Academic literature on the topic 'Time interval measurement'

This paper reports the results of two experiments that investigated interval-by-interval inter and intrajudge agreement for stuttered and nonstuttered speech intervals (4.0 sec). The first experiment demonstrated that interval-by-interval interjudge agreement could be significantly improved, and to satisfactory levels, by training judges to discriminate between experimenter-agreed intervals of stuttered and nonstuttered speech. The findings also showed that, independent of training, judges with relatively high intrajudge agreement also showed relatively higher interjudge agreement. The second experiment showed that interval-by-interval interjudge agreement was not significantly different if judges rated 4-sec speech intervals from different samples under three conditions: in random order, separated by 5-sec recording intervals; in correct order, also separated by 5-sec recording intervals; or after brief judgment signals that occurred every 4 sec during continuous samples. The implications of these findings for stuttering measurement are discussed.

The study reported in this article used a binary forced-choice judgment procedure to investigate the effects of sample duration on observers’ judgments of stuttering. Two groups of judges, differing in their previous experience with stuttering, categorized 270 speech intervals as stuttered or nonstuttered; the intervals were drawn from 30 persons who stuttered and ranged from 1 sec to 15 sec in duration. Results showed that judgments were consistently related to interval duration, with shorter intervals significantly more likely than longer intervals to be labeled nonstuttered. Interjudge agreement levels, however, were largely unaffected by the different interval durations for most speakers and for both judge groups, with the exception of the longest and shortest intervals drawn from speakers evidencing the mildest and most severe stuttering. An interval duration in the 3- to 5-sec region appeared to attract the most satisfactory level of agreement. The implications of these findings for interval-based clinical and experimental measurements of stuttering are discussed.

The study reported in this paper was designed to replicate and extend the results of an earlier study (Ingham, Cordes, & Gow, 1993) that investigated time-interval judgments of stuttering. Results confirmed earlier findings that interjudge agreement is higher for these interval-recording tasks than has been previously reported for event-based analyses of stuttering judgments or for time-interval analyses of event judgments. Results also confirmed an earlier finding that judges with intrajudge agreement levels of 90% or better show higher interjudge agreement than judges with lower intrajudge agreement scores. This study failed to find differences between audiovisual and audio-only judgment conditions; between relatively experienced and relatively inexperienced student judges; and, most importantly, between the judgments made, and the agreement levels achieved, by judges from two different clinical research settings. The implications of these findings for attempts to develop a reliable measurement method for stuttering are discussed.

Analog interpolation is the key technology of high-resolution short time-interval measurement. This study proposes a double interpolation method in time-interval measurement. The technique greatly improves the resolution of the analog time expander, which is based on the principle of charging and discharging of the capacitor. This method can significantly reduce the interpolation time, effectively solve the conflict between high measurement resolution and fast measurement rate. The principle of the time measurement expander based on double interpolation method is described in this paper and compared with the expander based on single interpolation method. Its measurement error is also analyzed in this study.

Abstract The designing process of high resolution time interval measurement systems creates many problems that need to be eliminated. The problems are: the latch error, the nonlinearity conversion, the different duty cycle coefficient of the clock signal, and the clock signal jitter. Factors listed above affect the result of measurement. The FPGA (Field Programmable Gate Array) structure also imposes some restrictions, especially when a tapped delay line is constructed. The article describes the high resolution time-to-digital converter, implemented in a FPGA structure, and the types of errors that appear there. The method of minimization and processing of data to reduce the influence of errors on the measurement is also described.

Smart watches in future will have smart wristband. This work analyses properties of new developed capacitive wristband sensor that measures ballistocardiogram (BCG) from single point on the wrist. In addition, it considers applications of this sensor to monitoring heart rate variability. Another application is in estimating changes (trend) in systolic blood pressure continuously when combined with lead one electrocardiogram (ECG). BP is one of the vital signs that indicates the health condition. It is commonly measured by cuff-based monitor using either auscultatory or oscillometric method. Cuff-based BP monitor is not portable and unable to measure BP continuously which means it is difficult to attach BP monitoring function on a wearable device. Significant research is conducted in estimating BP from pulse transit time (PTT) mathematically which would enable the cuffless BP measurement. In this work, a new time reference, RJ interval, which is the time delay between ECG and BCG signal peaks was tested whether it can be used as a surrogate of PTT in cuffless BP estimation. Based on the study done on 10 healthy people, it was shown that RJ intervals can be useful in evaluating trends of systolic blood pressure.

As further advances are made in semiconductor manufacturing technology the performance of circuits is continuously increasing. Unfortunately, as the technology node descends deeper into the nanometre region, achieving the potential performance gain is becoming more of a challenge; due not only to the effects of process variation but also to the reduced timing margins between signals within the circuit creating timing problems. Production Standard Automatic Test Equipment (ATE) is incapable of performing internal timing measurements due, first to the lack of accessibility and second to the overall timing accuracy of the tester which is grossly inadequate. To address these issue ‘on-chip’ time measurement circuits have been developed in a similar way that built in self-test (BIST) evolved for ‘on-chip’ logic testing. This thesis describes the design and analysis of three time amplifier circuits. The analysis undertaken considers the operational aspects related to gain and input dynamic range, together with the robustness of the circuits to the effects of process, voltage and temperature (PVT) variations. The design which had the best overall performance was subsequently compared to a benchmark design, which used the ‘buffer delay offset’ technique for time amplification, and showed a marked 6.5 times improvement on the dynamic range extending this from 40 ps to 300ps. The new design was also more robust to the effects of PVT variations. The new time amplifier design was further developed to include an adjustable gain capability which could be varied in steps of approximately 7.5 from 4 to 117. The time amplifier was then connected to a 32-stage tapped delay line to create a reconfigurable time measurement circuit with an adjustable resolution range from 15 down to 0.5 ps and a dynamic range from 480 down to 16 ps depending upon the gain setting. The overall footprint of the measurement circuit, together with its calibration module occupies an area of 0.026 mm2 The final circuit, overall, satisfied the main design criteria for ‘on-chip’ time measurement circuitry, namely, it has a wide dynamic range, high resolution, robust to the effects of PVT and has a small area overhead.

Abstract The aim of this thesis was to develop time-to-digital converters (TDC) for the integrated receiver of a pulsed time-of-flight (TOF) laser rangefinder aiming at cm-level accuracy over an input range of 10 m – 15 m. A simple structure, a high integration level and low power consumption are the desired features for such a TDC. From the pulsed TOF laser rangefinder point of view an integrated receiver consisting of both the TDC and the receiver channel on the same die offers the possibility of manufacturing these laser rangefinders with a high integration level and at a low price to fulfil the needs of mass industrial markets. The heart of the TDC is a CMOS ring oscillator, the clock frequency of which is used to calculate the full clock cycles between timing signals, the positions of the timing signals inside the clock period being determined by storing the state of the phase of the ring oscillator for each timing signal. This will improve the resolution of the TDC. Also, additional delay lines are used to generate multiple timing signals, each having a time difference of a fraction of that of the ring oscillator. This will further improve the resolution of the whole TDC. To achieve stable results regardless of temperature and supply voltage variations, the TDC is locked to an on-chip reference voltage, or the resolution of the TDC is calibrated before the actual time interval measurement. The systematic walk error in the receiver channel caused by amplitude variation in the received pulse is compensated for by the TDC measuring the slew rate of the received pulse. This time domain compensation method is not affected by the low supply voltage range of modern CMOS technologies. Three TDC prototypes were tested. A single-shot precision standard deviation of 16 ps (2.4 mm) and a power consumption of 5.3 mW/channel were achieved at best over an input range of 100 ns (15 m). The temperature drifts of an on-chip voltage reference-locked TDC and a TDC based on the calibration method were 90 ppm/°C and 0.27 ps/°C, respectively. The results also showed that a pulsed TOF laser rangefinder with cm-level accuracy over a 0 – 15 m input range can be realized using the integrated receiver with the time domain walk error compensation described here
Tiivistelmä Väitöskirjatyön tavoitteena oli kehittää aika-digitaalimuunninrakenteita valopulssin kulkuajan mittaukseen perustuvan lasertutkan integroituun vastaanottimeen. Tavoitteena oli saavuttaa senttimetriluokan tarkkuus 10 m – 15 m mittausalueella koko lasertutkan osalta. Aika-digitaalimuuntimelta vaaditaan yksinkertaista rakennetta, korkeaa integroimisastetta ja matalaa tehonkulutusta. Integroitu vastaanotin sisältää sekä aika-digitaalimuuntimen että vastaanotinkanavan ja tarjoaa mahdollisuuden korkeasti integroidun lasertutkan valmistukseen halvalla teollisuuden massamarkkinoiden tarpeisiin. Aika-digitaalimuuntimen ytimenä toimii monivaiheinen CMOS-rengasoskillaattori. Aika-digitaalimuunnos perustuu rengasoskillaattorin täysien kellojaksojen laskentaan laskurilla ajoitussignaalien välillä. Lisäksi rengasoskillaatorin jokaisesta vaiheesta otetaan näyte ajoitussignaaleilla niiden paikkojen määrittämiseksi kellojakson sisällä, jolloin aika-digitaalimuuntimen erottelutarkkuutta saadaan parannettua. Erottelutarkkuutta parannetaan lisää viivästämällä ajoitussignaaleja viive-elementeillä ja muodostamalla näin useita erillisiä ajoitussignaaleja, joiden väliset viive-erot ovat murto-osa rengasoskillaattorin viive-elementin viiveestä. Aika-digitaalimuunnin stabiloidaan käyttöjännite- ja lämpötilavaihteluja vastaan lukitsemalla se integroidun piirin sisäiseen jännitereferenssiin, tai sen erottelutarkkuus määritetään ennen varsinaista aikavälinmittausta erillisellä kalibrointimittauksella. Vastaanotetun valopulssin amplitudivaihtelun aiheuttama systemaattinen ajoitusvirhe integroidussa vastaanotinkanavassa kompensoidaan mittaamalla vastaanotetun valopulssin nousunopeus aika-digitaalimuuntimella. Tällainen aikatasoon perustuva kompensointimetodi on myös suorituskykyinen nykyisissä matalakäyttöjännitteisissä CMOS-teknologioissa. Työssä valmistettiin ja testattiin kolme aika-digitaalimuunninprototyyppiä. Muuntimien kertamittaustarkkuuden keskihajonta oli parhaimmillaan 16 ps (2,4 mm) ja tehonkulutus alle 5,3 mW/kanava mittausetäisyyden olessa alle 100 ns (15 m). Sisäiseen jännitereferenssiin lukitun aika-digitaalimuuntimen lämpötilariippuvuudeksi mitattiin 90 ppm/°C ja kalibrointimenetelmällä saavutettiin 0,27 ps/°C lämpötilariipuvuus. Työssä saavutetut tulokset osoittavat lisäksi, että valopulssin kulkuajan mittaukseen perustuvalla lasertutkalla on saavutettavissa senttimetriluokan tarkkuus 0 – 15 m mittausalueella käyttämällä tässä työssä esitettyä integroitua vastaanotinta ja aikatason ajoitusvirhekompensointia

Abstract The aim of this work was to develop time-to-digital converters(TDC) with a wide measurement range of several hundred microseconds and with a measurement precision of a few picoseconds. Because of these requirements, the focus of this work was mainly on TDC architectures based on the Nutt interpolation method, which has several advantages when a long measurement range is a requirement. Compared to conventional data converters the characteristics of a Nutt TDC differ significantly when, for example, quantization errors and linearity errors are considered. In this thesis, the operating principle of a Nutt TDC is analysed and, in particular, the effects of reference clock instabilities are studied giving new insight how the different phase noise processes can be reliably translated into time interval jitter, and how these affect the measurement precision when very long time intervals are measured. Furthermore, these analytical results are confirmed by measurements conducted with a long-range TDC designed as part of this work. Two long-range TDCs have been designed, each based on different interpolator architectures. The first TDC utilises discrete component time-to-voltage converters(TVC) as interpolators. Other key functionality is implemented on an FPGA. The interpolators use Miller integrators to improve the linearity and the single-shot precision of the converter. The TDC has a nominal measurement range of 84ms and it achieves a single-shot precision of 2ps for time intervals shorter than 2ms, after which the precision starts to deteriorate due to the phase noise of the reference clock. In addition to the discrete TDC, an integrated long-range CMOS TDC has been designed with 0.35μm technology. Instead of TVCs, this TDC features cyclic/algorithmic interpolators, which are based on switched-frequency ring oscillators(SRO). The frequency switching is used as a mechanism to amplify quantization error, a key functionality required by any cyclic or a pipeline converter. The interpolators are combined with a 16-bit main counter giving a total range of 327μs. The RMS single-shot precision of the TDC is 4.2ps without any nonlinearity compensation. Furthermore, a calibration functionality implemented partially on-chip ensures that the accuracy of the TDC varies only ±2.5ps in a temperature range of -30C to 70C. Although implemented with fairly old technology, the interpolators’ effective linear range and precision represent state-of-the-art performance
Tiivistelmä Tämän työn tavoitteena oli kehittää aika-digitaalimuuntia (TDC), joilla on laaja satojen mikrosekuntien mittausalue ja muutaman pikosekunnin kertamittaustarkkuus. Näistä vaatimuksista johtuen tässä työssä keskitytään pääasiassa Nuttin interpolointimenetelmään perustuviin TDC-arkkitehtuureihin. Verrattuna tavanomaisiin datamuuntimiin, Nutt TDC:n toiminta poikkeaa merkittävästi, kun tarkastellaan kvantisointi- ja lineaarisuusvirhettä. Tässä väitöskirjatyössä Nuttin menetelmään perustavan TDC:n toiminta analysoidaan, jonka yhteydessä tutkitaan erityisesti referenssioskillaattorin epästabiilisuuksien vaikutusta mittausepävarmuuteen. Tämän pohjalta vaihekohinan eri kohinaprosessit voidaan luotettavasti muuntaa taajuustason kohinatiheysmittauksista aika-tasossa kuvattavaksi aikavälijitteriksi. Nämä teoreettiset tulokset ovat varmistettu yhdellä osana tätä työtä suunnitellulla pitkän kantaman TDC:llä. Teoreettisen tarkastelun lisäksi kaksi pitkän kantaman TDC:tä on suunniteltu, toteutettu ja testattu. Ensimmäinen näistä perustuu erilliskomponenteilla toteutettuun aika-jännitemuunnokseen (TVC) pohjautuvaan interpolointimenetelmään. Analogisten interpolaattoreiden ohella muu olennainen toiminnallisuus toteutettiin FPGA:lle. Interpolaattorit käyttävät Miller-integraattoreita lineaarisuuden ja kertamittaustarkkuuden parantamiseksi. TDC:n nimellinen mittausalue on 84ms ja sillä saavutetaan 2ps:n kertamittaustarkkuus, kun mitattava aikaväli on lyhyempi kuin 2ms, minkä jälkeen mittaustarkkuus heikkenee referenssioskillaattorin vaihekohinan vaikutuksesta. Toinen pitkän kantaman TDC perustuu 0.35μm:n CMOS teknologialla totetutettuun integroituun piiriin. Aika-jännitemuunnoksen sijasta tämä TDC perustuu sykliseen/algoritmiseen interpolointitekniikkaan, jossa taajuusmoduloitua rengasoskillaattoria(SRO) käytetään kvantisointivirheen vahvistamiseksi. Interpolaattorit ovat yhdistetty 16-bittiseen referenssioskillaattorin laskuriin, jolloin TDC:n mittausalue on noin 327μs. Tämän TDC:n RMS kertamittaustarkkuus on 4.2ps, joka saavutetaan ilman epälineaarisuuden kompensointia. Samalle piirille on lisäksi toteutettu kalibrointitoiminnallisuus, jolla varmistetaan TDC:n hyvä mittaustarkkuus kaikissa olosuhteissa. Mittaustarkkuus poikkeaa maksimissaan vain ±2.5ps, kun lämpötila on välillä -30C-70C. Vaikka TDC on toteutettu kohtalaisen vanhalla CMOS teknologialla, interpolaattoreiden efektiivinen lineaarinen alue ja mittaustarkkuus edustavat alansa huippua

Abstract This thesis describes the development of a high precision time-to-digital converter (TDC) in which the conversion is based on a counter and three-stage stabilised delay line interpolation developed in this work. The biggest design challenges in the design of a TDC are related to the fact that the arrival moment of the hit signals (start and stop) is unknown and asynchronous with respect to the reference clock edges. Yet, the time interval measurement system must provide an immediate and unambiguous measurement result over the full dynamic range. It must be made sure that the readings from the counter and the interpolators are always consistent with very high probability. Therefore, the operation of the counter is controlled with a synchronising logic that is in turn controlled with the interpolation result. Another synchronising logic makes it possible to synchronise the timing signals with multiphase time-interleaved clock signals as if the synchronising was done with a GHz-level clock, and enables multi-stage interpolation. Multi-stage interpolation reduces the number of delay cells and registers needed. The delay line interpolators are stabilised with nested delay-locked loops, which leads to good stability and makes it possible to improve single-shot precision with a single look-up table containing the integral nonlinearities of the interpolators measured at the room temperature. A multi-channel prototype TDC was fabricated in a 0.6 μm digital CMOS process. The prototype reaches state-of-the-art rms single-shot precision of better than 20 ps and low power consumption of 50 mW as an integrated TDC.

Abstract The aim of this work was to improve the performance and usability of a digital time-to-digital converter (TDC) in CMOS technology. The characteristics of the TDC were improved especially for the needs of pulsed laser time-of-flight (TOF) distance measurement, where picosecond-level precision with a long µs-level measurement range is needed in order to approach mm-level measurement accuracy. Stability in the face of process, voltage and temperature variations, multiple measurement channels, alternative measurement modes, a high integration level, standard interfaces and simple usage were the main features for development. The measurement architecture is based on counter and timing signal interpolation on two levels. The counter counts the full reference clock cycles between the timing signals, while a new recycling delay line developed in this thesis interpolates within the reference clock cycle. This technique utilizes a short delay line several times per reference clock cycle, which minimizes the interpolation nonlinearity. The same structure also makes the use of a low, MHz-level reference frequency possible, and thus only a crystal is needed as an external oscillator component. The parallel load capacitor-scaled delay line structure acts as the second, sub-gate-delay interpolation level. The INL does not accumulate in elements connected in parallel, and the load capacitance differences enable high, ps-level resolution to be achieved. Four TDC circuits in 0.35 µm CMOS technology were designed and tested in the course of this work, of which the latest, a 7-channel TDC, is able to measure the time intervals between the start pulse and three separate stop pulses in one measurement and to resolve the pulse widths or rise times at the same time. In laser TOF distance measurement this functionality can be used when several echoes arrive at the receiver, and also to compensate for the detection threshold problem known as timing walk error. The TDC achieves 8.9 ps interpolation resolution within the cycle time of a 20 MHz reference clock using only 8 delay elements on the first interpolation level and 14 delay elements on the second. A measurement precision better than 9 ps was achieved without using result post-processing or look-up tables. This work shows that versatile, high performance TDCs can be created in standard CMOS technology
Tiivistelmä Väitöskirjatyön tavoitteena oli parantaa CMOS-aika-digitaalimuuntimien suorituskykyä ja käytettävyyttä. Muuntimen ominaisuuksia kehitettiin erityisesti laseretäisyysmittauksen tarpeita ajatellen, missä millimetritason mittaustarkkuus laajalla mittausaluella edellyttää aika-digitaalimuuntimelta pikosekuntitason tarkkuutta mikrosekuntien mittausalueella. Stabiilius prosessiparametri-, jännite- ja lämpötilavaihteluita vastaan, useat mittauskanavat, useat mittausmoodit, korkea integraatioaste, standardoidut liitäntäväylät ja helppo käytettävyys olivat erityisesti kehityksen kohteina. Suunniteltu mittausarkkitehtuuri koostuu laskurista ja kaksitasoisesta ajoitussignaali-interpolaattorista. Laskuri laskee kokonaiset referenssikellojaksot ajoitussignaalien välillä ja työssä kehitetty referenssiä kierrättävä viivelinjarakenne rekistereineen interpoloi ajoitussignaalien paikat referenssikellojaksojen sisältä. Referenssinkierrätystekniikka hyödyntää lyhyttä viivelinjaa useampaan kertaan kellojakson aikana, mikä minimoi epälineaarisuuden interpoloinnissa. Sama rakenne mahdollistaa myös MHz-tason referenssitaajuuden, jolloin matalataajuista kidettä voidaan käyttää referenssilähteenä. Toinen interpolointitaso koostuu rinnakkaisista kapasitanssiskaalatuista viive-elementeistä, mitkä mahdollistavat alle porttiviiveen mittausresoluution. Rinnakkaisessa rakenteessa elementtien epälineaarisuudet eivät summaudu, mikä mahdollistaa pikosekuntitason mittaustarkkuuden. Väitöskirjatyössä suunniteltiin ja toteutettiin neljä aikavälinmittauspiiriä käyttäen 0,35 µm CMOS-teknologiaa, joista viimeisin, 7-kanavainen muunnin kykenee mittaamaan aikavälin useampaan pulssiin yhdellä kertaa sekä voi selvittää samalla pulssien leveydet tai nousuajat. Laseretäisyysmittauksessa monikanavaisuutta voidaan käyttää kun useita kaikuja lähetetystä pulssista saapuu vastaanottimeen sekä kompensoimaan mittauksessa esiintyviä muita virhelähteitä. Käytettäessä 20 MHz:n kidettä referenssilähteenä muunnin saavuttaa alle 9 ps:n interpolointiresoluution ja tarkkuuden ilman epälineaarisuudenkorjaustaulukoita. Työ osoittaa, että edullisella CMOS-teknologialla voidaan toteuttaa monipuolinen ja erittäin suorituskykyinen aika-digitaalimuunnin

The measurement of engagement, or the interaction of a person with their environment, is an integral part of assessing the quality of an intervention program for young children diagnosed with autism spectrum disorder. Researchers and practitioners can and do measure engagement in many ways on the individual and group level. The purpose of this methodological study was to compare three commonly used recording systems: individual partial interval, group momentary time sampling, and group partial interval. These recording methods were compared across three classes of engagement: social, instructional, and non-instructional in a clinical setting with children with autism. Results indicate that group measurement systems were not sensitive to individual changes in engagement when child behaviors were variable. The results are discussed in the context of behavior analytic conceptual systems and the relative utility and future research directions for behavior analytic practice and research with young children in group settings.

A microcomputer based hardware, the Time Interval Board, was designed and the software interface control program was developed. The board measures time intervals between consecutive pulses from a discriminator output. The data is stored in on-board 16K x 16 memory. The microcomputer empties and processes the data when the on-board memory is filled. Data collection continues until the preset collection period is finished or a forced end is initiated. During this period, control is passed between the hardware and the microcomputer via the interface circuit. The designed hardware is IBM PC compatible.

AbstractClinical data is often collected and processed as time series: a sequence of data indexed by successive time points. Such time series can be from sources that are sampled over short time intervals to represent continuous biophysical wave-(one word waveforms) forms such as the voltage measurements representing the electrocardiogram, to measurements that are sampled daily, weekly, yearly, etc. such as patient weight, blood triglyceride levels, etc. When analyzing clinical data or designing biomedical systems for measurements, interventions, or diagnostic aids, it is important to represent the information contained within such time series in a more compact or meaningful form (e.g., noise filtering), amenable to interpretation by a human or computer. This process is known as feature extraction. This chapter will discuss some fundamental techniques for extracting features from time series representing general forms of clinical data.

AbstractIn addition to economic and on-time order fulfillment, the monitoring of the plant performance and its related key performance indicators is a central task of logistics management and control systems. Currently, the determination and calculation of performance figures within the framework of site acceptance tests of automated logistics systems are plant-specific and, therefore, require a lot of manual effort. In this chapter, the authors develop a concept for the automated determination of performance indicators for storage and conveying systems. Based on a comprehensive literature review, structured expert interviews and including various perspectives from industrial applications the approach is designed. Further, the impact of the proposed concept on the logistics performance of the plant and the adequate selection of a maintenance strategy is discussed.

AbstractPorous or biological materials comprise a multitude of micro-domains containing water. Diffusion-weighted magnetic resonance measurements are sensitive to the anisotropy of the thermal motion of such water. This anisotropy can be due to the domain shape, as well as the (lack of) dispersion in their orientations. Averaging over measurements that span all orientations is a trick to suppress the latter, thereby untangling it from the influence of the domains’ anisotropy on the signal. Here, we consider domains whose anisotropy is modeled as being the result of a Hookean (spring) force, which has the advantage of having a Gaussian diffusion propagator while still confining the spatial range for the diffusing particles. In fact, this confinement model is the effective model of restricted diffusion when diffusion is encoded via gradients of long durations, making the model relevant to a broad range of studies aiming to characterize porous media with microscopic subdomains. In this study, analytical expressions for the powder-averaged signal under this assumption are given for so-called single and double diffusion encoding schemes, which sensitize the MR signal to the diffusive displacement of particles in, respectively, one or two consecutive time intervals. The signal for one-dimensional diffusion is shown to exhibit power-law dependence on the gradient strength while its coefficient bears signatures of restricted diffusion.

AbstractSchool improvement and educational change can be facilitated by learning through reflection, as this allows teachers to discover ways to develop and adapt to change. Higher levels of engagement in reflection have been found to be beneficial, but it is unclear from which everyday routine in engagement in reflection higher levels arise, and thus whether occasions to make knowledge explicit should be organized with a certain constancy. In this study, we therefore used a conceptualization of teacher learning through reflection as a situated and dynamic process in which available environmental information, learning activities, and professional practices are interconnected, and co-develop. Seventeen Dutch Vocational Education and Training teachers participated over a period of 5 months. We explored the use of daily and monthly logs as measurement instruments and Recurrence Quantification Analysis (RQA) as the analysis technique applied to the time-series generated from the daily logs. The findings indicated that teachers who make information from their working environment explicit more are also able to make new insights explicit more. The routine with which teachers make information explicit was found to be mostly unrelated to making new insights explicit. To reach their levels of engagement in reflection, some teachers organized opportunities to reflect with determined intervals, others seemed to recognize those opportunities as the working environment provided them, and some used a combination thereof. Moreover, the use of daily and monthly logs seemed to fit better to some participants than others. Only sometimes does organizing constancy in engagement in reflection seem to relate to the levels thereof. This study provides an example of how logs and RQA can be adopted to tap into professional learning as a dynamic and situated process in support of school improvement and educational change.

1.1 Macroeconomic summary Economic recovery has consistently outperformed the technical staff’s expectations following a steep decline in activity in the second quarter of 2020. At the same time, total and core inflation rates have fallen and remain at low levels, suggesting that a significant element of the reactivation of Colombia’s economy has been related to recovery in potential GDP. This would support the technical staff’s diagnosis of weak aggregate demand and ample excess capacity. The most recently available data on 2020 growth suggests a contraction in economic activity of 6.8%, lower than estimates from January’s Monetary Policy Report (-7.2%). High-frequency indicators suggest that economic performance was significantly more dynamic than expected in January, despite mobility restrictions and quarantine measures. This has also come amid declines in total and core inflation, the latter of which was below January projections if controlling for certain relative price changes. This suggests that the unexpected strength of recent growth contains elements of demand, and that excess capacity, while significant, could be lower than previously estimated. Nevertheless, uncertainty over the measurement of excess capacity continues to be unusually high and marked both by variations in the way different economic sectors and spending components have been affected by the pandemic, and by uneven price behavior. The size of excess capacity, and in particular the evolution of the pandemic in forthcoming quarters, constitute substantial risks to the macroeconomic forecast presented in this report. Despite the unexpected strength of the recovery, the technical staff continues to project ample excess capacity that is expected to remain on the forecast horizon, alongside core inflation that will likely remain below the target. Domestic demand remains below 2019 levels amid unusually significant uncertainty over the size of excess capacity in the economy. High national unemployment (14.6% for February 2021) reflects a loose labor market, while observed total and core inflation continue to be below 2%. Inflationary pressures from the exchange rate are expected to continue to be low, with relatively little pass-through on inflation. This would be compatible with a negative output gap. Excess productive capacity and the expectation of core inflation below the 3% target on the forecast horizon provide a basis for an expansive monetary policy posture. The technical staff’s assessment of certain shocks and their expected effects on the economy, as well as the presence of several sources of uncertainty and related assumptions about their potential macroeconomic impacts, remain a feature of this report. The coronavirus pandemic, in particular, continues to affect the public health environment, and the reopening of Colombia’s economy remains incomplete. The technical staff’s assessment is that the COVID-19 shock has affected both aggregate demand and supply, but that the impact on demand has been deeper and more persistent. Given this persistence, the central forecast accounts for a gradual tightening of the output gap in the absence of new waves of contagion, and as vaccination campaigns progress. The central forecast continues to include an expected increase of total and core inflation rates in the second quarter of 2021, alongside the lapse of the temporary price relief measures put in place in 2020. Additional COVID-19 outbreaks (of uncertain duration and intensity) represent a significant risk factor that could affect these projections. Additionally, the forecast continues to include an upward trend in sovereign risk premiums, reflected by higher levels of public debt that in the wake of the pandemic are likely to persist on the forecast horizon, even in the context of a fiscal adjustment. At the same time, the projection accounts for the shortterm effects on private domestic demand from a fiscal adjustment along the lines of the one currently being proposed by the national government. This would be compatible with a gradual recovery of private domestic demand in 2022. The size and characteristics of the fiscal adjustment that is ultimately implemented, as well as the corresponding market response, represent another source of forecast uncertainty. Newly available information offers evidence of the potential for significant changes to the macroeconomic scenario, though without altering the general diagnosis described above. The most recent data on inflation, growth, fiscal policy, and international financial conditions suggests a more dynamic economy than previously expected. However, a third wave of the pandemic has delayed the re-opening of Colombia’s economy and brought with it a deceleration in economic activity. Detailed descriptions of these considerations and subsequent changes to the macroeconomic forecast are presented below. The expected annual decline in GDP (-0.3%) in the first quarter of 2021 appears to have been less pronounced than projected in January (-4.8%). Partial closures in January to address a second wave of COVID-19 appear to have had a less significant negative impact on the economy than previously estimated. This is reflected in figures related to mobility, energy demand, industry and retail sales, foreign trade, commercial transactions from selected banks, and the national statistics agency’s (DANE) economic tracking indicator (ISE). Output is now expected to have declined annually in the first quarter by 0.3%. Private consumption likely continued to recover, registering levels somewhat above those from the previous year, while public consumption likely increased significantly. While a recovery in investment in both housing and in other buildings and structures is expected, overall investment levels in this case likely continued to be low, and gross fixed capital formation is expected to continue to show significant annual declines. Imports likely recovered to again outpace exports, though both are expected to register significant annual declines. Economic activity that outpaced projections, an increase in oil prices and other export products, and an expected increase in public spending this year account for the upward revision to the 2021 growth forecast (from 4.6% with a range between 2% and 6% in January, to 6.0% with a range between 3% and 7% in April). As a result, the output gap is expected to be smaller and to tighten more rapidly than projected in the previous report, though it is still expected to remain in negative territory on the forecast horizon. Wide forecast intervals reflect the fact that the future evolution of the COVID-19 pandemic remains a significant source of uncertainty on these projections. The delay in the recovery of economic activity as a result of the resurgence of COVID-19 in the first quarter appears to have been less significant than projected in the January report. The central forecast scenario expects this improved performance to continue in 2021 alongside increased consumer and business confidence. Low real interest rates and an active credit supply would also support this dynamic, and the overall conditions would be expected to spur a recovery in consumption and investment. Increased growth in public spending and public works based on the national government’s spending plan (Plan Financiero del Gobierno) are other factors to consider. Additionally, an expected recovery in global demand and higher projected prices for oil and coffee would further contribute to improved external revenues and would favor investment, in particular in the oil sector. Given the above, the technical staff’s 2021 growth forecast has been revised upward from 4.6% in January (range from 2% to 6%) to 6.0% in April (range from 3% to 7%). These projections account for the potential for the third wave of COVID-19 to have a larger and more persistent effect on the economy than the previous wave, while also supposing that there will not be any additional significant waves of the pandemic and that mobility restrictions will be relaxed as a result. Economic growth in 2022 is expected to be 3%, with a range between 1% and 5%. This figure would be lower than projected in the January report (3.6% with a range between 2% and 6%), due to a higher base of comparison given the upward revision to expected GDP in 2021. This forecast also takes into account the likely effects on private demand of a fiscal adjustment of the size currently being proposed by the national government, and which would come into effect in 2022. Excess in productive capacity is now expected to be lower than estimated in January but continues to be significant and affected by high levels of uncertainty, as reflected in the wide forecast intervals. The possibility of new waves of the virus (of uncertain intensity and duration) represents a significant downward risk to projected GDP growth, and is signaled by the lower limits of the ranges provided in this report. Inflation (1.51%) and inflation excluding food and regulated items (0.94%) declined in March compared to December, continuing below the 3% target. The decline in inflation in this period was below projections, explained in large part by unanticipated increases in the costs of certain foods (3.92%) and regulated items (1.52%). An increase in international food and shipping prices, increased foreign demand for beef, and specific upward pressures on perishable food supplies appear to explain a lower-than-expected deceleration in the consumer price index (CPI) for foods. An unexpected increase in regulated items prices came amid unanticipated increases in international fuel prices, on some utilities rates, and for regulated education prices. The decline in annual inflation excluding food and regulated items between December and March was in line with projections from January, though this included downward pressure from a significant reduction in telecommunications rates due to the imminent entry of a new operator. When controlling for the effects of this relative price change, inflation excluding food and regulated items exceeds levels forecast in the previous report. Within this indicator of core inflation, the CPI for goods (1.05%) accelerated due to a reversion of the effects of the VAT-free day in November, which was largely accounted for in February, and possibly by the transmission of a recent depreciation of the peso on domestic prices for certain items (electric and household appliances). For their part, services prices decelerated and showed the lowest rate of annual growth (0.89%) among the large consumer baskets in the CPI. Within the services basket, the annual change in rental prices continued to decline, while those services that continue to experience the most significant restrictions on returning to normal operations (tourism, cinemas, nightlife, etc.) continued to register significant price declines. As previously mentioned, telephone rates also fell significantly due to increased competition in the market. Total inflation is expected to continue to be affected by ample excesses in productive capacity for the remainder of 2021 and 2022, though less so than projected in January. As a result, convergence to the inflation target is now expected to be somewhat faster than estimated in the previous report, assuming the absence of significant additional outbreaks of COVID-19. The technical staff’s year-end inflation projections for 2021 and 2022 have increased, suggesting figures around 3% due largely to variation in food and regulated items prices. The projection for inflation excluding food and regulated items also increased, but remains below 3%. Price relief measures on indirect taxes implemented in 2020 are expected to lapse in the second quarter of 2021, generating a one-off effect on prices and temporarily affecting inflation excluding food and regulated items. However, indexation to low levels of past inflation, weak demand, and ample excess productive capacity are expected to keep core inflation below the target, near 2.3% at the end of 2021 (previously 2.1%). The reversion in 2021 of the effects of some price relief measures on utility rates from 2020 should lead to an increase in the CPI for regulated items in the second half of this year. Annual price changes are now expected to be higher than estimated in the January report due to an increased expected path for fuel prices and unanticipated increases in regulated education prices. The projection for the CPI for foods has increased compared to the previous report, taking into account certain factors that were not anticipated in January (a less favorable agricultural cycle, increased pressure from international prices, and transport costs). Given the above, year-end annual inflation for 2021 and 2022 is now expected to be 3% and 2.8%, respectively, which would be above projections from January (2.3% and 2,7%). For its part, expected inflation based on analyst surveys suggests year-end inflation in 2021 and 2022 of 2.8% and 3.1%, respectively. There remains significant uncertainty surrounding the inflation forecasts included in this report due to several factors: 1) the evolution of the pandemic; 2) the difficulty in evaluating the size and persistence of excess productive capacity; 3) the timing and manner in which price relief measures will lapse; and 4) the future behavior of food prices. Projected 2021 growth in foreign demand (4.4% to 5.2%) and the supposed average oil price (USD 53 to USD 61 per Brent benchmark barrel) were both revised upward. An increase in long-term international interest rates has been reflected in a depreciation of the peso and could result in relatively tighter external financial conditions for emerging market economies, including Colombia. Average growth among Colombia’s trade partners was greater than expected in the fourth quarter of 2020. This, together with a sizable fiscal stimulus approved in the United States and the onset of a massive global vaccination campaign, largely explains the projected increase in foreign demand growth in 2021. The resilience of the goods market in the face of global crisis and an expected normalization in international trade are additional factors. These considerations and the expected continuation of a gradual reduction of mobility restrictions abroad suggest that Colombia’s trade partners could grow on average by 5.2% in 2021 and around 3.4% in 2022. The improved prospects for global economic growth have led to an increase in current and expected oil prices. Production interruptions due to a heavy winter, reduced inventories, and increased supply restrictions instituted by producing countries have also contributed to the increase. Meanwhile, market forecasts and recent Federal Reserve pronouncements suggest that the benchmark interest rate in the U.S. will remain stable for the next two years. Nevertheless, a significant increase in public spending in the country has fostered expectations for greater growth and inflation, as well as increased uncertainty over the moment in which a normalization of monetary policy might begin. This has been reflected in an increase in long-term interest rates. In this context, emerging market economies in the region, including Colombia, have registered increases in sovereign risk premiums and long-term domestic interest rates, and a depreciation of local currencies against the dollar. Recent outbreaks of COVID-19 in several of these economies; limits on vaccine supply and the slow pace of immunization campaigns in some countries; a significant increase in public debt; and tensions between the United States and China, among other factors, all add to a high level of uncertainty surrounding interest rate spreads, external financing conditions, and the future performance of risk premiums. The impact that this environment could have on the exchange rate and on domestic financing conditions represent risks to the macroeconomic and monetary policy forecasts. Domestic financial conditions continue to favor recovery in economic activity. The transmission of reductions to the policy interest rate on credit rates has been significant. The banking portfolio continues to recover amid circumstances that have affected both the supply and demand for loans, and in which some credit risks have materialized. Preferential and ordinary commercial interest rates have fallen to a similar degree as the benchmark interest rate. As is generally the case, this transmission has come at a slower pace for consumer credit rates, and has been further delayed in the case of mortgage rates. Commercial credit levels stabilized above pre-pandemic levels in March, following an increase resulting from significant liquidity requirements for businesses in the second quarter of 2020. The consumer credit portfolio continued to recover and has now surpassed February 2020 levels, though overall growth in the portfolio remains low. At the same time, portfolio projections and default indicators have increased, and credit establishment earnings have come down. Despite this, credit disbursements continue to recover and solvency indicators remain well above regulatory minimums. 1.2 Monetary policy decision In its meetings in March and April the BDBR left the benchmark interest rate unchanged at 1.75%.