Tone Duration Research Articles

Familial Influences on Mismatch Negativity and Its Association with Plasma Glutamate Level: A Magnetoencephalographic Study in Twins

Mismatch negativity (MMN) or its magnetic counterpart (magnetic mismatch negativity; MMNm) is regarded as a promising biomarker for schizophrenia. Previous electroencephalographic studies of MMN have demonstrated a moderate-to-high heritability for MMN amplitudes. N-methyl-<smlcap>D</smlcap>-aspartate receptor-dependent glutamatergic neurotransmission is implicated in MMN generation. We hypothesized that the differences between identical twins in MMNm variables might be associated with differences in plasma levels of amino acids involved in glutamatergic neurotransmission. Thirty-three pairs of monozygotic (MZ) and 10 pairs of dizygotic (DZ) twins underwent MMNm recording. The MMNm in response to tone duration changes, tone frequency changes, and phonemic changes was recorded using 204-channel magnetoencephalography. Of these, 26 MZ and 7 DZ twin pairs underwent blood sampling for determination of plasma amino acid levels. MMNm peak strength showed relatively high correlations in both MZ and DZ twin pairs. The differences in MMNm latencies tended to correlate with the differences in plasma amino acid levels within MZ pairs, while no significant correlation was observed after the Bonferroni correction. We observed a familial trait in MMNm strength. The differences in MMN latency in MZ twins might be influenced by changes in glutamate levels and glutamate-glutamine cycling; however, the results need to be replicated.

Accounting for rate-dependent category boundary shifts in speech perception

The perception of temporal contrasts in speech is known to be influenced by the speech rate in the surrounding context. This rate-dependent perception is suggested to involve general auditory processes because it is also elicited by nonspeech contexts, such as pure tone sequences. Two general auditory mechanisms have been proposed to underlie rate-dependent perception: durational contrast and neural entrainment. This study compares the predictions of these two accounts of rate-dependent speech perception by means of four experiments, in which participants heard tone sequences followed by Dutch target words ambiguous between /ɑs/ “ash” and /a:s/ “bait”. Tone sequences varied in the duration of tones (short vs. long) and in the presentation rate of the tones (fast vs. slow). Results show that the duration of preceding tones did not influence target perception in any of the experiments, thus challenging durational contrast as explanatory mechanism behind rate-dependent perception. Instead, the presentation rate consistently elicited a category boundary shift, with faster presentation rates inducing more /a:s/ responses, but only if the tone sequence was isochronous. Therefore, this study proposes an alternative, neurobiologically plausible account of rate-dependent perception involving neural entrainment of endogenous oscillations to the rate of a rhythmic stimulus.

Magnetoencephalographic recording of auditory mismatch negativity in response to duration and frequency deviants in a single session in patients with schizophrenia

Auditory mismatch negativity (MMN) and its magnetoencephalographic (MEG) counterpart (MMNm) are an established biological index in schizophrenia research. MMN in response to duration and frequency deviants may have differential relevance to the pathophysiology and clinical stages of schizophrenia. MEG has advantage in that it almost purely detects MMNm arising from the auditory cortex. However, few previous MEG studies on schizophrenia have simultaneously assessed MMNm in response to duration and frequency deviants or examined the effect of chronicity on the group difference. Forty-two patients with chronic schizophrenia and 74 matched control subjects participated in the study. Using a whole-head MEG, MMNm in response to duration and frequency deviants of tones was recorded while participants passively listened to an auditory sequence. Compared to healthy subjects, patients with schizophrenia exhibited significantly reduced powers of MMNm in response to duration deviant in both hemispheres, whereas MMNm in response to frequency deviant did not differ between the two groups. These results did not change according to the chronicity of the illness. These results, obtained by using a sequence-enabling simultaneous assessment of both types of MMNm, suggest that MEG recording of MMN in response to duration deviant may be a more sensitive biological marker of schizophrenia than MMN in response to frequency deviant. Our findings represent an important first step towards establishment of MMN as a biomarker for schizophrenia in real-world clinical psychiatry settings.

Developing an assessment approach for perceptual changes to tinnitus sound characteristics for adult cochlear implant recipients

Objective: To investigate the impact of cochlear implantation on tinnitus suppression, characteristics, localization, and duration. Design: A cochlear implant (CI) recipient-focused postal questionnaire survey. Study sample: The questionnaire was posted, with consent, to 100 adults who had received a unilateral CI at the RNTNEH between 1988 and 1999. All adults spoke English as their first language and were postlingually deafened. Sixty-eight adults (38 female, 29 male, one unspecified) aged 31–80 years (mean 61 years) completed and returned the questionnaire without interview. Results: With the processor ‘ON’, CI recipients experienced total or partial suppression of tinnitus ipsilateral to their CI in 57% of cases, and in 43% where tinnitus was perceived contralateral to the CI. The percentage of CI recipients who experienced high tone tinnitus was reduced from 60% pre-implant to 29% post-implant with the processor ‘ON’ while pulsatile tinnitus was reduced from 38% pre-implant to 13% post-implant. CIs were also found to reduce the tonal complexity and duration, and change the source localization of tinnitus post-implantation. Conclusions: Perceptual changes to tinnitus can take place post-implantation. Changes can occur within the four categories explored: tinnitus suppression, characteristics, localization, and duration of awareness per day.

Attention-dependent sound offset-related brain potentials.

When performing sensory tasks, knowing the potentially occurring goal-relevant and irrelevant stimulus events allows the establishment of selective attention sets, which result in enhanced sensory processing of goal-relevant events. In the auditory modality, such enhancements are reflected in the increased amplitude of the N1 ERP elicited by the onsets of task-relevant sounds. It has been recently suggested that ERPs to task-relevant sound offsets are similarly enhanced in a tone-focused state in comparison to a distracted one. The goal of the present study was to explore the influence of attention on ERPs elicited by sound offsets. ERPs elicited by tones in a duration-discrimination task were compared to ERPs elicited by the same tones in not-tone-focused attentional setting. Tone offsets elicited a consistent, attention-dependent biphasic (positive-negative--P1-N1) ERP waveform for tone durations ranging from 150 to 450 ms. The evidence, however, did not support the notion that the offset-related ERPs reflected an offset-specific attention set: The offset-related ERPs elicited in a duration-discrimination condition (in which offsets were task relevant) did not significantly differ from those elicited in a pitch-discrimination condition (in which the offsets were task irrelevant). Although an N2 reflecting the processing of offsets in task-related terms contributed to the observed waveform, this contribution was separable from the offset-related P1 and N1. The results demonstrate that when tones are attended, offset-related ERPs may substantially overlap endogenous ERP activity in the postoffset interval irrespective of tone duration, and attention differences may cause ERP differences in such postoffset intervals.

Decreasing auditory Simon effects across reaction time distributions.

The Simon effect for left-right visual stimuli previously has been shown to decrease across the reaction time (RT) distribution. This decrease has been attributed to automatic activation of the corresponding response, which then dissipates over time. In contrast, for left-right tone stimuli, the Simon effect has not been found to decrease across the RT distribution but instead tends to increase. It has been proposed that automatic activation occurs through visuomotor information transmission, whereas the auditory Simon effect reflects cognitive coding interference and not automatic activation. In 4 experiments, we examined distributions of the auditory Simon effect for RT, percentage error (PE), and an inverse efficiency score [IES = RT/(1 - PE)] as a function of tone frequency and duration to determine whether the activation-dissipation account is also applicable to auditory stimuli. Consistent decreasing functions were found for the RT Simon effect distribution with short-duration tones of low frequency and for the PE and IES Simon effect distributions for all durations and frequency sets. Together, these findings provide robust evidence that left and right auditory stimuli also produce decreasing Simon effect distribution functions suggestive of automatic activation and dissipation of the corresponding response.

Mission: Impossible? Modelling the Verbal Estimation of Duration

Three participants produced a large number of verbal estimates of tone durations in the range of 77–1183 ms. Data from this task were simulated by an ‘attractor model’, which used the idea of competition between ‘attractors’ (‘quantized’ values output as verbal estimates) which differed in weight, and distance from the stimulus duration to be estimated. To produce an estimate, all attractors competed for priority as output values, with the final value being decided probabilistically. The model embodied underlying scalar representations of time, in the form of mean accuracy and constant coefficient of variation. The model was able to reconcile such scalar properties of time with deviations from scalar properties often found in verbal estimation data, such as declining coefficients of variation with increasing duration value. The model furthermore showed that multiplicative and additive changes in underlying time representations should be translated veridically into behaviour, although the attractor competition process could distort patterns and absolute values of underlying variance.

Auditory streaming of tones of uncertain frequency, level, and duration.

Stimulus uncertainty is known to critically affect auditory masking, but its influence on auditory streaming has been largely ignored. Standard ABA-ABA tone sequences were made increasingly uncertain by increasing the sigma of normal distributions from which the frequency, level, or duration of tones were randomly drawn. Consistent with predictions based on a model of masking by Lutfi, Gilbertson, Chang, and Stamas [J. Acoust. Soc. Am. 134, 2160-2170 (2013)], the frequency difference for which A and B tones formed separate streams increased as a linear function of sigma in tone frequency but was much less affected by sigma in tone level or duration.

Auditory encoding abnormalities in children with autism spectrum disorder suggest delayed development of auditory cortex.

BackgroundFindings of auditory abnormalities in children with autism spectrum disorder (ASD) include delayed superior temporal gyrus auditory responses, pre- and post-stimulus superior temporal gyrus (STG) auditory oscillatory abnormalities, and atypical hemispheric lateralization. These abnormalities are likely associated with abnormal brain maturation. To better understand changes in brain activity as a function of age, the present study investigated associations between age and STG auditory time-domain and time-frequency neural activity.MethodsWhile 306-channel magnetoencephalography (MEG) data were recorded, 500- and 1000-Hz tones of 300-ms duration were binaurally presented. Evaluable data were obtained from 63 typically developing children (TDC) (6 to 14 years old) and 52 children with ASD (6 to 14 years old). T1-weighted structural MRI was obtained, and a source model created using single dipoles anatomically constrained to each participant’s left and right STG. Using this source model, left and right 50-ms (M50), 100-ms (M100), and 200-ms (M200) time-domain and time-frequency measures (total power (TP) and inter-trial coherence (ITC)) were obtained.ResultsPaired t tests showed a right STG M100 latency delay in ASD versus TDC (significant for right 500 Hz and marginally significant for right 1000 Hz). In the left and right STG, time-frequency analyses showed a greater pre- to post-stimulus increase in 4- to 16-Hz TP for both tones in ASD versus TDC after 150 ms. In the right STG, greater post-stimulus 4- to 16-Hz ITC for both tones was observed in TDC versus ASD after 200 ms. Analyses of age effects suggested M200 group differences that were due to a maturational delay in ASD, with left and right M200 decreasing with age in TDC but significantly less so in ASD. Additional evidence indicating delayed maturation of auditory cortex in ASD included atypical hemispheric functional asymmetries, including a right versus left M100 latency advantage in TDC but not ASD, and a stronger left than right M50 response in TDC but not ASD.ConclusionsPresent findings indicated maturational abnormalities in the development of primary/secondary auditory areas in children with ASD. It is hypothesized that a longitudinal investigation of the maturation of auditory network activity will indicate delayed development of each component of the auditory processing system in ASD.Electronic supplementary materialThe online version of this article (doi:10.1186/s13229-015-0065-5) contains supplementary material, which is available to authorized users.

A short treatise concerning a musical approach for the interpretation of gene expression data

Recent technical developments allow the genome-wide and near-complete analysis of gene expression in a given sample, e.g. by usage of high-density DNA microarrays or next generation sequencing. The generated data structure is usually multi-dimensional and requires extensive processing not only for analysis but also for presentation of the results. Today, such data are usually presented graphically, e.g. in the form of heat maps. In the present paper, we propose an alternative form of analysis and presentation which is based on the transformation of gene expression data into sounds that are characterized by their frequency (pitch) and tone duration. Using DNA microarray data from a panel of neuroblastoma and Ewing sarcoma cell lines as well as from Hodgkin’s lymphoma cell lines and normal B cells, we demonstrate that this Gene Expression Music Algorithm (GEMusicA) can be used for discrimination between samples with different biology and for the characterization of differentially expressed genes.

Effects of explicit knowledge and predictability on auditory distraction and target performance

This study tested effects of task requirements and knowledge on auditory distraction effects. This was done by comparing the response to a pitch change (an irrelevant, distracting tone feature) that occurred predictably in a tone sequence (every 5th tone) under different task conditions. The same regular sound sequence was presented with task conditions varying in what information the participant was given about the predictability of the pitch change, and when this information was relevant for the task to be performed. In all conditions, participants performed a tone duration judgment task. Behavioral and event-related brain potential (ERP) measures were obtained to measure distraction effects and deviance detection. Predictable deviants produced behavioral distraction effects in all conditions. However, the P3a amplitude evoked by the predictable pitch change was largest when participants were uninformed about the regular structure of the sound sequence, showing an effect of knowledge on involuntary orienting of attention. In contrast, the mismatch negativity (MMN) component was only modulated when the regularity was relevant for the task and not by stimulus predictability itself. P3a and behavioral indices of distraction were not fully concordant. Overall, our results show differential effects of knowledge and predictability on auditory distraction effects indexed by neurophysiological (P3a) and behavioral measures.

The effects of glutamatergic modulation on human auditory perception and behavioural changes in a Mismatch Negativity (MMN) paradigm

Subanasthetic doses of ketamine, a N-methyl-D-aspartate (NMDA)-receptor antagonist, have been used to model behavioural and neurophysiological effects reminiscent of schizophrenia in order to investigate the role of the glutamatergic system in the development of the disease. Significant alterations in event related potentials (ERPs) have been documented in schizophrenic patients and in healthy controls receiving ketamine. The Mismatch Negativity (MMN), a response to tone duration or frequency deviant, has been shown to be reduced. In the current study we examine the impact of ketamine on auditory perception with 64-channel EEG and a MMN paradigm. Twenty-five male, healthy volunteers were measured with pharmacological electroencephalography (EEG) using a single-blind, randomized, placebo-controlled crossover design. After placebo and ketamine intervention, psychopathological status was assessed using the Altered State of Consciousness (5D-ASC) Rating Scale and the Positive and Negative Syndrome Scale (PANSS). We found that MMN is diminished in the ketamine condition accompanied by significant changes of behavioural and cognitive scales in the 5D-ASC and the PANSS. Scores of the questionnaires describing alterations in auditory perception have increased indicating an impact of the NMDA-receptor in this domain. Our results suggest that a glutamatergic modulation mimics specific impairments as described for schizophrenia both in the EEG and at the behavioural level.

Ageing Effect on Air-Conducted Ocular Vestibular Evoked Myogenic Potential.

One of the recent diagnostic tests to assess the function of otolithic organs is through vestibular evoked myogenic potential (VEMP) testing. There are equivocal findings on effect of aging on ocular VEMP (oVEMP) parameters with reference to latencies. Hence this study was taken up to investigate the age related changes in oVEMP parameters. This present study considered 30 participants in each age group i.e., young adults, middle-aged adults and older adults. oVEMP were recorded using insert earphone at 100dBnHL at 500hZ short duration tone burst. The results showed in older adult significant difference in response rate, latencies and amplitude as compared to young and middle adult. Hence age should be taken into consideration when interpreting oVEMP results.

Transcutaneous induction of stimulus-timing-dependent plasticity in dorsal cochlear nucleus.

The cochlear nucleus (CN) is the first site of multisensory integration in the ascending auditory pathway. The principal output neurons of the dorsal cochlear nucleus (DCN), fusiform cells, receive somatosensory information relayed by the CN granule cells from the trigeminal and dorsal column pathways. Integration of somatosensory and auditory inputs results in long-term enhancement or suppression in a stimulus-timing-dependent manner. Here, we demonstrate that stimulus-timing-dependent plasticity (STDP) can be induced in DCN fusiform cells using paired auditory and transcutaneous electrical stimulation of the face and neck to activate trigeminal and dorsal column pathways to the CN, respectively. Long-lasting changes in fusiform cell firing rates persisted for up to 2 h after this bimodal stimulation, and followed Hebbian or anti-Hebbian rules, depending on tone duration, but not somatosensory stimulation location: 50 ms paired tones evoked predominantly Hebbian, while 10 ms paired tones evoked predominantly anti-Hebbian plasticity. The tone-duration-dependent STDP was strongly correlated with first inter-spike intervals, implicating intrinsic cellular properties as determinants of STDP. This study demonstrates that transcutaneous stimulation with precise auditory–somatosensory timing parameters can non-invasively induce fusiform cell long-term modulation, which could be harnessed in the future to moderate tinnitus-related hyperactivity in DCN.

V34. Paired associative stimulation of the temporal cortex

Background Paired associative stimulation (PAS) is a specific repetitive transcranial magnetic stimulation (rTMS) protocol where every pulse is combined with an external stimulus. Based on a close timing between the TMS induced action potential and the cortical arrival of the external stimulus in the stimulated area neural plasticity is induced by mechanisms of spike-timing dependent plasticity. After a first proof-of-principle study of PAS of the auditory cortex by our group, we here extend these findings by investigating the effects of stimulus duration and of sham stimulation on primary and secondary auditory cortical activity. Methods The left temporal cortex of 18 healthy controls with normal hearing was stimulated in two experimental parts. One PAS session consisted of 200 stimulations with an interstimulus interval of 45 ms between tone onset (400 ms length, 4 kHz frequency) and the TMS pulse proven to be effective in the pilot study. Part 1 contrasted effects of a short (23 ms) and a long (400 ms) PAS-tone on secondary auditory cortex activity (short vs. long condition); part 2 contrasted effects of verum and sham stimulation (6-fold reduced intensity, not targeting the cortex) on primary and secondary auditory cortex activity (verum vs. sham condition). Primary auditory cortex activity was measured with auditory steady state responses (ASSR) as elicited by 40 Hz amplitude-modulated (AM) sine tones. Secondary auditory cortex activity was elicited with ASSRs using a 20 Hz AM tone and late auditory evoked potentials (AEPs) for the 40 Hz and 20 Hz AM tone. Evoked activity was done for the PAS tone (4 kHz carrier frequency) and a control tone (1 kHz carrier frequency) - each tone presented 70 times (60 dB SL, 800 ms length). As STDP is based on close timing of pre- and post-synaptic activity we concentrated on evoked activity by using analyses time-locked to the tone onset. Results For part 1, the short PAS condition showed an increase in AEP amplitude accompanied by a decrease for the long PAS condition specific for the PAS carrier frequency. Verum and sham stimulation showed comparable decreases in AEP amplitude independent from the PAS protocol. Part 2 showed no effects for the contrast short vs. long condition. 20 Hz ASSR amplitude showed sham-controlled decreases for the PAS-specific carrier frequency. ASSR amplitudes of the control tone or of the 40 Hz AM tone showed no significant effects. Discussion PAS of the auditory cortex seem to be restricted to the secondary auditory cortex as effects could only be found for the AEPs and the 20 Hz ASSRs which have neural generators rather in secondary than in primary auditory cortex. AEPs findings raise the importance of habituation effects and of duration of the PAS tone and challenge the validity of the transfer of PAS using sine tones to evoked potentials using AM tones.

Cross-modal effects of auditory magnitude on visually guided grasping.

Recent research has established the role of objects' semantic properties in the planning of motor actions with respect to these objects. It has been shown that visual numerical magnitude affects visuomotor control in a similar direction to the effect of physical size: The larger the numerical value, the larger the grip aperture even when physical size remains invariant. The relationship has been attributed to a common mechanism, in particular to a neural network within the parietal lobe, which mediates the processing of magnitude across different domains. In this study, we show that the effect of magnitude on grasping is not limited to visual numerical information and is in fact cross-modal in nature; presentations of auditory signals of different types of auditory-based magnitudes affected visually guided actions in two different experiments. In Experiment 1, symbolic representations of magnitudes (numerals) affected initial grasping trajectories. In Experiment 2, a nonsymbolic presentation of magnitude, i.e., tone duration, had similar effects on grasping trajectories. We conclude that different types of magnitude representations are processed by a common mechanism that cooperates with visuomotor control.

Octuplicate this interval! Axiomatic examination of the ratio properties of duration perception.

The relationship between the physical intensity of a stimulus and its perceived magnitude can be described by Stevens' power law (Stevens, American Journal of Psychology, 69(1), 1-15, 1956), i.e., a power function with an exponent depending on the sensory modality studied. Direct scaling methods used to determine the power function exponent are based on the assumption that subjects are capable of processing ratios of magnitudes. The present experiments investigate whether this assumption holds for duration perception by empirically testing (Narens, Journal of Mathematical Psychology, 40(2), 109-129, 1996) fundamental axioms of monotonicity, commutativity, and multiplicativity. To determine whether the exponent can be interpreted in a meaningful way, i.e., whether it is invariant under changes of the reference stimulus, two further axioms, invertibility and weak multiplicativity (Augustin, Acta Psychologica, 128(1), 176-185, 2008) are evaluated. N=25 participants were required to adjust the duration of a comparison tone to specific ratios of different standard durations in two experiments. In accordance with previous findings for other sensory continua, monotonicity held for the duration adjustments of most participants. Significant violations of the commutativity axiom were found in 12.5% of all pertinent tests, whereas multiplicativity was violated in 32% of such tests. The axioms of weak multiplicativity and invertibility, however, were violated in over 50% of the tests. These results indicate that even though a ratio scale for perceived duration exists, the numbers as used by the participants cannot always be taken at face value and that even though power functions fit the data quite well, the exponent depends on the size of the standard and therefore cannot always be interpreted in a meaningful way.

Diverse cortical codes for scene segmentation in primate auditory cortex.

The temporal coherence of amplitude fluctuations is a critical cue for segmentation of complex auditory scenes. The auditory system must accurately demarcate the onsets and offsets of acoustic signals. We explored how and how well the timing of onsets and offsets of gated tones are encoded by auditory cortical neurons in awake rhesus macaques. Temporal features of this representation were isolated by presenting otherwise identical pure tones of differing durations. Cortical response patterns were diverse, including selective encoding of onset and offset transients, tonic firing, and sustained suppression. Spike train classification methods revealed that many neurons robustly encoded tone duration despite substantial diversity in the encoding process. Excellent discrimination performance was achieved by neurons whose responses were primarily phasic at tone offset and by those that responded robustly while the tone persisted. Although diverse cortical response patterns converged on effective duration discrimination, this diversity significantly constrained the utility of decoding models referenced to a spiking pattern averaged across all responses or averaged within the same response category. Using maximum likelihood-based decoding models, we demonstrated that the spike train recorded in a single trial could support direct estimation of stimulus onset and offset. Comparisons between different decoding models established the substantial contribution of bursts of activity at sound onset and offset to demarcating the temporal boundaries of gated tones. Our results indicate that relatively few neurons suffice to provide temporally precise estimates of such auditory "edges," particularly for models that assume and exploit the heterogeneity of neural responses in awake cortex.

Contralateral efferent suppression of human hearing sensitivity.

The present study aimed at characterizing the suppressing effect of contralateral medial olivocochlear (MOC) efferents on human auditory sensitivity and mechanical cochlear responses at sound levels near behavioral thresholds. Absolute thresholds for pure tones of 500 and 4000 Hz with durations between 10–500 ms were measured in the presence and in the absence of a contralateral broadband noise. The intensity of the noise was fixed at 60 dB SPL to evoke the contralateral MOC reflex without evoking the middle-ear muscle reflex. In agreement with previously reported findings, thresholds measured without the contralateral noise decreased with increasing tone duration, and the rate of decrease was faster at 500 than at 4000 Hz. Contralateral stimulation increased thresholds by 1.07 and 1.72 dB at 500 and 4000 Hz, respectively. The mean increase (1.4 dB) just missed statistical significance (p = 0.08). Importantly, the across-frequency mean threshold increase was significantly greater for long than for short probes. This effect was more obvious at 4000 Hz than at 500 Hz. Assuming that thresholds depend on the MOC-dependent cochlear mechanical response followed by an MOC-independent, post-mechanical detection mechanism, the present results at 4000 Hz suggest that MOC efferent activation suppresses cochlear mechanical responses more at lower than at higher intensities across the range of intensities near threshold, while the results at 500 Hz suggest comparable mechanical suppression across the threshold intensity range. The results are discussed in the context of central masking and of auditory models of efferent suppression of cochlear mechanical responses.

Mismatch negativity (MMN) deficiency: A break-through biomarker in predicting psychosis onset

Currently, the mismatch negativity (MMN) deficit is one of the most robust and replicable findings in schizophrenia, reflecting cognitive and functional decline, psychosocial and socio-occupational impairment, and executive dysfunction in these patients. An important break-through has very recently taken place here in the prediction of conversion to psychosis when the MMN in particular to change in tone duration was recorded in clinically at risk-mental state (ARMS) individuals. Attenuations in the MMN in these patients may be very useful in helping clinicians determine who are most likely to develop a psychotic disorder, as we will review in the present article.