Temporal Assimilation Research Articles

Basin Scale Soil Moisture Estimation with Grid SWAT and LESTKF Based on WSN.

This research utilized in situ soil moisture observations in a coupled grid Soil and Water Assessment Tool (SWAT) and Parallel Data Assimilation Framework (PDAF) data assimilation system, resulting in significant enhancements in soil moisture estimation. By incorporating Wireless Sensor Network (WSN) data (WATERNET), the method captured and integrated local soil moisture characteristics, thereby improving regional model state estimations. The use of varying observation search radii with the Local Error-subspace Transform Kalman Filter (LESTKF) resulted in improved spatial and temporal assimilation performance, while also considering the impact of observation data uncertainties. The best performance (improvement of 0.006 m3/m3) of LESTKF was achieved with a 20 km observation search radii and 0.01 m3/m3 observation standard error. This study assimilated wireless sensor network data into a distributed model, presenting a departure from traditional methods. The high accuracy and resolution capabilities of WATERNET's regional soil moisture observations were crucial, and its provision of multi-layered soil temperature and moisture observations presented new opportunities for integration into the data assimilation framework, further enhancing hydrological state estimations. This study's implications are broad and relevant to regional-scale water resource research and management, particularly for freshwater resource scheduling at small basin scales.

Heterogeneous graph-based knowledge tracing with spatiotemporal evolution

Knowledge tracing (KT), in which the future performance of students is estimated by tracing their knowledge states based on their responses to exercises, is widely applied in the field of intelligent education. However, existing mainstream KT models explore the importance of knowledge relations but ignore the key role of cognitive factors. According to the knowledge construction theory, the human cognitive system performs both spatial accommodation and temporal assimilation to internalize knowledge. In this paper, we propose an innovative heterogeneous graph-based Knowledge tracing method with spatiotemporal evolution (TSKT), in which knowledge state evolution is traced along both temporal and spatial dimensions. We construct a heterogeneous graph with multiple exercise attributes, including content, concepts, and difficulty, to obtain a knowledge space with richer exercise representations through hierarchical aggregation. We design a spatial updating module in which each interaction updates the current node’s state of the knowledge space and transfers its influence to its neighbors. We also design a temporal updating module to further update the knowledge state through short-term memory enhancing and long-term memory forgetting. Finally, we stack these modules to obtain deeper features by using alternate spatiotemporal updating. Extensive experiments on three datasets reveal the superiority of the proposed method and its variants in terms of future performance prediction.

Improving trophic niche and diet resolution of the salmonid community of Lake Ontario using three stable isotopes and multiple tissues

Salmonids are ecologically and economically important fishes in Lake Ontario but declines in Alewife (Alosa pseudoharengus), recently the primary prey item, may cause shifts in salmonid diets. Improving our understanding of salmonid trophic niches and diets and whether these have changed over time will provide insight into salmonid foraging patterns, ecology, and management. Using three stable isotopes (δ13C, δ15N and δ34S) and Bayesian models, we estimated core trophic niches, niche overlaps among species, and diets for six salmonid species from Lake Ontario sampled during 2018. We used fin and muscle tissue with different temporal assimilation periods to assess seasonal variability in diet, and investigated salmonid trophic niches and diets among three major spatial units (East, Central, West). Overall, core trophic niches overlapped across all species, except Lake Trout (Salvelinus namaycush). Consistent with previous lake-wide analyses of Lake Ontario salmonid diets, Alewife were the preferred prey fish, although Lake Trout and Atlantic Salmon (Salmo salar) had more varied diets, particularly based on white muscle. Fin-based isotope mixing models predicted greater consumption of shallow (< 30 m depth) Round Goby (Neogobius melanostomus) for Lake Trout, Brown Trout (Salmo trutta), and Rainbow Trout (Oncorhynchus mykiss) than other salmonids, indicating seasonal variation in diets. Lake Trout and Brown Trout also varied across spatial units with greater Round Goby consumption in western Lake Ontario. Spatially distinct diets suggest that Brown Trout and Lake Trout populations should be monitored regionally. Understanding prey consumption trends are important to effectively manage fish populations, especially considering on-going ecological changes in the Great Lakes.

Metabolism in action: stable isotope probing using vibrational spectroscopy and SIMS reveals kinetic and metabolic flux of key substrates.

Microbial communities play essential functions which drive various ecosystems supporting animal and aquatic life. However, linking bacteria with specific metabolic functions is difficult, since microbial communities consist of numerous and phylogenetically diverse microbes. Stable isotope probing (SIP) combined with single-cell tools has emerged as a novel culture-independent strategy for unravelling microbial metabolic roles and intertwined interactions in complex communities. In this study, we applied Raman and Fourier-transform infrared (FT-IR) spectroscopies, secondary ion mass spectrometry (SIMS) with SIP to probe the rate of 13C incorporation in Escherichia coli at 37 and 25 °C. Our results indicate quantitative enrichment and flow of 13C into E. coli at various time points. Multivariate and univariate analyses of Raman and FT-IR data demonstrated distinctive 13C concentration-dependent trends that were due to vibrational bands shifting to lower frequencies and these shifts were a result of incubation time and metabolic rate. SIMS results were in complete agreement with the spectroscopy findings, and confirmed the detected levels of 13C incorporation into microbial biomass at the investigated conditions. Having established that FT-IR and Raman spectroscopy with SIP can measure metabolism kinetics in this simple system, we have applied the kinetics concept to study the metabolism of phenol by Pseudomonas putida and metabolic interactions within a two-species consortia with E. coli that could not degrade phenol. Raman spectroscopy combined with SIP identified quantitative shifts in P. putida due to temporal assimilation of phenol. Although E. coli was unable to grow on phenol, in co-culture with P. putida, general metabolic probing using deuterated water for SIP revealed that E. coli displayed increasing metabolic activity, presumably due to cross feeding from metabolites generated by P. putida. This study clearly demonstrates that Raman and FT-IR combined with SIP provide rapid and sensitive detection of carbon incorporation rates and microbial interactions. These novel findings may guide the identification of primary substrate consumers in complex microbial communities in situ, which is a key step towards the characterisation of novel genes, enzymes and metabolic flux analysis in microbial consortia.

Spatiotemporal reconstruction of MODIS land surface temperature with the help of GLDAS product using kernel-based nonparametric data assimilation

Spatiotemporal inconsistency in MODIS land surface temperature (LST), one of the most widely used geospatial data parameters, is a concern for its application in various studies. Moreover, there are limited methods that can address spatiotemporal reconstruction of LST in diverse physiography. The use of kernel-based spatiotemporal assimilation in a multitemporal approach to reconstruct LST in a complex physiographic region, northeast India, is addressed. Global land skin temperature (Ts) from Global Land Data Assimilation System (GLDAS) is chosen as a temporal covariate for MODIS LST due to its consistent temporal resolution. Considering the high temporal correlation between GLDAS Ts and MODIS LST, temporal assimilation is done in the first stage followed by spatial assimilation in the second stage. Due to data gaps, a kernel-based nonparametric estimator is adopted to map the spatiotemporal distribution and reconstruct LST with spatiotemporal consistency. This approach shows satisfactory performance in restoration of spatial variation in the study area with a coefficient of determination (R2 = 0.98), root mean square error (RMSE = 0.61 K), and absolute value of bias (B = 0.22 K). Also, the credibility of reconstructed LST from this method is found to be as good as the baseline data (MODIS LST) given that there is no severe data deficiency with uneven spatial availability in the baseline data itself. Comparison of gap-filled LST showed positive correlation with ground-based measurements (average R = 0.71), reflecting decent agreement with seasonality. Hence, the kernel-based nonparametric assimilation could be used to reconstruct LST using a multitemporal approach in complex physiographic regions, which could be used to fill the spatiotemporal data gaps and increase data consistency in MODIS LST.

Adjoint‐Based Climate Model Tuning: Application to the Planet Simulator

AbstractThe adjoint method is used to calibrate the medium complexity climate model “Planet Simulator” through parameter estimation. Identical twin experiments demonstrate that this method can retrieve default values of the control parameters when using a long assimilation window of the order of 2 months. Chaos synchronization through nudging, required to overcome limits in the temporal assimilation window in the adjoint method, is employed successfully to reach this assimilation window length. When assimilating ERA‐Interim reanalysis data, the observations of air temperature and the radiative fluxes are the most important data for adjusting the control parameters. The global mean net longwave fluxes at the surface and at the top of the atmosphere are significantly improved by tuning two model parameters controlling the absorption of clouds and water vapor. The global mean net shortwave radiation at the surface is improved by optimizing three model parameters controlling cloud optical properties. The optimized parameters improve the free model (without nudging terms) simulation in a way similar to that in the assimilation experiments. Results suggest a promising way for tuning uncertain parameters in nonlinear coupled climate models.

Spatiotemporal brain dynamics of auditory temporal assimilation

Time is a fundamental dimension, but millisecond-level judgments sometimes lead to perceptual illusions. We previously introduced a “time-shrinking illusion” using a psychological paradigm that induces auditory temporal assimilation (ATA). In ATA, the duration of two successive intervals (T1 and T2), marked by three auditory stimuli, can be perceived as equal when they are not. Here, we investigate the spatiotemporal profile of human temporal judgments using magnetoencephalography (MEG). Behavioural results showed typical ATA: participants judged T1 and T2 as equal when T2 − T1 ≤ +80 ms. MEG source-localisation analysis demonstrated that regional activity differences between judgment and no-judgment conditions emerged in the temporoparietal junction (TPJ) during T2. This observation in the TPJ may indicate its involvement in the encoding process when T1 ≠ T2. Activation in the inferior frontal gyrus (IFG) was enhanced irrespective of the stimulus patterns when participants engaged in temporal judgment. Furthermore, just after the final marker, activity in the IFG was enhanced specifically for the time-shrinking pattern. This indicates that activity in the IFG is also related to the illusory perception of time-interval equality. Based on these observations, we propose neural signatures for judgments of temporal equality in the human brain.

Perceptual inequality between two neighboring time intervals defined by sound markers: correspondence between neurophysiological and psychological data.

Brain activity related to time estimation processes in humans was analyzed using a perceptual phenomenon called auditory temporal assimilation. In a typical stimulus condition, two neighboring time intervals (T1 and T2 in this order) are perceived as equal even when the physical lengths of these time intervals are considerably different. Our previous event-related potential (ERP) study demonstrated that a slow negative component (SNCt) appears in the right-frontal brain area (around the F8 electrode) after T2, which is associated with judgment of the equality/inequality of T1 and T2. In the present study, we conducted two ERP experiments to further confirm the robustness of the SNCt. The stimulus patterns consisted of two neighboring time intervals marked by three successive tone bursts. Thirteen participants only listened to the patterns in the first session, and judged the equality/inequality of T1 and T2 in the next session. Behavioral data showed typical temporal assimilation. The ERP data revealed that three components (N1; contingent negative variation, CNV; and SNCt) emerged related to the temporal judgment. The N1 appeared in the central area, and its peak latencies corresponded to the physical timing of each marker onset. The CNV component appeared in the frontal area during T2 presentation, and its amplitude increased as a function of T1. The SNCt appeared in the right-frontal area after the presentation of T1 and T2, and its magnitude was larger for the temporal patterns causing perceptual inequality. The SNCt was also correlated with the perceptual equality/inequality of the same stimulus pattern, and continued up to about 400 ms after the end of T2. These results suggest that the SNCt can be a signature of equality/inequality judgment, which derives from the comparison of the two neighboring time intervals.

Mutual adaptive timing in interpersonal action coordination.

Coperformers in musical ensembles continuously adapt the timing of their actions to maintain interpersonal coordination. The current study used a dyadic finger-tapping task to investigate whether such mutual adaptive timing is predominated by assimilation (i.e., copying relative timing, akin to mimicry) or compensation (local error correction). Our task was intended to approximate the demands that arise when coperformers coordinate complementary parts with a in an ensemble. In two experiments, paired musicians (the coperformers) were required to tap in alternation, in synchrony with an auditory pacing signal (the section). Serial dependencies between successive asynchronies produced by alternating individuals' taps relative to the pacing tones revealed greater evidence for temporal assimilation than compensation. By manipulating the availability of visual and auditory feedback across experiments, it was shown that this assimilation was strongest when coactors' taps triggered sounds, while the effects of visual information were negligible. These results suggest that interpersonal temporal assimilation was mediated by perception-action coupling in the auditory modality. Mutual temporal assimilation may facilitate coordination in musical ensembles by automatically increasing stylistic compatibility between coperformers, thereby assisting them to sound cohesive.Keywords: interpersonal coordination, sensorimotor synchronization, behavioral assimilationEveryday life typically entails the coordination of one's actions with those of other individuals. Such social interaction frequently requires specific relations in interpersonal movement timing to be produced, as is epitomized in musical ensemble performance (Keller, 2008; Repp, 2006). In ensembles, the actions of multiple individuals must be temporally coordinated in a specific manner in order for the group to produce sounds that give the impression of a coherent musical performance. Thus, each ensemble member temporally tunes his or her actions to those of coperformers. This process relies on sensitivity to deviations from temporal regularity, however subtle, which must be anticipated and reacted to by adjusting the timing of subsequent actions (Keller, 2008; Maduell & Wing, 2007). These adjustments are driven by adaptive timing mechanisms that allow an individual to alter his or her ongoing rhythmic behavior to accommodate the effects of another individ- ual's actions or other external events. The present study used a dyadic finger-tapping task to investigate mutual adaptive timing in interpersonal action coordination.Our aim was to examine mutual adaptive timing in a tightly controlled experimental setting that nevertheless captures some of the basic demands of temporal coordination between coperformers in musical ensembles. We were specifically interested in demands that arise when coperformers are required to produce complemen- tary actions (i.e., to produce different sounds at different times) in synchrony with a common underlying pulse. This situation is common in modern popular ensemble music (e.g., jazz, rock, and pop), where a rhythm section comprising instruments such as the bass guitar and drums provides a basic quasi-periodic pulse rela- tive to which rhythms produced by other instruments are timed. The basso continuo (a bass line performed by a keyboard instru- ment, often supported by another low-pitched instrument) served a similar function in Baroque and other early Western art music (Brendel, 2007). Members of the ensemble must coordinate their performance with this basic pulse, as well as with each other's sounds, to achieve a well-synchronized holistic musical interplay.However, synchrony is never (objectively) perfect in human music making owing to perceptual and motor constraints, errors, and uncertainty associated with aesthetically motivated timing deviations that coperformers introduce for expressive purposes (Rasch, 1988). …

P19-3 Electrophysiological correlate of auditory temporal assimilation between two neighboring time intervals: a principal component analysis

P19-3 Electrophysiological correlate of auditory temporal assimilation between two neighboring time intervals: a principal component analysis

A neural decoding approach to auditory temporal assimilation

By constructing Gaussian Naive Bayes Classifiers, we have re-analyzed data from an earlier event-related potential (ERP) study of an illusion in time perception known as auditory temporal assimilation. In auditory temporal assimilation, two neighboring physically unequal time intervals marked by three successive tone bursts are illusorily perceived as equal if the two time intervals satisfy a certain relationship. The classifiers could discriminate whether or not the subject was engaged in the task, which was judgment of the subjective equality between the two intervals, at an accuracy of >79%, and from principal component scores of individual average ERP waveforms, we were able to predict their subjective judgments to each stimulus at an accuracy of >70%. Chernoff information, unlike accuracy or Kullback–Leibler (KL) distance, suggested brain activation associated with auditory temporal assimilation at an early pre-decision stage. This may provide us with a simple and useful neural decoding scheme in analyzing information processing of temporal patterns in the brain.

105. A study on “temporal assimilation” in the visual modality

105. A study on “temporal assimilation” in the visual modality

48. Brain mechanisms of auditory temporal assimilation

48. Brain mechanisms of auditory temporal assimilation

Electrophysiological Evidence of Auditory Temporal Perception Related to the Assimilation Between Two Neighboring Time Intervals

We conducted two event-related potential (ERP) experiments that examined the mechanisms of auditory temporal assimilation. Stimulus patterns consisted of two neighboring time intervals marked by three successive tone bursts (20 ms, 1000 Hz). Six stimuli were used in which the first time interval (T1) varied from 100 to 280 ms, while the second time interval (T2) was fixed at 200 ms. Two other stimuli of different T1/T2 combinations were employed. Participants judged whether T1 and T2 had the same duration or not by pressing a button. ERPs were recorded from 11 electrodes over the scalp. Behavioral data showed symmetrical assimilation; the participants judged the two neighboring time intervals as equal when the difference between the time intervals (T1-T2) was -40 to +40 ms. Electrophysiological data showed that two ERP components (P300 and CNV) emerged related to the temporal judgment. The P300 appeared in the parietal area at 400 ms after the 2nd tone burst, and its amplitude decreased as a function of T1. The CNV component appeared in the frontal area during T2 presentation, and its amplitude increased as a function of T1. In Experiment 2, 11 stimulus patterns were presented. In seven stimuli, T1 varied from 80 to 320 ms, and T2 was fixed at 200 ms. ERPs were recorded from 19 electrodes over the scalp. In this experiment, behavioral data showed asymmetrical assimilation; participants judged the two neighboring time intervals as equal when T1-T2 was -80 to +40 ms. Consistent with the results of Experiment 1, electrophysiological data showed the P300 and the CNV during T2. In addition, a slow negative component (SNCt) appeared in the right prefrontal area after the 3rd tone burst, and continued up to about 400 ms after the stimuli. The magnitude of this component was smaller when temporal assimilation occurred. These three ERP signatures seem to correlate with the process of temporal assimilation; (a) the P300 augmentation, which could be related to the participants' attention to the 1st interval and reflect the monitoring of the passage of time, (b) the CNV in the frontal area, which might have accompanied the process of memorizing the lengths of the time intervals, and (c) the SNCt in the right prefrontal area, which showed a reduction when temporal assimilation occurred. Our results showed spatiotemporal characteristics of the cortical processing of short time intervals and may assist the neurophysiological understanding of illusions in time and time perception in general.

Time-Shrinking: The Process of Unilateral Temporal Assimilation

Our previous research on auditory time perception showed that the duration of empty time intervals shorter than about 250 ms can be underestimated hugely if they are immediately preceded by shorter time intervals. We named this illusion 'time-shrinking' (TS). This study comprises four experiments in which the preceding interval, t1, was followed by a standard interval, t2. When t1 < or = 200 ms, and t1 < or = t2, the underestimation of t2 came into view clearly. The absolute difference between t2 and t1 was the crucial factor for the illusion to appear. The underestimation increased when t2 increased from t1 to t1 + 65 ms, stayed at about 45 ms when t2 was between t1 + 65 ms and t1 + 95 ms, and disappeared suddenly when t2 exceeded t1 + 95 ms. This pattern of results was observed across all values of t1 < or = 200 ms. A model was fit to the data to elucidate the underlying process of the illusion. The model states that the perceived duration difference between t1 and t2 is reduced by cutting mental processing time for t2; in other words, that t2 assimilates to t1.

Effects of consonantal context on perceptual assimilation of American English vowels by Japanese listeners.

This study investigated the extent to which adult Japanese listeners' perceived phonetic similarity of American English (AE) and Japanese (J) vowels varied with consonantal context. Four AE speakers produced multiple instances of the 11 AE vowels in six syllabic contexts /b-b, b-p, d-d, d-t, g-g, g-k/ embedded in a short carrier sentence. Twenty-four native speakers of Japanese were asked to categorize each vowel utterance as most similar to one of 18 Japanese categories [five one-mora vowels, five two-mora vowels, plus/ei, ou/ and one-mora and two-mora vowels in palatalized consonant CV syllables, C(j)a(a), C(j)u(u), C(j)o(o)]. They then rated the "category goodness" of the AE vowel to the selected Japanese category on a seven-point scale. None of the 11 AE vowels was assimilated unanimously to a single J response category in all context/speaker conditions; consistency in selecting a single response category ranged from 77% for /eI/ to only 32% for /ae/. Median ratings of category goodness for modal response categories were somewhat restricted overall, ranging from 5 to 3. Results indicated that temporal assimilation patterns (judged similarity to one-mora versus two-mora Japanese categories) differed as a function of the voicing of the final consonant, especially for the AE vowels, /see text/. Patterns of spectral assimilation (judged similarity to the five J vowel qualities) of /see text/ also varied systematically with consonantal context and speakers. On the basis of these results, it was predicted that relative difficulty in the identification and discrimination of AE vowels by Japanese speakers would vary significantly as a function of the contexts in which they were produced and presented.

Categorical Rhythm Perception as a Result of Unilateral Assimilation in Time-Shrinking

In previous studies, we established an illusion of time perception that we called time-shrinking: an empty time interval, immediately preceded by a slightly shorter time interval, is underestimated. In the first experiment of the present study, we examined the perceived duration not only of the second interval (t2), but also of the first interval (tl). The empty time intervals tl and t2, making a total duration of 90,180, 360, or 720 ms, were presented such that the time ratio between them changed systematically. The points of subjective equality of tl and t2 were established by the method of adjustment. In the patterns typically susceptible to timeshrinking, that is, in which t2 was underestimated, tl was perceived almost vertically. In the second experiment, listeners had to bisect an empty duration of 180 ms, marked by sound bursts. The bisecting sound marker was positioned closer to the initial marker than to the final one. Thus, tl had to be shorter than t2 in order for a regular pattern to be perceived. In the third experiment, just-noticeable forward and backward displacements of the middle sound marker were measured by a transformed updown method. The prediction that the interval of uncertainty was closer to the initial than to the final sound marker was confirmed. The three experiments demonstrated the existence of unilateral temporal assimilation, and it is argued that this perceptual mechanism causes a category of 1:1 rhythms, despite a considerable change in temporal ratio between two contiguous time intervals.

Perceptual assimilation of American English vowels by Japanese listeners

The present study examined Japanese (J) speakers' perceptual assimilation of 11 American English (AE) vowels produced by four male speakers in two sets of materials: /hVba/ disyllables spoken in citation-form (lists) and in /hVb/ syllables embedded in a short carrier sentence. J listeners were asked to select the J vowel category to which each AE vowel was most similar and to rate its category goodness on a 7-point scale. While the overall pattern of assimilation to the five Japanese (J) vowel qualities (spectral assimilation pattern) was partially predictable on the basis of cross-language phonetic similarities, there were some unexpected results, and spectral assimilation patterns differed across disyllable and sentence conditions for 4 of the 11 vowels. There were also large differences across the two sets of materials in assimilation of long and short AE vowels to J long (2-mora) and short (1-mora) vowel categories (temporal assimilation pattern). The long AE vowels were perceived as similar to long J vowels only when they were produced and presented in sentence context. In a second study in which the final /a/ portions of the disyllables were electronically shortened, assimilation of long AE vowels to long J categories did not differ from the original disyllable condition. This suggests that the better temporal differentiation of long and short AE vowels in the sentence condition was due to the presence of a larger rhythmic context. Acoustical analysis of the stimuli indicated that some, but not all, of the differences in spectral and temporal perceptual assimilation patterns across speakers and conditions could be accounted for by differences in acoustic structure (production differences). Implications for theories of L2 speech learning and for training studies of L2 vowels are discussed.

Perceptual assimilation of Japanese vowels by American English listeners: effects of speaking style

Our previous research on perceptual assimilation of non-native vowels to native categories showed that patterns of spectral and temporal assimilation vary with speaking style (citation vs sentence) and consonantal context. Japanese (J) listeners’ perceptual assimilation of American English (AE) long and short vowels to long (2-mora) and short (1-mora) categories was more consistent when the target syllables were presented in sentences (Strange, et al. ATR Technical Report, TR-H-218, 1997). In the present study, AE listeners categorized 4 speakers’ tokens of 10 J vowels /ii, i, ee, e, aa, a, oo, o, uu, u/ into 11 native AE categories and rated their goodness-of-fit on a 7-point scale (7 = native). Results indicated that patterns of temporal assimilation of the J short vowels /e, a, u/ differed with speaking style. Assimilation of /e/ to mid or high front spectral AE categories also varied with context and individual speakers. Goodness-of-fit ratings suggested that all 10 J vowels were considered relatively ‘‘good’’ instances of AE categories (medians = 5 to 7). In comparison with J listeners’ perception of AE vowels, AE listeners judged cross-language similarities between J and AE vowels more on the basis of their spectral characteristics than on their temporal characteristics.

A New Illusion of Time Perception—II

When one very short empty time interval follows right after another, the second one can be underestimated considerably, but only if it is longer than the first one. We coined the term "time-shrinking" for this illusory phenomenon in our previous studies. Although we could relate our finding to some studies of rhythm perception, we were not able to explain the illusion. The present article presents our attempt to understand the mechanism that causes the time-shrinking. Four experiments are reported. The first one ruled out the possibility that the illusion results from a difficulty in resolving the temporal structure. The second experiment showed that the listener was not inadvertently judging the duration of the first interval instead of that of the second one. In addition, this experiment yielded more information about the time window within which the illusion occurs. The third experiment showed that forward masking of the sound markers, delimiting the empty durations, could not explain the illusion either. Furthermore, this experiment revealed a clue to the mechanism of time-shrinking: competition between expected and observed temporal positions. The fourth experiment further examined the temporal conditions that give rise to the illusion and showed that categorical perception plays a crucial role in the formation of the illusion. In the general discussion, we argue that the illusion is due to an asymmetric process of temporal assimilation.