
0.05; ACC vs. COR: F(1,15) = 7.15, P b 0.05] and at PZ
[DAT vs. COR: F(1,15) = 14.44, P b 0.01; ACC vs. COR:
F(1,15) = 12.51, P b 0.01]. Again, the violation conditions
did not differ from one another at CZ or PZ (both F b 1).
Over lateral sites, there was a main effect of Violation
[F(2,30) = 6.84, P b 0.01] due to a positivity for both DAT
[F(1,15) = 7.12, P b 0.05] and ACC [F(1,15) = 11.08, P b
0.01] compared to correct sentences. However, there was no
difference between the two violation conditions (F b 1).
There was no interaction Violation ? ROI [F(10,150) =
1.98, P = 0.12].
Over
4.2.3. Summary
In sum, the statistical results of the ERPs confirm the
visual inspection that both violation conditions induce an
N400 followed by a P600 in comparison to the correct
condition, whereas the two incorrect conditions differ from
one another neither in the N400 nor the P600 time
window.
4.3. Symbolic resonance analysis
4.3.1. Descriptive analysis
The optimal thresholds for the condition DAT versus
ACC at the nine electrodes F5, FZ, F6, C3, CZ, C6, P5, PZ,
and P6 plotted in Fig. 6 are given in Table 7 for the time
windows 300 to 600 ms and 700 to 1000 ms.
According to the results given in Table 7, the Reversi
transformed symbol distributions were averaged (I) over
thresholds from 3.4 to 4.8 AV and (II) from 3.0 to 5.3 AV.
Fig. 6 displays the relative frequencies of the symbol b0Q
(denoting negativity) of the Reversi transformed three-
symbol encoded ERPs in all three conditions in the
threshold range (I) averaged over all 16 subjects at a subset
of 9 electrodes.
As can be seen from the figure, both violation
conditions DAT and ACC induce an N400 in the
threshold range (I) compared to the correct condition.
Moreover, the two violation conditions also differ from
one another in this threshold range, in that the DAT
condition shows a larger N400 compared to the ACC
condition.
Fig. 7 displays the relative frequencies of the symbol b2Q
(denoting positivity) of the Reversi transformed three-
symbol distributions in the threshold range (II) averaged in
each of the three conditions over all 16 subjects at a subset
of 9 electrodes.
As can be seen from the figure, both violation conditions
DAT and ACC induce a P600 in the threshold range (II)
compared to the correct condition. Additionally, the two
violation conditions differ in this threshold range, too,
showing a larger P600 for the ACC condition compared to
the DAT condition.
4.3.2. Statistical analysis
4.3.2.1. Negativity time window (300 to 600 ms).
threshold range (I) (3.4 to 4.8 AV) over midline sites,
there was a main effect of Violation [F(2,30) =
110.23, P b 0.01]. Compared to the correct condition,
there was a higher proportion of the symbol b0Q (meaning
negativity) in the dative [F(1,15) = 231.94, P b 0.01]
and in the accusative violation condition [F(1,15) =
120.16, P b 0.01]. Interestingly, there were also more
b0Qs for sentences with a mismatching dative compared to
sentences with a mismatching accusative argument
[F(1,15) = 11.65, P b 0.01]. Additionally, we found an
interaction Violation ? Electrode [F(4,60) = 83.77,
P b 0.01], whose resolution revealed a main effect of
Violation at each of the three midline electrodes FZ
[F(2,30) = 17.22, P b 0.01], CZ [F(2,30) = 138.51, P b
0.01], and PZ [F(2,30) = 156.46, P b 0.01]. Both violation
conditions were more negative going compared to the correct
condition at all midline electrodes: DAT vs. COR [FZ,
F(1,15) = 52.07, P b 0.01; CZ, F(1,15) = 264.46, P b 0.01;
PZ, F(1,15) = 307.33, P b 0.01] and ACC vs. COR [FZ,
F(1,15) = 6.25 P b 0.05; CZ, F(1,15) = 170.09, P b 0.01;
PZ, F(1,15) = 171.01, P b 0.01]. More importantly, we
For the
Table 7
Optimal thresholds for the comparison DAT versus ACC
Optimal threshold
(AV) at channel
Time window (I)
N400: 300 to 600 ms
Time window (II)
P600: 700 to 1000 ms
F5
FZ
F6
C3
CZ
C6
P5
PZ
P6
3.9
4.0
4.1
3.8
4.5
3.8
3.4
4.8
3.9
3.6
3.9
3.0
4.2
4.8
3.6
4.1
5.3
4.5
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observed that the symbolically encoded ERPs for the DAT
condition were more negative than those for the ACC
condition at all three midline sites: FZ [F(1,15) = 8.35, P b
0.05], CZ [F(1,15) = 6.61, P b 0.05], and PZ [F(1,15) =
14.05, P b 0.01].
Over lateral sites, there was a main effect of Violation
[F(2,30) = 74.94, P b 0.01] due to more coherence of the
symbol b0Q (denoting threshold crossing events with
negative polarity) in both mismatching datives [F(1,15) =
136.08, P b 0.01] and accusatives [F(1,15) = 65.67, P b
0.01] in comparison to correct sentences. In the SRA, we
additionally got a difference between the two violation
conditions [F(1,15) = 14.07, P b 0.01] due to more b0Qs in
DAT compared to ACC. We found an interaction
Violation ? ROI [F(10,150) = 50.10, P b 0.01] due to
main effects of Violation in all six ROIs [left-anterior:
F(2,30) = 6.41, P b 0.01; right-anterior: F(2,30) = 40.98, P b
0.01; left-central: F(2,30) = 26.76, P b 0.01; right-central:
F(2,30) = 133.32, P b 0.01; left-posterior: F(2,30) = 76.27,
P b 0.01; right-posterior: F(2,30) = 158.73, P b 0.01].
Mismatching datives and accusatives induced negative
coherent resonances compared to correct sentences in each
of these ROIs [left-anterior: DAT: F(1,15) = 8.14, P b 0.05,
ACC: F(1,15) b 1; right-anterior: DAT: F(1,15) = 78.04, P b
0.01, ACC: F(1,15) = 38.43, P b 0.01; left-central: DAT:
F(1,15) = 49.63, P b 0.01, ACC: F(1,15) = 17.93, P b 0.01;
right-central: DAT: F(1,15) = 207.78, P b 0.01, ACC:
F(1,15) = 204.53, P b 0.01; left-posterior: DAT: F(1,15) =
143.28, P b 0.01, ACC: F(1,15) = 64.40, P b 0.01; right-
posterior: DAT: F(1,15) = 287.80, P b 0.01, ACC: F(1,15) =
156.98, P b 0.01]. More interestingly, both violation
conditions differed from each other in the all lateral ROIs
[left-anterior: F(1,15) = 12.78, P b 0.01; right-anterior:
F(1,15) = 4.64, P = 0.07; left-central: F(1,15) = 9.24, P b
0.01; right-central: F(1,15) = 5.90, P b 0.05; left-posterior:
F(1,15) = 12.09, P b 0.01; right-posterior: F(1,15) = 23.20,
P b 0.01]. These differences were due to more b0Qs in DAT
compared to ACC.
4.3.2.2. Positivity time window (700 to 1000 ms).
statistical analysis of the final distribution of b2Qs in the
late time window and in threshold range (II) (3.0 to 5.3
AV) at midline electrodes revealed a main effect of
Violation [F(2,30) = 16.95, P b 0.01] due to a greater
number of positive ERP trials both in the dative violation
condition [F(1,15) = 16.85, P b 0.01] and in the accusative
violation condition [F(1,15) = 23.09, P b 0.01] compared
to the correct condition. The two violation conditions did
not differ from one another [F(1,15) = 3.05, P = 0.15].
Resolving an interaction Violation ? Electrode
[F(4,60) = 8.52, P b 0.01] revealed main effects of
Violation at FZ [F(2,30) = 6.64, P b 0.01], CZ
[F(2,30) = 14.29, P b 0.01], and PZ [F(2,30) = 24.33,
P b 0.01]. Both violation conditions differed from the
correct condition at CZ [DAT: F(1,15) = 19.54, P b 0.01;
ACC: F(1,15) = 17.76, P b 0.01] and at PZ [DAT: F(1,15) =
The
28.72, P b 0.01; ACC: F(1,15) = 28.73, P b 0.01]. At FZ,
there was only a significant difference of the mismatching
accusative condition against the correct condition [DAT:
F(1,15) = 2.04, P = 0.26; ACC: F(1,15) = 11.57, P b
0.01] due to a higher proportion of b2Qs in ACC. Both
violation conditions DAT vs. ACC differed only at FZ
[F(1,15) = 6.79, P b 0.05], but not at CZ [F(1,15) = 1.14,
P = 0.30] or PZ (F b 1). There were more b2Qs in ACC
compared to DAT.
In the lateral ROIs, we observed a main effect of
Violation [F(2,30) = 28.79, P b 0.01]. Compared to the
correct condition, there were more b2Qs in both the
mismatching dative [F(1,15) = 29.23, P b 0.01] and the
mismatching accusative condition [F(1,15) = 38.33, P b
0.01]. By contrast, there was no global difference between
the two violation conditions [F(1,15) = 3.58, P = 0.12].
An interaction Violation ? ROI [F(10,150) = 8.33, P b
0.01] was due to main effects of Violation in all six
ROIs [left-anterior: F(2,30) = 10.57, P b 0.01; right-
anterior: F(2,30) = 6.82, P b 0.01; left-central: F(2,30) =
36.37, P b 0.01; right-central: F(2,30) = 20.66, P b 0.01;
left-posterior: F(2,30) = 27.02, P b 0.01; right-posterior:
F(2,30) = 35.62, P b 0.01]. In both violation conditions,
we observed higher coherence of positive threshold cross-
ing events in comparison to the correct condition in all
ROIs except in right-anterior, where only the difference
ACC vs. COR became significant [left-anterior: DAT:
F(1,15) = 6.76, P b 0.05, ACC: F(1,15) = 17.24, P b
0.01; right-anterior: DAT: F(1,15) = 3.99, P = 0.09, ACC:
F(1,15) = 11.72, P b 0.01; left-central: DAT: F(1,15) =
42.98, P b 0.01, ACC: F(1,15) = 50.58, P b 0.01; right-
central: DAT: F(1,15) = 25.54, P b 0.01, ACC: F(1,15) =
22.91, P b 0.01; left-posterior: DAT: F(1,15) = 29.45, P b
0.01, ACC: F(1,15) = 31.61, P b 0.01; right-posterior:
DAT: F(1,15) = 45.15, P b 0.01, ACC: F(1,15) = 44.81, P b
0.01]. The violation conditions differed from each other only
marginally at frontal and left sites [left-anterior: F(1,15) =
4.78, P = 0.07; right-anterior: F(1,15) = 3.44, P = 0.12; left-
central: F(1,15) = 5.37, P = 0.05; right-central: F(1,15) b 1;
left-posterior: F(1,15) = 3.51, P = 0.12; right-posterior:
F(1,15) b 1], these differences being due to more b2Qs in
ACC.
4.3.3. Summary
Summing up, the statistical results of the symbolic
resonance analysis of ERPs confirm the results from the
voltage averaging analysis in that both violation conditions
induce an N400 followed by a P600 in comparison to the
correct condition. In addition, the symbolic resonance
analysis was able to reveal a difference between the two
incorrect conditions, too. We observed a larger N400
component for the mismatching dative condition compared
to the mismatching accusative and a marginally larger P600
component at frontal electrode sites for the mismatching
accusative condition in comparison with the mismatching
dative condition.
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5. Discussion
Previous ERP studies have shown that sentences in
which the number of NP arguments does not match the
number of arguments specified in the verb’s lexical entry
lead to a biphasic N400–P600 response [11,15]. This
pattern, which had been found with both intransitive [15]
and transitive constructions [11], has been replicated with
ditransitive constructions in the present study. As would
have been expected, sentences with verbs that could not
integrate either an accusative object or a dative object
elicited a biphasic N400–P600 pattern in the ERP. In the
context of argument structure violations, the N400 has been
interpreted to signal the thematic–semantic integration
problem, whereas the P600 has been argued to reflect the
fact that the syntactic structure is not licensed by the lexicon
information of the specific verb [10,15]. This view supports
the theoretical characterization of argument structure infor-
mation as an interface between syntactic (i.e., syntactic
structure) as well as semantic (i.e., propositional) aspects of
sentences in a crucial way.
In the voltage average analysis, there was no difference
between the two incorrect conditions, that is, between
sentences in which a dative (i.e., indirect) object cannot be
integrated compared to sentences with verbs which could
not take an accusative (i.e., direct) object argument.
However, such a difference was found in the symbolic
resonance analysis (SRA), a specific type of data analysis
that – to our knowledge – was applied to a neurophysio-
logical data set here for the first time. The SRA not only
replicated the voltage average findings of differences
between each of the violation conditions to the correct
condition, but also revealed that a surplus dative construc-
tion leads to a stronger bN400Q (i.e., higher proportion of
symbol b0Q) and a weaker bP600Q (i.e., lower proportion of
symbol b2Q) in the symbolic resonance analysis compared to
a condition with a surplus accusative. Since the N400 has
been seen as a marker of semantic–thematic integration
problems, whereas the P600 has been interpreted as
reflecting syntactic ill-formedness (cf. [10]), one might
conclude that an incorrect dative argument induces more
semantic and less syntactic processing effort compared to an
incorrect accusative argument. Although it should be kept in
mind that the bN400 = semanticsQ versus bP600 = syntaxQ
distinction is only a rule of thumb, it would not be
implausible with respect to the present data to assume that
a surplus dative violation induces a weaker syntactic
mismatch but a stronger semantic mismatch correlate
compared to the mismatching accusative condition. This
would make sense insofar as these two cases in German
exhibit different characteristics: Transitive nominative–
accusative verbs in German allow for an additional dative
expressing who is profiting from what is entailed in the
proposition (i.e., expressing a beneficent). Adding such a
benefactive dative seems to be in principal (syntactically)
possible in these types of verbs, but is semantically
restricted [34,37]. One could therefore speculate that if
such a construction is rejected by a speaker, this could be for
reasons which are primarily semantic in nature. It might
suggest that the language processing system spends more
effort in the semantic analysis, in order to judge whether the
free dative is semantically acceptable. By contrast, a
mismatching accusative argument leads to a violation which
might be more principal in nature, that is, which might also
include syntactic restrictions, seeing that adding an accusa-
tive is not possible at all. One might dispute the possibility
of a free accusative in German also exists in sentences such
as (15).
(15). Anna reparierte das Motorrad den ganzen Tag.
Anna repaired the motorcycle the whole day.
We do not think that this possibility is a problem for our
argument for the following reasons: Free accusatives such as
bden ganzen TagQ (the whole day) are extremely limited
with respect to lexicon, semantics, and syntax (that is, they
are limited to nouns expressing a duration). For example,
leaving out the adjective already results in an argument
structure violation, see (16).
(16). *Anna reparierte das Motorrad den Tag.
Anna repaired the motorcycle the day.
Furthermore, as (15) also shows, the accusative can be
added in a sentence that already has a direct object in
accusative case, which clearly demonstrates that it is not
an argument of the verb at all. The same is shown by the
fact that the free accusative is not involved in processes of
argument reassignment as in passive constructions, see
(17).
(17). *Der ganze Tag wurde von Anna repariert.
the whole day was repaired by Anna.
Benefactive datives in German, by contrast, meet all
requirements for an argument status (cf. [9,12] and
Footnote 1).
We admit that the above interpretation of the difference
between extra-datives and extra-accusatives might be
tentative. In any case, more theoretical and especially
empirical work has to be done in other languages with
morphological case marking as well, in order to further
elucidate how this central issue of sentence processing,
namely, argument interpretation, is achieved by our brains.
What we can clearly say, however, is that our finding of
differences between extra-datives and extra-accusatives in
processing is limited to a specific type of data analysis that
we present here for the first time. As we have shown in the
present paper, the symbolic resonance analysis, in which the
intrinsic noise of the EEG is utilized for enhancing the ERP
signal, offers a new way to distinguish ERP reflections
where the conventional voltage average technique fails.
Thus, the symbolic resonance analysis is more sensitive than
conventional methods, complementing these techniques.
This offers a promising starting point for revealing fine-
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