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Journal articles on the topic 'Interval Sequences'

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Published: 10 June 2023

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1

Bar-Noy, Amotz, Keerti Choudhary, David Peleg, and Dror Rawitz. "Efficiently Realizing Interval Sequences." SIAM Journal on Discrete Mathematics 34, no. 4 (January 2020): 2318–37. http://dx.doi.org/10.1137/20m1326489.

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2

Dewsnap and Fischer. "INTERVAL MAPS AND KOENIGS' SEQUENCES." Real Analysis Exchange 25, no. 1 (1999): 205. http://dx.doi.org/10.2307/44153071.

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3

Lychak, M. M. "Interval characteristics of chaotic sequences." Cybernetics and Systems Analysis 40, no. 5 (September 2004): 678–88. http://dx.doi.org/10.1007/s10559-005-0005-z.

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4

Cysarz, D., H. Bettermann, and P. van Leeuwen. "Entropies of short binary sequences in heart period dynamics." American Journal of Physiology-Heart and Circulatory Physiology 278, no. 6 (June 1, 2000): H2163—H2172. http://dx.doi.org/10.1152/ajpheart.2000.278.6.h2163.

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Dynamic aspects of R-R intervals have often been analyzed by means of linear and nonlinear measures. The goal of this study was to analyze binary sequences, in which only the dynamic information is retained, by means of two different aspects of regularity. R-R interval sequences derived from 24-h electrocardiogram (ECG) recordings of 118 healthy subjects were converted to symbolic binary sequences that coded the beat-to-beat increase or decrease in the R-R interval. Shannon entropy was used to quantify the occurrence of short binary patterns (length N = 5) in binary sequences derived from 10-min intervals. The regularity of the short binary patterns was analyzed on the basis of approximate entropy (ApEn). ApEn had a linear dependence on mean R-R interval length, with increasing irregularity occurring at longer R-R interval length. Shannon entropy of the same sequences showed that the increase in irregularity is accompanied by a decrease in occurrence of some patterns. Taken together, these data indicate that irregular binary patterns are more probable when the mean R-R interval increases. The use of surrogate data confirmed a nonlinear component in the binary sequence. Analysis of two consecutive 24-h ECG recordings for each subject demonstrated good intraindividual reproducibility of the results. In conclusion, quantification of binary sequences derived from ECG recordings reveals properties that cannot be found using the full information of R-R interval sequences.

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5

Belfer, Alexander, and Martin C. Golumbic. "Counting endpoint sequences for interval orders and interval graphs." Discrete Mathematics 114, no. 1-3 (April 1993): 23–39. http://dx.doi.org/10.1016/0012-365x(93)90353-u.

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6

Repp, Bruno H., Justin London, and Peter E. Keller. "Phase Correction in Sensorimotor Synchronization with Nonisochronous Sequences." Music Perception 26, no. 2 (December 1, 2008): 171–75. http://dx.doi.org/10.1525/mp.2008.26.2.171.

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PHASE CORRECTION, WHICH IS NECESSARY for synchronization of movements with a rhythm, has been studied primarily with isochronous sequences.We used a phase perturbation method to examine phase correction in synchronization with nonisochronous sequences (3:2 interval ratios), using musically trained participants. In isochronous control sequences, the phase correction response (PCR) of the tap following a small phase shift was larger when the intervals were long (600 ms) than when they were short (400 ms). In nonisochronous cyclic two-interval patterns, we found a similar dependence of the PCR on the duration of the interval following a phase shift. In three-interval patterns, however, there was no clear dependence on interval duration. The metrical interpretation of the sequences (downbeat location) had no effect on phase correction. In general, phase correction was as effective with nonisochronous as with isochronous sequences.

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7

Agafonov, A. Y., A. D. Fomicheva, G. A. Starostin, and A. P. Kryukova. "Implicit Learning of the Time Interval Sequence." Experimental Psychology (Russia) 14, no. 1 (2021): 108–21. http://dx.doi.org/10.17759/exppsy.2021140104.

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The article considers the studies performed in the «Sequence Learning» paradigm. A special case of this experimental approach is the method of temporal sequences memorization. The elements of such sequences are time intervals instead of stimulus or their spatial localization. The item of the conducted and described study was implicit learning of the time interval sequence. The goal of the experiment was to check the possibility of unconscious acquisition of the temporal sequences, not related to the sequences of another type of organization. To process the obtained results, mixed linear models were used. It was found that the learning of time interval sequences can occur regardless of the presence of regularity in the reaction order (motor sequence) and without rules in stimuli organization (structural sequence) or in the order of their localization (spatial sequence).

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8

Bentbib, A. H. "Acceleration of convergence of interval sequences." Journal of Computational and Applied Mathematics 51, no. 3 (June 1994): 395–409. http://dx.doi.org/10.1016/0377-0427(92)00120-x.

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9

Roh, Jong-Won, and Byoung-Kee Yi. "Efficient indexing of interval time sequences." Information Processing Letters 109, no. 1 (December 2008): 1–12. http://dx.doi.org/10.1016/j.ipl.2008.08.003.

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10

Debnath, Shyamal, and Subrata Saha. "Matrix transformation on statistically convergent sequence spaces of interval number sequences." Proyecciones (Antofagasta) 35, no. 2 (June 2016): 187–95. http://dx.doi.org/10.4067/s0716-09172016000200004.

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11

Matcharashvili, T., T. Chelidze, and Z. Javakhishvili. "Nonlinear analysis of magnitude and interevent time interval sequences for earthquakes of the Caucasian region." Nonlinear Processes in Geophysics 7, no. 1/2 (June 30, 2000): 9–20. http://dx.doi.org/10.5194/npg-7-9-2000.

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Abstract. It is well known that lithospheric seismic processes are characterized by self-similarity or scale invariance in terms of earthquake-size, time, space and space-time distributions, although precise details of underlying dynamics are not clear. In this study we apply nonlinear dynamics theory tools, such as a correlation dimension, "surrogate" data analysis and positive Lyapunov exponent calculation, to investigate dynamical characteristics of seismicity in the Caucasian region. Interevent time intervals and magnitude sequences are considered for different area and magnitude windows. We find significant evidence of a low dimensional nonlinear structure of earthquake time distribution, obtained by consideration of time interval sequences between all events encountered, above some threshold magnitude, in the original catalogue. However nonlinear structure is absent in artificially generated sequences of time intervals between independent events as well as time intervals between aftershocks. It seems that this kind of filtration of the original catalogue destroys the existing temporal structure of considered lithospheric processes. Unlike artificial inter-aftershock time interval sequences, obtained by removing independent events from the original series, the time interval sequence between the Racha earthquake aftershocks reveals clear evidence of nonlinear structure. Earthquake magnitude dynamics. for all considered regions and magnitude windows, reveal high dimensional nonlinearity.

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12

KEMPE, STEFFEN, JOCHEN HIPP, CARSTEN LANQUILLON, and RUDOLF KRUSE. "MINING FREQUENT TEMPORAL PATTERNS IN INTERVAL SEQUENCES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16, no. 05 (October 2008): 645–61. http://dx.doi.org/10.1142/s0218488508005546.

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Recently a new type of data source came into the focus of knowledge discovery from temporal data: interval sequences. In contrast to event sequences, interval sequences contain labeled events with a temporal extension. However, existing algorithms for mining patterns from interval sequences proved to be far from satisfying our needs. In brief, we missed an approach that, at the same time, defines support as the number of pattern instances, allows input data that consists of more than one sequence, implements time constraints on a pattern instance, and counts multiple instances of a pattern within one interval sequence. In this paper we propose a new support definition which incorporates these properties. We also describe FSMSet, an algorithm that employs the new support definition, and demonstrate its performance on field data from the automotive business.

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13

Skelly, Bezlyak, Liew, Kap, and Sagkriotis. "Treat and Extend Treatment Interval Patterns with Anti-VEGF Therapy in nAMD Patients." Vision 3, no. 3 (August 26, 2019): 41. http://dx.doi.org/10.3390/vision3030041.

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Treat and extend (T&E) is a standard treatment regimen for treating neovascular age-related macular degeneration (nAMD) with anti-vascular endothelial growth factors (anti-VEGFs), but the treatment intervals attained are not well documented. This retrospective, non-comparative, non-randomised study of eyes with nAMD classified treatment interval sequences in a T&E cohort in Australia using Electronic Medical Records (EMR) data. We analysed data from 632 treatment-naïve eyes from 555 patients injected with ranibizumab, aflibercept or unlicensed bevacizumab between January 2012 and June 2016 (mean baseline age 78.0). Eyes were categorised into non-overlapping clusters of interval sequences based on the first 12 months of follow-up. We identified 523 different treatment interval sequences. The largest cluster of 197 (31.5%) eyes attained an 8-week treatment interval before dropping to a shorter frequency, followed by 168 (26.8%) eyes that did not reach or attained a single 8-week interval at the end of the study period. A total of 65 (10.4%) and 83 (13.3%) eyes reached and sustained (≥2 consecutive injection intervals of the same length) an 8 and 12 weekly interval, respectively. This study demonstrates highly individualised treatment patterns in the first year of anti-VEGF therapy in Australia using T&E regimens, with the majority of patients requiring more frequent injections than once every 8 weeks.

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14

Chen, E. Jack, and W. David Kelton. "Confidence interval estimation using quasi-independent sequences." IIE Transactions 42, no. 1 (October 30, 2009): 83–93. http://dx.doi.org/10.1080/07408170903232266.

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15

Parnami, J. C. "Interval filling sequences and completely additive functions." Acta Mathematica Hungarica 58, no. 3-4 (September 1991): 229–40. http://dx.doi.org/10.1007/bf01903953.

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16

ten Hoopen, Gert, Rob Hartsuiker, Takayuki Sasaki, Yoshitaka Nakajima, Masako Tanaka, and Takashi Tsumura. "Auditory Isochrony: Time Shrinking and Temporal Patterns." Perception 24, no. 5 (May 1995): 577–93. http://dx.doi.org/10.1068/p240577.

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It has previously been reported that the duration of short time intervals is conspicuously underestimated if they are preceded by shorter neighbouring time intervals. This illusion was called ‘time shrinking’ and it was argued that it strongly affects the perception of auditory rhythms. In the present study this supposition has been pursued in three experiments. In the first, temporal patterns consisting of two, three, and four intervals had to be judged for anisochrony, which was invoked by offsetting the last sound from its isochronous position. By a constant method, it was determined that the last sound of fast sequences (50 ms base interval) had to be delayed by about 30 ms in order for isochronous rhythms to be perceived. Another interesting finding was that for sound sequences with base intervals up to 200 ms it was the difference limen, rather than Weber's ratio, that was constant for anisochrony detection. In the second experiment, the temporal patterns comprised two intervals, presented serially or separately. The deviation of isochrony could be on either the first or the second interval. The data, gathered by an adaptive method, showed time shrinking to be effective even up to a base interval of 200 ms. The third experiment involved a constant method and anisochrony was implemented on the first interval of two interval patterns. Time shrinking affected perceived isochrony in sequences with base intervals of 50, 100, and 200 ms. It is argued that the paradoxical results of anisochrony detection can be explained in terms of time shrinking. Some anomalies of rhythm perception and production that are the result of time shrinking are discussed. Finally, a tentative setup for a model of anisochrony detection that defies Weber's law is offered.

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17

Ito, Masanobu. "Simple Reaction Time as a Function of Number and Similarity of Sequenced Elements in Rapid Force Production." Perceptual and Motor Skills 85, no. 1 (August 1997): 307–20. http://dx.doi.org/10.2466/pms.1997.85.1.307.

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Two experiments were conducted to examine the effects of number and similarity of sequenced elements on simple reaction time (RT). In Exp. 1, subjects were required to initiate and execute sequences of one to three homogeneous or heterogeneous force elements by squeezing the handle as quickly and accurately as possible. Simple RTs and premotor times increased from one to two elements, with no further increases thereafter, regardless of whether the sequences were comprised of homogeneous or heterogeneous elements. The number of elements did not affect the production of interelement interval. In Exps. 1 and 2, however, simple RTs and premotor times to initiate the sequences were longer for the heterogeneous conditions than for the homogeneous conditions. These findings did not support the assumption of the 1978 subprogram retrieval model of Sternberg, Monsell, Knoll, and Wright that only the first element in the sequence is retrieved and programmed during a simple-RT interval. These findings also suggest that similarity of sequenced elements is one factor which affects the complexity of the motor-programming process.

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18

Croonen, W. L. M., and P. F. M. Kop. "Tonality, Tonal Scheme, and Contour in Delayed Recognition of Tone Sequences." Music Perception 7, no. 1 (1989): 49–67. http://dx.doi.org/10.2307/40285448.

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Two experiments were conducted to test Bartlett and Dowling's conclusion (1980) that the key of a tone sequence strongly influences recognition for short retention intervals, that the influence decreases with increasing retention time, and that the importance of the melodic interval information increases during the retention interval. Five different retention times were used (1,5,8,15, and 30 sec), together with standard tone sequences with a clear tonal scheme and two different contours (two or four directional contour changes). Subjects with moderate musical experience were able to discriminate tonal imitations and transpositions of the standards at all retention times; the number of contour changes did not influence the responses. It was concluded that interval information can be extracted from sequences with strong cues for a particular key within a very short period of time and that one of the major dimensions of tone sequences is not tonality or nontonality, but rather the degree of tonal clarity. This characteristic even may be superior to the number of contour changes.

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19

Repp, Bruno H., and Rachel J. Marcus. "No Sustained Sound Illusion in Rhythmic Sequences." Music Perception 28, no. 2 (December 1, 2010): 121–34. http://dx.doi.org/10.1525/mp.2010.28.2.121.

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Recent Research has shown that subdivision of intervals between beats makes the beat tempo seem slower——a "divided time illusion" (DTI) in music. Another temporal illusion described in the psychophysical literature is that a sustained sound seems longer than a silent interval of the same duration. This "sustained sound illusion" (SSI) may be due to acceleration of an internal pacemaker by continuous sound, or it may result from slower perception of sound offsets than of sound onsets. Experiment 1 tested the pacemaker acceleration hypothesis in a rhythmic context by asking musicians to compare or reproduce the tempi of isochronous tone sequences played legato ("filled") or staccato ("unfilled"). There was no indication that legato sequences were perceived as slower than staccato sequences. Experiment 2 tested the delayed offset perception hypothesis by asking musicians to judge the relative time of occurrence of abrupt or decaying tone offsets in the interonset intervals of isochronous sequences. There was no evidence of delayed perception of abrupt offsets, and decaying offsets were perceived only slightly late. These results suggest that the SSI, unlike the DTI, does not occur in rhythmic contexts and thus is probably not of musical relevance. More generally, the results challenge some proposed explanations of this illusion and call for further research on the conditions under which it does occur.

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20

Repp, Bruno H., and Rachel J. Marcus. "No Sustained Sound Illusion in Rhythmic Sequences." Music Perception 28, no. 2 (December 1, 2010): 121–34. http://dx.doi.org/10.1525/mp.2010.28.2.121online.

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Recent research has shown that subdivision of intervals between beats makes the beat tempo seem slower——a "divided time illusion" (DTI) in music. Another temporal illusion described in the psychophysical literature is that a sustained sound seems longer than a silent interval of the same duration. This "sustained sound illusion" (SSI) may be due to acceleration of an internal pacemaker by continuous sound, or it may result from slower perception of sound offsets than of sound onsets. Experiment 1 tested the pacemaker acceleration hypothesis in a rhythmic context by asking musicians to compare or reproduce the tempi of isochronous tone sequences played legato ("filled") or staccato ("unfilled"). There was no indication that legato sequences were perceived as slower than staccato sequences. Experiment 2 tested the delayed offset perception hypothesis by asking musicians to judge the relative time of occurrence of abrupt or decaying tone offsets in the interonset intervals of isochronous sequences. There was no evidence of delayed perception of abrupt offsets, and decaying offsets were perceived only slightly late. These results suggest that the SSI, unlike the DTI, does not occur in rhythmic contexts and thus is probably not of musical relevance. More generally, the results challenge some proposed explanations of this illusion and call for further research on the conditions under which it does occur.

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21

Hwang, S. F., H. U. Ahmed, Q. Zhou, H. Fu, G. D. Turnbull, R. Fredua-Agyeman, S. E. Strelkov, B. D. Gossen, and G. Peng. "Influence of resistant cultivars and crop intervals on clubroot of canola." Canadian Journal of Plant Science 99, no. 6 (December 1, 2019): 862–72. http://dx.doi.org/10.1139/cjps-2019-0018.

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Clubroot, caused by Plasmodiophora brassicae, is an important constraint on canola (Brassica napus) production in Canada. Rotations of clubroot-resistant (CR) canola cultivars in various sequences and planting intervals between canola with non-host crops and fallow periods were evaluated to determine their effects on clubroot severity and P. brassicae resting spore populations under field and micro-plot conditions. Under micro-plot conditions, the rotation sequences including CR canola, continuous fallow, and the non-host barley reduced gall weight by 63%–100% and clubroot severity by 34%–100% compared with continuous planting of susceptible canola. No visible clubroot symptoms developed following continuous fallow or the non-host crop. Under field conditions, clubroot severity was very high (78% disease index) in the continuous susceptible canola sequence. Most of the CR canola rotation sequences significantly reduced clubroot severity by 12%–23%, but continuous fallow, continuous barley, and alternating the CR canola cultivars ‘45H29’ or ‘73-47’ with ‘TC72429-10’ reduced clubroot severity by 32%–36%. A comparison of intervals between canola crops and four cropping sequences (continuous susceptible canola, alternating canola with barley or pea, a 2-yr non-host interval between canola crops, and a 3-yr non-host interval between canola crops) was conducted over 5 yr. A 2- or 3-yr non-host interval improved plant height, plant biomass, and seed yield, and reduced gall mass, P. brassicae propagules in the soil, and clubroot severity. A significant yield increase of more than 3600% was observed in a 3-yr non-host interval.

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22

Iacò, Maria Rita, and Volker Ziegler. "Discrepancy of Generalized LS-Sequences." Uniform distribution theory 12, no. 2 (December 20, 2017): 37–63. http://dx.doi.org/10.1515/udt-2017-0014.

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Abstract The LS-sequences are a parametric family of sequences of points in the unit interval. They were introduced by Carbone [4], who also proved that under an appropriate choice of the parameters L and S, such sequences are lowdiscrepancy. The aim of the present paper is to provide explicit constants in the bounds of the discrepancy of LS-sequences. Further, we generalize the construction of Carbone [4] and construct a new class of sequences of points in the unit interval, the generalized LS-sequences.

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23

Janicki, Ryszard, and Maciej Koutny. "Operational Semantics, Interval Orders and Sequences of Antichains." Fundamenta Informaticae 169, no. 1-2 (October 10, 2019): 31–55. http://dx.doi.org/10.3233/fi-2019-1838.

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24

Giri, F., F. Z. Chaoui, and Y. Rochdi. "Interval-excitation through impulse sequences. A technical lemma." Automatica 38, no. 3 (March 2002): 457–65. http://dx.doi.org/10.1016/s0005-1098(01)00222-9.

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25

Hill, Toby J. W., and Ian R. Summers. "Discrimination of interval size in short tone sequences." Journal of the Acoustical Society of America 121, no. 4 (April 2007): 2376–83. http://dx.doi.org/10.1121/1.2697059.

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26

Liao, S. S., T. H. Tang, and W. Y. Liu. "Finding Relevant Sequences in Time Series Containing Crisp, Interval, and Fuzzy Interval Data." IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 34, no. 5 (October 2004): 2071–79. http://dx.doi.org/10.1109/tsmcb.2004.833597.

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27

Goss, Peter J. E., and R. C. Lewontin. "Detecting Heterogeneity of Substitution Along DNA and Protein Sequences." Genetics 143, no. 1 (May 1, 1996): 589–602. http://dx.doi.org/10.1093/genetics/143.1.589.

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Abstract Regions of differing constraint, mutation rate or recombination along a sequence of DNA or amino acids lead to a nonuniform distribution of polymorphism within species or fixed differences between species. The power of five tests to reject the null hypothesis of a uniform distribution is studied for four classes of alternate hypothesis. The tests explored are the variance of interval lengths; a modified variance test, which includes covariance between neighboring intervals; the length of the longest interval; the length of the shortest third-order interval; and a composite test. Although there is no uniformly most powerful test over the range of alternate hypotheses tested, the variance and modified variance tests usually have the highest power. Therefore, we recommend that one of these two tests be used to test departure from uniformity in all circumstances. Tables of critical values for the variance and modified variance tests are given. The critical values depend both on the number of events and the number of positions in the sequence. A computer program is available on request that calculates both the critical values for a specified number of events and number of positions as well as the significance level of a given data set.

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Xiong, Pingping, Yue Zhang, Bo Zeng, and Tian-Xiang Yao. "MGM(1,m) model based on interval grey number sequence and its applications." Grey Systems: Theory and Application 7, no. 3 (November 6, 2017): 310–19. http://dx.doi.org/10.1108/gs-07-2017-0022.

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Purpose Aiming at the traditional multivariate grey forecasting model only considers the modelling of real numbers; therefore, the purpose of this paper is to construct an MGM(1, m) model based on the interval grey number sequences according to the grey modelling theory. Design/methodology/approach First, the multivariable grey number sequences are transformed into the kernel and grey radius sequences which are two feature sequences of interval grey number sequences. Then the MGM(1, m) model for kernel sequences and grey radius sequences are established, respectively. Finally, the simulation and prediction of the upper and lower bounds of the interval grey number sequences are realized by the reductive calculation of the predicted values of the kernel and grey radius. Findings The model is applied to the prediction of visibility and relative humidity, the identification factors of the haze. The results show that the model has high accuracy on the simulation and prediction of multivariable grey number sequences, which is reasonable and practical. Originality/value The main contribution of this paper is to propose a method to simulate and forecast the multivariable grey number sequence that is to establish the prediction models for the whitening sequences of multivariable grey number sequences which are kernel and grey radius sequences and extend the possibility boundary of kernel by grey radius. The model can reflect the development trend of multivariable grey number sequence accurately. When the grey information is continuously complemented, the multivariable grey number prediction model is transformed into the traditional MGM(1, m) model. Therefore, the MGM(1, m) model based on interval grey number sequence is the generalisation and expansion of the traditional MGM(1, m) model.

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Nowakowski, Piotr. "When the algebraic difference of two central Cantor sets is an interval?" Annales Fennici Mathematici 48, no. 1 (January 15, 2023): 163–85. http://dx.doi.org/10.54330/afm.126014.

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Let \(C(a ),C(b)\subset \lbrack 0,1]\) be the central Cantor sets generated by sequences \(a,b \in \left( 0,1\right)^{\mathbb{N}}\). The first main result of the paper gives a necessary and a sufficient condition for sequences \(a\) and \(b\) which inform when \(C(a )-C(b)\) is equal to \([-1,1]\) or is a finite union of closed intervals. One of the corollaries following from this results shows that the product of thicknesses of two central Cantor sets, the algebraic difference of which is an interval, may be arbitrarily small. We also show that there are sets \(C(a)\) and \(C(b)\) with the Hausdorff dimension equal to 0 such that their algebraic difference is an interval. Finally, we give a full characterization of the case, when \(C(a )-C(b)\) is equal to \([-1,1]\) or is a finite union of closed intervals.

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Xu, Cheng-Zhong, and Gen-Qi Xu. "New Sequence Spaces and Function Spaces on Interval[0,1]." Journal of Function Spaces and Applications 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/601490.

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We study the sequence spaces and the spaces of functions defined on interval0,1in this paper. By a new summation method of sequences, we find out some new sequence spaces that are interpolating into spaces betweenℓpandℓqand function spaces that are interpolating into the spaces between the polynomial spaceP0,1andC∞0,1. We prove that these spaces of sequences and functions are Banach spaces.

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Jirenhed, Dan-Anders, Anders Rasmussen, Fredrik Johansson, and Germund Hesslow. "Learned response sequences in cerebellar Purkinje cells." Proceedings of the National Academy of Sciences 114, no. 23 (May 22, 2017): 6127–32. http://dx.doi.org/10.1073/pnas.1621132114.

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Associative learning in the cerebellum has previously focused on single movements. In eyeblink conditioning, for instance, a subject learns to blink at the right time in response to a conditional stimulus (CS), such as a tone that is repeatedly followed by an unconditional corneal stimulus (US). During conditioning, the CS and US are transmitted by mossy/parallel fibers and climbing fibers to cerebellar Purkinje cells that acquire a precisely timed pause response that drives the overt blink response. The timing of this conditional Purkinje cell response is determined by the CS–US interval and is independent of temporal patterns in the input signal. In addition to single movements, the cerebellum is also believed to be important for learning complex motor programs that require multiple precisely timed muscle contractions, such as, for example, playing the piano. In the present work, we studied Purkinje cells in decerebrate ferrets that were conditioned using electrical stimulation of mossy fiber and climbing fiber afferents as CS and US, while alternating between short and long interstimulus intervals. We found that Purkinje cells can learn double pause responses, separated by an intermediate excitation, where each pause corresponds to one interstimulus interval. The results show that individual cells can not only learn to time a single response but that they also learn an accurately timed sequential response pattern.

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Janicki, Ryszard, and Łukasz Mikulski. "Algebraic Structure of Step Traces and Interval Traces." Fundamenta Informaticae 175, no. 1-4 (September 28, 2020): 253–80. http://dx.doi.org/10.3233/fi-2020-1956.

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Traces and their extensions as comtraces, step traces and interval traces are quotient monoids over sequences or step sequences that play an important role in the formal analysis and verification of concurrent systems. Step traces are generalizations of comtraces and classical traces while interval traces are specialized traces that can deal with interval order semantics. The algebraic structures and their properties as projections, hidings, canonical forms and other invariants are very well established for traces and fairly well established for comtraces. For step traces and interval traces they are the main subject of this paper.

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Askeland, Bjørn, Halvor Hobæk, and Rolf Mjelde. "Semiperiodic chirp sequences reduce autocorrelation side lobes of pulsed signals." GEOPHYSICS 73, no. 3 (May 2008): Q19—Q27. http://dx.doi.org/10.1190/1.2903820.

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A time-coded sequence of source pulses has been designed to allow for increased range to the target and reduced side-lobe energy with correlation. The method was designed for a new type of marine-combustion seismic source that can be fired repeatedly, but the method also can be applied to other acoustic-pulsed sources. The basic concept is that one can reduce autocorrelation side lobes by using semiperiodic sequences to concentrate much of the side-lobe noise into time intervals corresponding to the semiperiod. Signals can then be detected with better sensitivity in the time interval after the first autocorrelation peak and before the first periodic side lobe, because this interval contains only lower-level crosscorrelations between the sequence components. Compared with a source which fires pulses randomly, an 8-dB reduction of autocorrelation side lobes has been simulated for sequences of [Formula: see text] duration.

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Terrazas Gonzalez, Jesus D., and Witold Kinsner. "A Modular Dynamical Cryptosystem Based on Continuous-Interval Cellular Automata." International Journal of Cognitive Informatics and Natural Intelligence 5, no. 4 (October 2011): 83–109. http://dx.doi.org/10.4018/jcini.2011100106.

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This paper presents a new cryptosystem based on chaotic continuous-interval cellular automata (CCA) to increase data protection as demonstrated by their flexibility to encrypt and decrypt information from distinct sources. Enhancements to cryptosystems are also presented including (i) a model based on a new chaotic CCA attractor, (ii) the dynamical integration of modules containing dynamical systems to generate complex sequences, and (iii) an enhancement for symmetric cryptosystems by allowing them to generate an unlimited number of keys. This paper also presents a process of mixing chaotic sequences obtained from cellular automata, instead of using differential equations, as a basis to achieve higher security and higher speed for the encryption and decryption processes, as compared to other recent approaches. The complexity of the mixed sequences is measured using the variance fractal dimension trajectory to compare them to the unmixed chaotic sequences to verify that the former are more complex. This type of polyscale measure and evaluation has never been done in the past outside this research group.

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Blaber, A. P., Y. Yamamoto, and R. L. Hughson. "Change in phase relationship between SBP and R-R interval during lower body negative pressure." American Journal of Physiology-Heart and Circulatory Physiology 268, no. 4 (April 1, 1995): H1688—H1693. http://dx.doi.org/10.1152/ajpheart.1995.268.4.h1688.

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We have investigated the hypothesis that beat-by-beat interaction of systolic blood pressure (SBP) to R-R interval (the spontaneous baroreflex) is dependent on the length of the R-R interval. Data were collected from eight healthy men while heart rate was slow (R-R interval 1,043 +/- 34 ms) and accelerated (R-R interval 804 +/- 18 ms) by application of lower body negative pressure (LBNP greater than or equal to -40 mmHg). Time series data of SBP and R-R interval were searched for spontaneous baroreflex sequences in which R-R interval changed in the same (lag 0), next (lag 1), or next following (lag 2) beat as SBP. This phase relationship was also quantified by cross-spectral analysis. At rest, 85% of all spontaneous baroreflex sequences occurred with no lag (lag 0). With LBNP, there was a significant reduction in the number of lag 0 sequences (26%), whereas lag 1 and lag 2 sequences increased (10–26% and 5–29%, respectively). Cross-spectral phase also changed significantly from -2.3 +/- 6.3 degrees at rest to 70.5 +/- 7.4 degrees during LBNP. These data supported the hypothesis that the lag of a baroreflex event was dependent on the prevailing R-R interval.

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Medková, Kateřina, Edita Pelantová, and Laurent Vuillon. "Derived sequences of complementary symmetric Rote sequences." RAIRO - Theoretical Informatics and Applications 53, no. 3-4 (July 2019): 125–51. http://dx.doi.org/10.1051/ita/2019004.

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Complementary symmetric Rote sequences are binary sequences which have factor complexity C(n) = 2n for all integers n ≥ 1 and whose languages are closed under the exchange of letters. These sequences are intimately linked to Sturmian sequences. Using this connection we investigate the return words and the derived sequences to the prefixes of any complementary symmetric Rote sequence v which is associated with a standard Sturmian sequence u. We show that any non-empty prefix of v has three return words. We prove that any derived sequence of v is coding of three interval exchange transformation and we determine the parameters of this transformation. We also prove that v is primitive substitutive if and only if u is primitive substitutive. Moreover, if the sequence u is a fixed point of a primitive morphism, then all derived sequences of v are also fixed by primitive morphisms. In that case we provide an algorithm for finding these fixing morphisms.

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Esi, Ayhan, Shyamal Debnath, and Subrata Saha. "Asymptotically double λ2 - statistically equivalent sequences of interval numbers." MATHEMATICA 62 (85), no. 1 (May 25, 2020): 39–46. http://dx.doi.org/10.24193/mathcluj.2020.1.05.

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Esi, Ayhan, Shyamal Debnath, and Subrata Saha. "Asymptotically Double Lacunary Statistically Equivalent Sequences of Interval Numbers." Proyecciones (Antofagasta) 35, no. 4 (December 30, 2016): 469–79. http://dx.doi.org/10.4067/s0716-09172016000400008.

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Arulnayagam Thuraisingham, Ranjit. "Generation of synthetic RR interval sequences of healthy patients." Biomedical Signal Processing and Control 77 (August 2022): 103843. http://dx.doi.org/10.1016/j.bspc.2022.103843.

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Shaar, A. A., C. E. Woodcock, and P. A. Davies. "Prime sequences for asynchronous pulse repetition interval agile radar." IEEE Transactions on Aerospace and Electronic Systems 35, no. 2 (April 1999): 543–48. http://dx.doi.org/10.1109/7.766936.

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Shankwitz, C. R., and T. T. Georgiou. "On the maximum entropy method for interval covariance sequences." IEEE Transactions on Acoustics, Speech, and Signal Processing 38, no. 10 (1990): 1815–17. http://dx.doi.org/10.1109/29.60117.

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Fanping, Zeng. "Kneading sequences for unimodal expanding maps of the interval." Acta Mathematica Sinica, English Series 14, no. 4 (October 1998): 457–62. http://dx.doi.org/10.1007/bf02580402.

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Daróczy, Z., and I. Kátai. "On functions additive with respect to interval filling sequences." Acta Mathematica Hungarica 51, no. 1-2 (March 1988): 185–200. http://dx.doi.org/10.1007/bf01903631.

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Esi, Ayhan. "Double sequences of interval numbers defined by Orlicz functions." Acta et Commentationes Universitatis Tartuensis de Mathematica 17, no. 1 (May 24, 2013): 57. http://dx.doi.org/10.12697/acutm.2013.17.04.

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Roh, Jong-won, Seung-won Hwang, and Byoung-Kee Yi. "Efficient bitmap-based indexing of time-based interval sequences." Information Sciences 194 (July 2012): 38–56. http://dx.doi.org/10.1016/j.ins.2011.08.013.

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Larcher, Gerhard. "On the discrepancy of sequences in the unit-interval." Indagationes Mathematicae 27, no. 2 (March 2016): 546–58. http://dx.doi.org/10.1016/j.indag.2015.11.003.

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Dar�czy, Z., I. K�tai, and T. Szab�. "On completely additive functions related to interval-filling sequences." Archiv der Mathematik 54, no. 2 (February 1990): 173–79. http://dx.doi.org/10.1007/bf01198114.

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Wörgötter, Florentin, and Klaus Funke. "Fine structure analysis of temporal patterns in the light response of cells in the lateral geniculate nucleus of cat." Visual Neuroscience 12, no. 3 (May 1995): 469–84. http://dx.doi.org/10.1017/s0952523800008373.

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AbstractThis study focuses on the analysis of temporal patterns in the spike train of cells in the lateral geniculate nucleus (LGN) of cat. Two-hundred eighty-three units have been recorded extracellularly in anesthetized animals during visual stimulation with flashing spot stimuli of different size. We used a novel method of temporally local computed interval distributions (intervalogram; Funke & Wörgötter, 1995) to visualize the statistical distribution of interspike intervals during different phases of the visual response. Multimodal interval distributions were observed mainly in X- and Y-ON cells, reflecting the tendency of these cells to fire with preferred intervals during the sustained light response. The shortest preferred interval is called the fundamental interval and the longer ones (higher-order intervals) are, in general, multiples thereof. During increasing surround inhibition a redistribution of the intervals towards the higher orders was observed. We regarded the different peaks in the interval distributions as different components of possible temporal spike sequences and performed a pattern search up to the level of five subsequent intervals. While it is obvious, that the dominant peak is most strongly represented in any interval sequence, we also show that a significant overrepresentation of short sequences of similar intervals exists. The repetition rate is rather small (4–5 intervals) and, therefore, no long-lasting oscillatory pattern was observed in the autocorrelograms. Power spectral analysis of the peristimulus-time histograms, however, revealed that the sequential firing pattern is strongly stimulus locked at least for the majority of sweeps in the records.The mean firing rate of an LGN cell decreases with increasing stimulus size as well as with decreasing contrast. Therefore, the mean rate cannot be used to distinguish between these situations. While in the whole network this tradeoff can be resolved by the combined activity of multiple cells, our findings additionally suggest that contrast and size can be distinguished already at the single-cell level using different temporal patterns.

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Esi, Ayhan, Naim L. Braha, and Agim Rushiti. "Wijsman $\lambda-$statistical convergence of interval numbers." Boletim da Sociedade Paranaense de Matemática 35, no. 2 (December 16, 2017): 9–18. http://dx.doi.org/10.5269/bspm.v35i2.29215.

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In this paper we introduce and study the concepts of Wijsman $\lambda-$statistical convergence and Wijsman strong $\lambda-$statistical convergenceof sequences for interval numbers and prove some inclusion relations.

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Mungan, Esra, and Ece Kaya. "Some Time Violations Go Less Noticed: Gestalt Grouping? A Brief Report." Timing & Time Perception 8, no. 3-4 (November 5, 2020): 350–62. http://dx.doi.org/10.1163/22134468-bja10010.

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This brief report is inspired by Bolton’s (1894, Am. J. Psychol., 6, 145–238) tick-tock phenomenon, which describes an illusionary accented grouping of isochronous, non-accented click sequences. It has repeatedly been shown that in stimulus-wise grouped sequences of an XXXOOO character (where X differs from O in terms of intensity, pitch level, or filled or unfilled duration), gap deviations between groups are more prone to go unnoticed compared to deviations within a group (e.g., Fitzgibbons et al., 1974, Percept. Psychophys., 16, 522–528.). Yet, not much is known about whether comparable anisochrony insensitivities might also occur in equal-accented sequences (XXXXX). In a same/different task setting, listeners had to detect isochrony deviations that appeared in different empty-interval locations across 800 trials within a five-pulse sequence of 250 ms interonset intervals. Findings revealed a major location dependency, with least detection accuracy for gap deviations occurring in the last interval, particularly if the 250 ms gap was lengthened rather than shortened. Results are discussed in relation to potential Gestalt grouping and Nakajima et al.’s (2014, Perception, 33, 1061–1079) perceptual assimilation and contrast observations in three-tone sequences.

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