Poincare Analysis Research Articles

Enhancing Wearable Gait Monitoring Systems: Identifying Optimal Kinematic Inputs in Typical Adolescents.

Machine learning-based gait systems facilitate the real-time control of gait assistive technologies in neurological conditions. Improving such systems needs the identification of kinematic signals from inertial measurement unit wearables (IMUs) that are robust across different walking conditions without extensive data processing. We quantify changes in two kinematic signals, acceleration and angular velocity, from IMUs worn on the frontal plane of bilateral shanks and thighs in 30 adolescents (8-18 years) on a treadmills and outdoor overground walking at three different speeds (self-selected, slow, and fast). Primary curve-based analyses included similarity analyses such as cosine, Euclidean distance, Poincare analysis, and a newly defined bilateral symmetry dissimilarity test (BSDT). Analysis indicated that superior-inferior shank acceleration (SI shank Acc) and medial-lateral shank angular velocity (ML shank AV) demonstrated no differences to the control signal in BSDT, indicating the least variability across the different walking conditions. Both SI shank Acc and ML shank AV were also robust in Poincare analysis. Secondary parameter-based similarity analyses with conventional spatiotemporal gait parameters were also performed. This normative dataset of walking reports raw signal kinematics that demonstrate the least to most variability in switching between treadmill and outdoor walking to help guide future machine learning models to assist gait in pediatric neurological conditions.

Early transient dysautonomia predicts the risk of infantile epileptic spasm syndrome onset: A prospective cohort study.

Infantile epileptic spasm syndrome (IESS) is an age-dependent epileptic encephalopathy with a significant risk of developmental regression. This study investigates the association between heart rate variability (HRV) in infants at risk of IESS and the clinical onset of IESS. Sixty neonates at risk of IESS were prospectively followed from birth to 12 months with simultaneous electroencephalogram (EEG) and electrocardiogram recordings for 60 min at every 2-month interval. HRV metrics were calculated from 5 min time-epoch during sleep including frequency domain measures, Poincare analysis including cardiac vagal index (CVI) and cardiac sympathetic index (CSI), and detrended fluctuation analysis (DFA α1, DFA α2). To assess the effect of each HRV metric at the 2-month baseline on the time until the first occurrence of either hypsarrhythmia on EEG and/or clinical spasm, univariate cox-proportional hazard models were fitted for each HRV metric. Infantile epileptic spasm syndrome was diagnosed in 20/60 (33%) of the cohort in a 12-month follow-up and 3 (5%) were lost to follow-up. The median age of developing hypsarrhythmia was 25 (7-53) weeks and clinical spasms at 24 (8-40) weeks. Three (5%) patients had clinical spasms without hypsarrhythmia, and 5 (8%) patients had hypsarrhythmia before clinical spasms at the initial presentation. The infants with high CSI (hazard ratio 2.5, 95% CI 1.2-5.2, P = 0.01) and high DFA α1 (hazard ratio 16, 95% CI 1.1-240, P = 0.04) at 2 months were more likely to develop hypsarrhythmia by the first year of age. There was a trend toward decreasing CSI and DFA α1 and increasing CVI in the first 8 months of age. Our data suggest that relative sympathetic predominance at an early age of 2 months may be a potential predictor for developing IESS. Hence, early HRV patterns may provide valuable prognostic information in children at risk of IESS allowing early detection and optimization of cognitive outcomes. Whether early intervention to restore sympathovagal balance per se would provide clinical benefit must be addressed by future studies.

Abstract 290: Early Monitoring Of Neurological Recovery Using Poincare Analysis Index Of Heart Rate Variability - A Potential Biomarker For Asphyxial Cardiac Arrest Related Brain Injury

Heart rate variability (HRV) is influenced by autonomic nervous system including subcortical structures such as brainstem. We hypothesized that HRV would reflect graded response to hypoxic ischemic brain injury after cardiac arrest (CA). We investigated HRV based on the Poincare analysis method during the hyperacute recovery period after resuscitation to define its role in assessing neurologic recovery. Adult male Wistar rats (360±20g) were subjected to either 5 /7-min of asphyxial CA and grouped based on neurologic recovery - good (n=17) and bad (n=16), assessed at 4 hr post resuscitation using a standardized Neurological Deficit Scale (NDS). A good outcome (GO) was defined as a NDS sub score (arousal+brainstem) of 36-40 and bad outcome (BO) as 23-35, with 40 as good and 0 as brain dead. A Poincare plot showing successive heart rate intervals was developed and analysed on 5-min ECG segments (first 1 hr) owing to the nonstationary HRV patterns during early recovery period. Several machine learning models were trained to assess the results from the standard deviations (SD1, SD2), to decipher the parasympathetic and sympathetic activities, and evaluated by the area under receiver operating characteristic curve (AUC). GO group demonstrated an NDS of 39.65±0.99, while the BO group had an NDS of (30±2.65) showing a statistical difference between groups (p<0.01). GO group exhibited an immediate increase post resuscitation in SD1 (0.55±0.23) and SD2 (0.67±0.29) with a gradual decrease ~1 hr, SD1 (0.20±0.12) and SD2 (0.13±0.09). No significant differences in initial SD1 (0.30±0.14) and SD2 (0.28±0.16) vs after 1 hr of recovery (SD1 (0.29±0.08), SD2 (0.30±0.16)) were observed across BO group. For GO, all parameters indicated a faster return to baseline values- SD1 (0.21±0.08) SD2 (0.15±0.16), showing a better recovery of the cardiac autonomic control, in agreement with the evolution of NDS. Logistic regression and naïve bayes performed best with SD2, giving an accuracy of 72% (AUC: 0.75) and 75% (AUC: 0.88) for recovery prognostication in 5-fold cross validation. Unlike previous studies to find biomarkers for CA related brain injury focused on cortical assessment, our results indicate that the novel HRV method can fill the gap in assessing subcortical injury after CA.

Cardiac autonomic nerve function in polycystic ovary syndrome is not related to oxidative stress: A Poincaré analysis of heart rate variability

Background: Polycystic ovary syndrome (PCOS) is a well recognized reproductive hormone disorder. It is often associated with dysautonomia and increased oxidative stress Objective: To assess the relationship between cardiac autonomic nerve function (CANF) and oxidative stress in patients with PCOS. Methods: This cross sectional study enrolled 30 newly diagnosed PCOS patients 20-35 years of age and 30 apparently healthy, regularly menstruating women of similar age and BMI. The patients were enrolled from outpatient Department of Endocrinology, BSMMU, Dhaka. CANF was assessed by poincare analysis of RR interval, a non linear method of Heart Rate Variability (HRV) analysis. HRV data of all subjects were recorded by a digital data acquisition device, Power lab 8/35, AD instruments, Australia, with lab chart software analysis. Oxidative stress was assessed by plasma catalase and plasma Malondialdehyde (MDA) levels. For statistical analysis unpaired “t” test and Pearson’s correlation test were used. Results: In this study, resting pulse rate, systolic blood pressure(SBP), diastolic blood pressure(DBP) were significantly higher (p<0.001, p<0.01, p<0.01 respectively) and standard deviation of the short term RR interval variability (SD1), ratio of short term and long term variability (SD1/SD2) ratio were significantly lower (p<0.001) in PCOS than those of healthy controls. In addition, plasma catalase levels was significantly lower (p<0.01) and plasma MDA levels was significantly higher (p<0.001) in PCOS patients compared to controls. On correlation analysis, SD1 showed negative correlation with plasma catalase and plasma MDA levels (p>0.05) in PCOS patients. In addition SD1/SD2 ratio showed positive correlation with plasma catalase and negative correlation with plasma MDA levels (p>0.05) in these group of patients. But all these correlations were statistically not significant. Conclusion: The present study reveals association of autonomic dysfunction and higher oxidative stress with PCOS but it failed to show evidence for any interrelationship between them. J Bngladesh Soc Physiol 2021;16(1): 88-94

Novel Measures of Similarity and Asymmetry in Upper Limb Activities for Identifying Hemiparetic Severity in Stroke Survivors.

Stroke survivors are often characterized by hemiparesis, i.e., paralysis in one half of the body, severely affecting upper limb movements. Monitoring the progression of hemiparesis requires manual observation of limb movements at regular intervals, and hence is a labour intensive process. In this work, we use wrist-worn accelerometers for automated assessment of hemiparesis in acute stroke. We propose novel measures of similarity and asymmetry in hand activities through bivariate Poincaré analysis between two-hand accelerometer data for quantifying hemiparetic severity. The proposed descriptors characterize the distribution of activity surrogates derived from acceleration of the two hands, on a 2D bivariate Poincaré Plot. Experiments show that while the descriptors CSD1 and CSD2 can identify hemiparetic patients from control subjects, their normalized difference CSDR and the descriptors Complex Cross-Correlation Measure ( C3M) and Activity Asymmetry Index ( AAI) can distinguish between mild, moderate and severe hemiparesis. These measures are compared with traditional measures of cross-correlation and evaluated against the National Institutes of Health Stroke Scale (NIHSS), the clinical gold standard for hemiparetic severity estimation. This study, undertaken on 40 acute stroke patients with varying levels of hemiparesis and 15 healthy controls, validates the use of short length ( 5 minutes) wearable accelerometry data for identifying hemiparesis with greater clinical sensitivity. Results show that the proposed descriptors with a hierarchical classification model outperform state-of-the-art methods with overall accuracy of 0.78 and 0.85 for 4-class and 3-class hemiparesis identification respectively.

Measuring the Local and Global Variabilities in Body Sway by Nonlinear Poincaré Technology

To date, the human balance assessment is mainly achieved by measuring the center of pressure (COP) trajectory of upright posture. However, COP-based metrics provide inconclusive results under certain circumstances, due to the lack of relevance with the body balance mechanism. This paper developed a novel framework to measure the variability in body sway based on the Poincare analysis to enhance the balance assessment. It provided nonlinear parameters SD1, SD2, and their ratio SD1/SD2 as quantitative indicators of the local and global balance regulation capacities. 136 healthy adults were categorized into young and elderly groups and received test on a force platform. COP signals were recorded for 30 s under eyes-opened and eyes-closed vision conditions. The results were analyzed using the two-way mixed-design analysis of variance and show that the technology is able to reveal the effect of age and vision on the balance control by SD1, SD2, and SD1/SD2. SD1 mainly responded to vision, and SD2 was more influenced by age. Due to the information about the subtle adjustment during quiet standing, these Poincare indexes surpassed the conventional COP measurements in demonstrating the balance control behavior. It can be concluded that the supposed method of estimating the local and global variabilities is a valuable approach for the balance assessment.

Input-to-State Stability of Periodic Orbits of Systems With Impulse Effects via Poincaré Analysis

In this paper, we investigate the relation between robustness of periodic orbits exhibited by systems with impulse effects and robustness of their corresponding Poincare maps. In particular, we prove that input-to-state stability (ISS) of a periodic orbit under external excitation in both continuous and discrete time is equivalent to ISS of the corresponding zero-input fixed point of the associated forced Poincare map. This result extends the classical Poincare analysis for asymptotic stability of periodic solutions to establish orbital ISS of such solutions under external excitation. In our proof, we define the forced Poincare map, and use it to construct ISS estimates for the periodic orbit in terms of ISS estimates of this map under mild assumptions on the input signals. As a consequence of the availability of these estimates, the equivalence between exponential stability (ES) of the fixed point of the zero-input (unforced) Poincare map and the ES of the corresponding orbit is recovered. The results can be applied naturally to study the robustness of periodic orbits of continuous-time systems as well. Although our motivation for extending classical Poincare analysis to address ISS stems from the need to design robust controllers for limit-cycle walking and running robots, the results are applicable to a much broader class of systems that exhibit periodic solutions.

P4375Quantitative evaluation of heart beat interval time series via Poincare analysis reveals distinct patterns of cardiac rate dynamics during cycles of vagus nerve stimulation heart failure patients

P4375Quantitative evaluation of heart beat interval time series via Poincare analysis reveals distinct patterns of cardiac rate dynamics during cycles of vagus nerve stimulation heart failure patients

Poincare Analysis of Spontaneous Respiratory Sinus Arrhythmia during High Altitude Ascent: Effects on oxygenation

Respiratory sinus arrhythmia (RSA) is the transient fluctuation in heart rate (HR) in phase with the respiratory cycle. Poincare spectral analysis is used to (a) quantify heart rate variability (HRV) through short term (SD1; i.e., RSA) and long term (SD2) fluctuations in heart rate and (b) determine components of autonomic nervous system activity (low and high frequency; LF and HF; sympathetic and parasympathetic, respectively). Although RSA likely represents the dominance of the parasympathetic nervous system at rest, there is controversy regarding the mechanisms underlying RSA, as well as the possible physiological utility. RSA may improve ventilation and perfusion (V/Q) matching in the lungs, and may protect against oxygen desaturation in the context of hypoxic exposure. We aimed to investigate the relationship between RSA magnitude and peripheral oxygen saturation (SpO2) during incremental ascent to high altitude (4370m). We hypothesized that (a) RSA magnitude (SD1/SD2) ratio would decrease during ascent to high altitude as a result of sympathetic nervous system activation and (b) individuals with a larger SD1/SD2 ratio during ascent would have increased SpO2 through improved V/Q matching. Measurements were conducted over eleven days at 1045m (baseline, day 1), 3440m (day 7), 3860m (day 9), and 4370m (day 11) during a trek to altitude in the Nepal Himalaya. Participants (26±2.1 years; BMI 23.8±1.1 kg/m2; 9 females, n=12) were instrumented with an ECG and finger pulse oximeter (SpO2 %) and tested on rest days after one night at each altitude. Spontaneous RSA was measured from the ECG periods during the last 7‐min of a 10‐min baseline and evaluated using Poincare plots. There was no significant difference between the SD1/SD2 ratio during incremental ascent to 4370m (P=0.65). There was also no significant difference observed in the LF/HF ratios during ascent to 4370m (P=0.66), suggesting that the sympathetic/parasympathetic ratio remained unchanged with ascent. Additionally, we correlated SD1/SD2 ratio and SpO2 at 4370m when individuals were most hypoxic at rest (SpO2 87.2±0.8%) and found no significant correlation (r=0.32, P=0.31). Our data suggests that during slow incremental ascent to high altitude, there is no difference in spontaneous RSA or the balance between sympathetic and parasympathetic nervous system activity. Individuals with larger SD1/SD2 ratios do not have improved SpO2, suggesting that RSA magnitude does not improve V/Q matching during high altitude ascent.Support or Funding InformationNatural Sciences and Engineering Research Council of Canada, Student Temporary Employment Program of Alberta, Alberta Innovates Health Solutions Summer Studentship,

The Effect of Pottery Therapy on Heart Rate Variability in College Students with Mental Health Problems

Objective: Pottery therapy is an art therapy technique, with effects having been reported by questionnaire analysis and case studies. However, it is not precisely clear what physiological changes are caused by pottery therapy. The aim of this study was to investigate the effects of pottery therapy using heart rate variability analysis. Methods: Participants for this study were 11 undergraduate students at Saga University in Japan who had a mental health problem. The pottery therapy consisted of a group session of up to 5 persons once a week. Each session took place for about 90 min. Heart rate variability (HRV) was measured for 5 minutes before and after the pottery therapy. Participants were divided into two groups: a therapy group and a control group. HRV was calculated for time and frequency domains using the check my heart software. Results: In the pottery therapy group, the Poincare plot parameters SD1, SD2, S, and RMSSD were significantly increased following therapy (p<0.05). There was no significant change of LF/HF between pre-test and post-test (p=0.374). In the control group, no parameters were significantly changed during a session without pottery therapy. Conclusion: The new finding from this study is that pottery therapy is effective as demonstrated by Poincare analysis.

Three-dimensional segmented poincare plot analysis - A new approach of cardiovascular and cardiorespiratory regulation analysis.

Hypertensive pregnancy disorders affect 6 to 8 percent of all pregnancies which can cause severe complications for the mother and the fetus. The aim of this study was to develop a new method suitable for a three dimensional coupling analysis. Therefore, the three-dimensional segmented Poincaré plot analysis (SPPA3) is introduced that represents the Poincare analysis based on a cubic box model representation. The box representing the three dimensional phase space is (based on the SPPA method) subdivided into 12×12×12 equal cubelets according to the predefined range of signals and all single probabilities of occurring points in a specific cubelet related to the total number of points are calculated. From 10 healthy non-pregnant women, 66 healthy pregnant women and 56 hypertensive pregnant women suffering from chronic hypertension, gestational hypertension and preeclampsia, 30 minutes of beat-to-beat intervals (BBI), noninvasive blood pressure and respiration (RESP) were continuously recorded and analyzed. Couplings between the different signals were analyzed. The ability of SPPA3 for a screening could be confirmed by multivariate discriminant analysis differentiating between all pregnant woman and preeclampsia (index BBI3_SBP9_RESP6/ BBI8_SBP11_RESP4 leads to an area under the ROC curve of AUC=91.2%). In conclusion, SPPA3 could be a useful method for enhanced risk stratification in pregnant women.

Role of initial conditions in the dynamics of a double pendulum at low energies

We consider the low energy dynamics of the double pendulum. Low energy implies energies close to the critical value required to make the outer pendulum rotate. All the known interesting results for the double pendulum are at high energies, that is, energies higher than that required to make both pendulums rotate. We show that interesting behavior can occur at low energies as well by which we mean energies just sufficient to make the outer pendulum rotate. A harmonic balance and the Lindstedt–Poincare analysis at the low energies establish that at small, but finite amplitude; the two normal modes behave differently. While the frequency of the “in-phase” mode is almost unchanged with increasing amplitude, the frequency of the “out-of-phase” mode drops sharply. Numerical analysis verifies this analytic result and since the perturbation theory indicates a mode softening for the out-of-phase mode at a critical amplitude, we did a careful numerical analysis of the low energy region just above the threshold for onset of rotation for the outlying pendulum. We find chaotic behavior, but the chaos is a strong function of the initial condition.

Anabolic steroid treatment induces cardiac autonomic dysfunction in rats: time-course of heart rate variability

The aim of this study was to investigate time-course of cardiac autonomic activity in rats treated with nandrolonedecanoate (DECA). Twenty male Wistar rats received weekly 10 mg.Kg-1 of DECA (DG) or vehicle (CG) during 8 weeks. To heart rate variability analysis SDNN (standard deviation of RR intervals), RMSSD (square root of the mean squared differences of successive RR intervals), pNN5 (percentage of successive RR interval differences greater than 5ms) and Poincare analysis was applied in time-domain. Additionally, power spectral was decomposed into high (HF: 0.8-2.5Hz) and low-frequency (LF: 0.2-0.85Hz). For the HF component, differences were found between DG and CG during 4th, 6th and 8th weeks. Progressive increase in the LF-HF ratio was found in DG, resulting in significant differences between groups in 4th, 6th, 7th and 8th weeks. DG showed decreased from 24.5±7.2ms2 to 3.9±2.55ms2 in HF corresponding (83.9% of alteration). Power spectral density function for HF corresponded to 26.3±8.3% and 26.5±4.1% in the 1st and 8th weeks (P=NS) for CG, whereas the DG showed reduced significantly from 26.4±3.6% (1st) to 18.99±2.7% (8th week). Cardiac autonomic dysfunction may constitute an early consequence of DECA administration and an important marker of arrhythmia vulnerability and sudden death identification.

Extended Electrocardiographic Poincare Analysis (EPA) for Better Identification of Patients with Paroxysmal Atrial Fibrillation

Background: Atrial fibrillation (AF) – be it permanent or paroxysmal – is the most frequent and most effectively treatable cause of stroke. However, when paroxysmal, even electrocardiography for 24 hours (24h-ECG) misses AF in more than 50% of cases. We assessed whether extended Poincare analysis of ECG R-R intervals (EPA) can help to identify electrocardiographic remodeling suggestive of paroxysmal AF (PAF). Methods: Twenty-nine patients with previously diagnosed PAF were re-assessed by 24h-ECG using conventional analysis and EPA based on a previously trained algorithm considering among other ratios of R-R interval duration, number of premature atrial complexes, approximate entropy, and standard deviation of Poincare plots-axes. 24h-ECG from 21 healthy subjects without a history of AF served as negative, and 9 patients with permanent AF as positive controls. Results: PAF during 24h-ECG was detected in 4 out of 29 (14%) patients with a history of PAF by conventional analysis. EPA classified ECGs of these and 22 additional patients with a history of PAF, i.e. a total 90%, as suggestive of PAF. All patients with permanent AF were identified by both tools. EPA additionally classified the ECG in 4 out of 21 control subjects as suggestive of PAF. Conclusions: Extended Poincare analysis in patients with a history of PAF is more sensitive to electrocardiographic abnormalities than is conventional 24h- ECG analysis. These findings warrant prospective studies of EPA in patients with a high likelihood of PAF, i.e. with stroke of undetermined origin.

Nadi Yantra: a robust system design to capture the signals from the radial artery for assessment of the autonomic nervous system non-invasively

Ayurvedic and other alternative medical practi-tioners throughout the world have been using pulse diagnosis to detect disease and the organ at distress by feeling the palpations at three close yet precise positions of the radial artery. This paper presents a robust electro-mechanical system, ‘Nadi Yantra’ which uses piezoelectric based pressure sensors to capture the signals from the radial artery. Morphology of the waveforms obtained from our system concurs with standard physiological arterial signals. Reproducibility and stability of the system has been verified. Signal processing techniques were applied to obtain features such as amplitude, power spectral density, bandpower and spectral centroid to reflect variations in signals from the three channels. Further, wavelet based techniques were used to process the pressure signals and percussion peaks were identified. The interval between the percussion peaks was used to calculate Heart Rate Varibility (HRV), a useful tool for assessing the status of the autonomic nervous system of the human body non-invasively. Time domain indices were calculated from direct measurement of peak-peak (PP) intervals and from differences between the PP intervals. Frequency domain indices such as very low frequency (VLF) power, low frequency (LF) power, high frequency (HF) power, LF/HF ratio were also calculated. Thereafter, nonlinear Poincare analysis was carried out. A map of consecutive PP intervals was fitted to an ellipse using least squares method. Results from 7 datasets are depicted in this paper. A novel pressure pulse recording instrument is deve loped for the objective assessment of the ancient sci-ence of pulse diagnosis. The features calculated using multi resolution wavelet analysis show potential in the evaluation of the autonomic nervous system of the human body.

Reasoning by mathematical induction in children's arithmetic

Acknowledgements. Summary. Introduction. Mathematical Induction. Mathematical induction, logical deduction, and empirical induction. Poincare's analysis of mathematical induction. Frege's and Russell's analysis of mathematical induction. Critical review. Conclusion. Reasoning by Mathematical Induction: Piaget's Critique. Piaget on the analysis of Frege and Russell. Piaget on Poincare's analysis. Inhelder and Piaget's (1963) study. Conclusion. Research on the Development of Children's Reasoning. Reasoning. Deduction. Induction. Mathematical induction. Reasoning, Reasons and Responses. Critical method. Rationale for a critical method. Children's Reasoning by Mathematical Induction. Method. Results: statistical analysis of responses. Results: epistemological analysis of reasons for responses. Conservation task. Teams tasks. Recurrence task. Discussion. Hypotheses. Developmental mechanism. Educational Implications in a Constructivist Model of Education. Piaget's model of education. Educational implications in a constructivist pedagogy. Commentary by Damon Berridge. References. Boxes, figures, tables.

Holism a century ago: The elaboration of Duhem's thesis

Duhem first expounds the holistic thesis, according to which an experimental test always involves several hypotheses, in articles dating from the 1890s. Poincare's analysis of a recent experiment in optics provides the incentive, but Duhem generalizes this analysis and develops a highly original methodological position. He is led to reject inductivism. I will endeavor to show the crucial role history of science comes to play in the development of Duhem's holism.

The French Connection: Giffard's Injector and the Nature of Heat

In 1858 a Parisian inventor, Henri Giffard, patented the injector, a device to feed water into steam boilers. In 1908 Henri Poincare, in his Thermodynamique, presented an original theoretical analysis of the injector.1 That a scientist of Poincare's stature would take interest in a steam-engine apparatus that had been introduced fifty years earlier may seem surprising. However, Poincare was only one of a large number of scientists and engineers intrigued by the device. For it was observed from the very outset that the operation of the injector was paradoxical. As one engineer commented: Seldom has an invention caused so much astonishment and wild speculation among mechanics, and even among scientists, as the injector did.... It was regarded as a case of perpetual motion-the means of doing work without power, or, as the Americans expressed it, by the same means a man could raise himself by pulling on his bootstraps.2 The purpose of Poincare's analysis was to show that the paradox of the injector could be explained on the basis of the laws of thermodynamics. At the very least, an explanation of its operation required an understanding of the interconvertibility of heat and mechanical work (a corollary of the first law of thermodynamics). The foundations for the first law were established before 1850, primarily by Joule and Helmholtz. Between 1843 and 1849 Joule published the results of a series of experiments which culminated in a very precise