Wordline approach to higher spin fields

The main object of this thesis is the analysis and the quantization of spinning particle models which employ extended ”one dimensional supergravity” on the worldline, and their relation to the theory of higher spin fields (HS). In the first part of this work we have described the classical theory of massless spinning particles with an SO(N) extended supergravity multiplet on the worldline, in flat and more generally in maximally symmetric backgrounds. These (non)linear sigma models describe, upon quantization, the dynamics of particles with spin N/2. Then we have analyzed carefully the quantization of spinning particles with SO(N) extended supergravity on the worldline, for every N and in every dimension D. The physical sector of the Hilbert space reveals an interesting geometrical structure: the generalized higher spin curvature (HSC). We have shown, in particular, that these models of spinning particles describe a subclass of HS fields whose equations of motions are conformally invariant at the free level; in D = 4 this subclass describes all massless representations of the Poincar´e group. In the third part of this work we have considered the one-loop quantization of SO(N) spinning particle models by studying the corresponding partition function on the circle. After the gauge fixing of the supergravity multiplet, the partition function reduces to an integral over the corresponding moduli space which have been computed by using orthogonal polynomial techniques. Finally we have extend our canonical analysis, described previously for flat space, to maximally symmetric target spaces (i.e. (A)dS background). The quantization of these models produce (A)dS HSC as the physical states of the Hilbert space; we have used an iterative procedure and Pochhammer functions to solve the differential Bianchi identity in maximally symmetric spaces. Motivated by the correspondence between SO(N) spinning particle models and HS gauge theory, and by the notorious difficulty one finds in constructing an interacting theory for fields with spin greater than two, we have used these one dimensional supergravity models to study and extract informations on HS. In the last part of this work we have constructed spinning particle models with sp(2) R symmetry, coupled to Hyper K¨ahler and Quaternionic-K¨ahler (QK) backgrounds.

The assessment of change in rural landscape and the analysis of the driving forces. Proposal of a spatial model for the rural built environment

The presented study carried out an analysis on rural landscape changes. In particular the study focuses on the understanding of driving forces acting on the rural built environment using a statistical spatial model implemented through GIS techniques. It is well known that the study of landscape changes is essential for a conscious decision making in land planning. From a bibliography review results a general lack of studies dealing with the modeling of rural built environment and hence a theoretical modelling approach for such purpose is needed. The advancement in technology and modernity in building construction and agriculture have gradually changed the rural built environment. In addition, the phenomenon of urbanization of a determined the construction of new volumes that occurred beside abandoned or derelict rural buildings. Consequently there are two types of transformation dynamics affecting mainly the rural built environment that can be observed: the conversion of rural buildings and the increasing of building numbers. It is the specific aim of the presented study to propose a methodology for the development of a spatial model that allows the identification of driving forces that acted on the behaviours of the building allocation. In fact one of the most concerning dynamic nowadays is related to an irrational expansion of buildings sprawl across landscape. The proposed methodology is composed by some conceptual steps that cover different aspects related to the development of a spatial model: the selection of a response variable that better describe the phenomenon under study, the identification of possible driving forces, the sampling methodology concerning the collection of data, the most suitable algorithm to be adopted in relation to statistical theory and method used, the calibration process and evaluation of the model. A different combination of factors in various parts of the territory generated favourable or less favourable conditions for the building allocation and the existence of buildings represents the evidence of such optimum. Conversely the absence of buildings expresses a combination of agents which is not suitable for building allocation. Presence or absence of buildings can be adopted as indicators of such driving conditions, since they represent the expression of the action of driving forces in the land suitability sorting process. The existence of correlation between site selection and hypothetical driving forces, evaluated by means of modeling techniques, provides an evidence of which driving forces are involved in the allocation dynamic and an insight on their level of influence into the process. GIS software by means of spatial analysis tools allows to associate the concept of presence and absence with point futures generating a point process. Presence or absence of buildings at some site locations represent the expression of these driving factors interaction. In case of presences, points represent locations of real existing buildings, conversely absences represent locations were buildings are not existent and so they are generated by a stochastic mechanism. Possible driving forces are selected and the existence of a causal relationship with building allocations is assessed through a spatial model. The adoption of empirical statistical models provides a mechanism for the explanatory variable analysis and for the identification of key driving variables behind the site selection process for new building allocation. The model developed by following the methodology is applied to a case study to test the validity of the methodology. In particular the study area for the testing of the methodology is represented by the New District of Imola characterized by a prevailing agricultural production vocation and were transformation dynamic intensively occurred. The development of the model involved the identification of predictive variables (related to geomorphologic, socio-economic, structural and infrastructural systems of landscape) capable of representing the driving forces responsible for landscape changes.. The calibration of the model is carried out referring to spatial data regarding the periurban and rural area of the study area within the 1975-2005 time period by means of Generalised linear model. The resulting output from the model fit is continuous grid surface where cells assume values ranged from 0 to 1 of probability of building occurrences along the rural and periurban area of the study area. Hence the response variable assesses the changes in the rural built environment occurred in such time interval and is correlated to the selected explanatory variables by means of a generalized linear model using logistic regression. Comparing the probability map obtained from the model to the actual rural building distribution in 2005, the interpretation capability of the model can be evaluated. The proposed model can be also applied to the interpretation of trends which occurred in other study areas, and also referring to different time intervals, depending on the availability of data. The use of suitable data in terms of time, information, and spatial resolution and the costs related to data acquisition, pre-processing, and survey are among the most critical aspects of model implementation. Future in-depth studies can focus on using the proposed model to predict short/medium-range future scenarios for the rural built environment distribution in the study area. In order to predict future scenarios it is necessary to assume that the driving forces do not change and that their levels of influence within the model are not far from those assessed for the time interval used for the calibration.

Sustainable improvement of water networks : to achieve best decisions for rehabilitation plans using advanced GIS and statistical techniques

Many of developing countries are facing crisis in water management due to increasing of population, water scarcity, water contaminations and effects of world economic crisis. Water distribution systems in developing countries are facing many challenges of efficient repair and rehabilitation since the information of water network is very limited, which makes the rehabilitation assessment plans very difficult. Sufficient information with high technology in developed countries makes the assessment for rehabilitation easy. Developing countries have many difficulties to assess the water network causing system failure, deterioration of mains and bad water quality in the network due to pipe corrosion and deterioration. The limited information brought into focus the urgent need to develop economical assessment for rehabilitation of water distribution systems adapted to water utilities. Gaza Strip is subject to a first case study, suffering from severe shortage in the water supply and environmental problems and contamination of underground water resources. This research focuses on improvement of water supply network to reduce the water losses in water network based on limited database using techniques of ArcGIS and commercial water network software (WaterCAD). A new approach for rehabilitation water pipes has been presented in Gaza city case study. Integrated rehabilitation assessment model has been developed for rehabilitation water pipes including three components; hydraulic assessment model, Physical assessment model and Structural assessment model. WaterCAD model has been developed with integrated in ArcGIS to produce the hydraulic assessment model for water network. The model have been designed based on pipe condition assessment with 100 score points as a maximum points for pipe condition. As results from this model, we can indicate that 40% of water pipeline have score points less than 50 points and about 10% of total pipes length have less than 30 score points. By using this model, the rehabilitation plans for each region in Gaza city can be achieved based on available budget and condition of pipes. The second case study is Kuala Lumpur Case from semi-developed countries, which has been used to develop an approach to improve the water network under crucial conditions using, advanced statistical and GIS techniques. Kuala Lumpur (KL) has water losses about 40% and high failure rate, which make severe problem. This case can represent cases in South Asia countries. Kuala Lumpur faced big challenges to reduce the water losses in water network during last 5 years. One of these challenges is high deterioration of asbestos cement (AC) pipes. They need to replace more than 6500 km of AC pipes, which need a huge budget to be achieved. Asbestos cement is subject to deterioration due to various chemical processes that either leach out the cement material or penetrate the concrete to form products that weaken the cement matrix. This case presents an approach for geo-statistical model for modelling pipe failures in a water distribution network. Database of Syabas Company (Kuala Lumpur water company) has been used in developing the model. The statistical models have been calibrated, verified and used to predict failures for both networks and individual pipes. The mathematical formulation developed for failure frequency in Kuala Lumpur was based on different pipeline characteristics, reflecting several factors such as pipe diameter, length, pressure and failure history. Generalized linear model have been applied to predict pipe failures based on District Meter Zone (DMZ) and individual pipe levels. Based on Kuala Lumpur case study, several outputs and implications have been achieved. Correlations between spatial and temporal intervals of pipe failures also have been done using ArcGIS software. Water Pipe Assessment Model (WPAM) has been developed using the analysis of historical pipe failure in Kuala Lumpur which prioritizing the pipe rehabilitation candidates based on ranking system. Frankfurt Water Network in Germany is the third main case study. This case makes an overview for Survival analysis and neural network methods used in water network. Rehabilitation strategies of water pipes have been developed for Frankfurt water network in cooperation with Mainova (Frankfurt Water Company). This thesis also presents a methodology of technical condition assessment of plastic pipes based on simple analysis. This thesis aims to make contribution to improve the prediction of pipe failures in water networks using Geographic Information System (GIS) and Decision Support System (DSS). The output from the technical condition assessment model can be used to estimate future budget needs for rehabilitation and to define pipes with high priority for replacement based on poor condition. rn

Progression of age-related geographic atrophy: role of the fellow eye

PURPOSE. To evaluate the role of fellow eye status in determining progression of geographic atrophy (GA) in patients with age-related macular degeneration (AMD). METHODS. A total of 300 eyes with GA of 193 patients from the prospective, longitudinal, natural history FAM Study were classified into three groups according to the AMD manifestation in the fellow eye at baseline examination: (1) bilateral GA, (2) early/intermediate AMD, and (3) exudative AMD. GA areas were quantified based on fundus autofluorescence images using a semiautomated image-processing method, and progression rates (PR) were estimated using two-level, linear, mixed-effects models. RESULTS. Crude GA-PR in the bilateral GA group (mean, 1.64 mm(2)/y; 95% CI, 1.478-1.803) was significantly higher than in the fellow eye early/intermediate group (0.74 mm(2)/y, 0.146-1.342). Although there was a significant difference in baseline GA size (P = 0.0013, t-test), and there was a significant increase in GA-PR by 0.11 mm(2)/y (0.05-0.17) per 1 disc area (DA; 2.54 mm(2)), an additional mean change of -0.79 (-1.43 to -0.15) was given to the PR beside the effect of baseline GA size. However, this difference was only significant when GA size was ?1 DA at baseline with a GA-PR of 1.70 mm(2)/y (1.54-1.85) in the bilateral and 0.95 mm(2)/y (0.37-1.54) in the early/intermediate group. There was no significant difference in PR compared with that in the fellow eye exudative group. CONCLUSIONS. The results indicate that the AMD manifestation of the fellow eye at baseline serves as an indicator for disease progression in eyes with GA ? 1 DA. Predictive characteristics not only contribute to the understanding of pathophysiological mechanisms, but also are useful for the design of future interventional trials in GA patients.

Counterbalancing effects of competition for resources and facilitation against grazing in alpine snowbed communities

Alpine snowbeds are habitats where the major limiting factors for plant growth are herbivory and a small time window for growth due to late snowmelt. Despite these limitations, snowbed vegetation usually forms a dense carpet of palatable plants due to favourable abiotic conditions for plant growth within the short growing season. These environmental characteristics make snowbeds particularly interesting to study the interplay of facilitation and competition. We hypothesised an interplay between resource competition and facilitation against herbivory. Further, we investigated whether these predicted neighbour effects were species-specific and/or dependent on ontogeny, and whether the balance of positive and negative plant–plant interactions shifted along a snowmelt gradient. We determined the neighbour effects by means of neighbour removal experiments along the snowmelt gradient, and linear mixed model analyses. The results showed that the effects of neighbour removal were weak but generally consistent among species and snowmelt dates, and depended on whether biomass production or survival was considered. Higher total biomass and increased fruiting in removal plots indicated that plants competed for nutrients, water, and light, thereby supporting the hypothesis of prevailing competition for resources in snowbeds. However, the presence of neighbours reduced herbivory and thereby also facilitated survival. For plant growth the facilitative effects against herbivores in snowbeds counterbalanced competition for resources, leading to a weak negative net effect. Overall the neighbour effects were not species-specific and did not change with snowmelt date. Our finding of counterbalancing effects of competition and facilitation within a plant community is of special theoretical value for species distribution models and can explain the success of models that give primary importance to abiotic factors and tend to overlook interrelations between biotic and abiotic effects on plants.

Modeling of red blood cell life-spans in hematologically normal populations

Despite the impact of red blood cell (RBC) Life-spans in some disease areas such as diabetes or anemia of chronic kidney disease, there is no consensus on how to quantitatively best describe the process. Several models have been proposed to explain the elimination process of RBCs: random destruction process, homogeneous life-span model, or a series of 4-transit compartment model. The aim of this work was to explore the different models that have been proposed in literature, and modifications to those. The impact of choosing the right model on future outcomes prediction--in the above mentioned areas--was also investigated. Both data from indirect (clinical data) and direct life-span measurement (biotin-labeled data) methods were analyzed using non-linear mixed effects models. Analysis showed that: (1) predictions from non-steady state data will depend on the RBC model chosen; (2) the transit compartment model, which considers variation in life-span in the RBC population, better describes RBC survival data than the random destruction or homogenous life-span models; and (3) the additional incorporation of random destruction patterns, although improving the description of the RBC survival data, does not appear to provide a marked improvement when describing clinical data.

Concomitant Vascular Reconstruction During Pancreatectomy for Malignant Disease: A Propensity Score-Adjusted, Population-Based Trend Analysis Involving 10 206 Patients

OBJECTIVE To assess trends in the frequency of concomitant vascular reconstructions (VRs) from 2000 through 2009 among patients who underwent pancreatectomy, as well as to compare the short-term outcomes between patients who underwent pancreatic resection with and without VR. DESIGN Single-center series have been conducted to evaluate the short-term and long-term outcomes of VR during pancreatic resection. However, its effectiveness from a population-based perspective is still unknown. Unadjusted, multivariable, and propensity score-adjusted generalized linear models were performed. SETTING Nationwide Inpatient Sample from 2000 through 2009. PATIENTS A total of 10 206 patients were involved. MAIN OUTCOME MEASURES Incidence of VR during pancreatic resection, perioperative in-hospital complications, and length of hospital stay. RESULTS Overall, 10 206 patients were included in this analysis. Of these, 412 patients (4.0%) underwent VR, with the rate increasing from 0.7% in 2000 to 6.0% in 2009 (P < .001). Patients who underwent pancreatic resection with VR were at a higher risk for intraoperative (propensity score-adjusted odds ratio, 1.94; P = .001) and postoperative (propensity score-adjusted odds ratio, 1.36; P = .008) complications, while the mortality and median length of hospital stay were similar to those of patients without VR. Among the 25% of hospitals with the highest surgical volume, patients who underwent pancreatic surgery with VR had significantly higher rates of postoperative complications and mortality than patients without VR. CONCLUSIONS The frequency of VR during pancreatic surgery is increasing in the United States. In contrast with most single-center analyses, this population-based study demonstrated that patients who underwent VR during pancreatic surgery had higher rates of adverse postoperative outcomes than their counterparts who underwent pancreatic resection only. Prospective studies incorporating long-term outcomes are warranted to further define which patients benefit from VR.

An in vitro study on spontaneous myometrial contractility in the mare during estrus and diestrus

Uterine smooth muscle specimens were collected from euthanatized mares in estrus and diestrus. Longitudinal and circular specimens were mounted in organ baths and the signals transcribed to a Grass polygraph. After equilibration time and 2 g preload, their physiologic isometric contractility was recorded for a continuous 2.0 h. Area under the curve, frequency and time occupied by contractions were studied. Differences between cycle phases, between muscle layers, and over the recorded time periods were statistically evaluated using linear mixed-effect models. In the mare, physiologic contractility of the uterus decreased significantly over time for all variables evaluated (time as covariate on a continuous scale). For area under the curve, there was a significant effect of muscle layer (longitudinal > circular). For frequency, higher values were recorded in estrus for circular smooth muscle layer, whereas higher values were seen in longitudinal smooth muscle layers during diestrus. In longitudinal layer and in diestrus, more time was occupied by contractions than in circular layer, and in estrus. This study is describing physiologic myometrial motility in the organ bath depending on cycle phase.

Milk cortisol concentration in automatic milking systems compared with auto-tandem milking parlors

Milk cortisol concentration was determined under routine management conditions on 4 farms with an auto-tandem milking parlor and 8 farms with 1 of 2 automatic milking systems (AMS). One of the AMS was a partially forced (AMSp) system, and the other was a free cow traffic (AMSf) system. Milk samples were collected for all the cows on a given farm (20 to 54 cows) for at least 1 d. Behavioral observations were made during the milking process for a subset of 16 to 20 cows per farm. Milk cortisol concentration was evaluated by milking system, time of day, behavior during milking, daily milk yield, and somatic cell count using linear mixed-effects models. Milk cortisol did not differ between systems (AMSp: 1.15 +/- 0.07; AMSf: 1.02 +/- 0.12; auto-tandem parlor: 1.01 +/- 0.16 nmol/L). Cortisol concentrations were lower in evening than in morning milkings (1.01 +/- 0.12 vs. 1.24 +/- 0.13 nmol/L). The daily periodicity of cortisol concentration was characterized by an early morning peak and a late afternoon elevation in AMSp. A bimodal pattern was not evident in AMSf. Finally, milk cortisol decreased by a factor of 0.915 in milking parlors, by 0.998 in AMSp, and increased by a factor of 1.161 in AMSf for each unit of ln(somatic cell count/1,000). We conclude that milking cows in milking parlors or AMS does not result in relevant stress differences as measured by milk cortisol concentrations. The biological relevance of the difference regarding the daily periodicity of milk cortisol concentrations observed between the AMSp and AMSf needs further investigation.

Impact of weather and climate on the incidence of acute coronary syndromes

BACKGROUND: First investigations of the interactions between weather and the incidence of acute myocardial infarctions date back to 1938. The early observation of a higher incidence of myocardial infarctions in the cold season could be confirmed in very different geographical regions and cohorts. While the influence of seasonal variations on the incidence of myocardial infarctions has been extensively documented, the impact of individual meteorological parameters on the disease has so far not been investigated systematically. Hence the present study intended to assess the impact of the essential variables of weather and climate on the incidence of myocardial infarctions. METHODS: The daily incidence of myocardial infarctions was calculated from a national hospitalization survey. The hourly weather and climate data were provided by the database of the national weather forecast. The epidemiological and meteorological data were correlated by multivariate analysis based on a generalized linear model assuming a log-link-function and a Poisson distribution. RESULTS: High ambient pressure, high pressure gradients, and heavy wind activity were associated with an increase in the incidence of the totally 6560 hospitalizations for myocardial infarction irrespective of the geographical region. Snow- and rainfall had inconsistent effects. Temperature, Foehn, and lightning showed no statistically significant impact. CONCLUSIONS: Ambient pressure, pressure gradient, and wind activity had a statistical impact on the incidence of myocardial infarctions in Switzerland from 1990 to 1994. To establish a cause-and-effect relationship more data are needed on the interaction between the pathophysiological mechanisms of the acute coronary syndrome and weather and climate variables.

Model Checking for ROC Regression Analysis

The Receiver Operating Characteristic (ROC) curve is a prominent tool for characterizing the accuracy of continuous diagnostic test. To account for factors that might invluence the test accuracy, various ROC regression methods have been proposed. However, as in any regression analysis, when the assumed models do not fit the data well, these methods may render invalid and misleading results. To date practical model checking techniques suitable for validating existing ROC regression models are not yet available. In this paper, we develop cumulative residual based procedures to graphically and numerically assess the goodness-of-fit for some commonly used ROC regression models, and show how specific components of these models can be examined within this framework. We derive asymptotic null distributions for the residual process and discuss resampling procedures to approximate these distributions in practice. We illustrate our methods with a dataset from the Cystic Fibrosis registry.

Zidovudine impairs immunological recovery on first-line antiretroviral therapy: collaborative analysis of cohort studies in southern Africa

OBJECTIVES Zidovudine (ZDV) is recommended for first-line antiretroviral therapy (ART) in resource-limited settings. ZDV may, however, lead to anemia and impaired immunological response. We compared CD4+ cell counts over 5 years between patients starting ART with and without ZDV in southern Africa. DESIGN Cohort study. METHODS Patients aged at least 16 years who started first-line ART in South Africa, Botswana, Zambia, or Lesotho were included. We used linear mixed-effect models to compare CD4+ cell count trajectories between patients on ZDV-containing regimens and patients on other regimens, censoring follow-up at first treatment change. Impaired immunological recovery, defined as a CD4+ cell count below 100 cells/μl at 1 year, was assessed in logistic regression. Analyses were adjusted for baseline CD4+ cell count and hemoglobin level, age, sex, type of regimen, viral load monitoring, and calendar year. RESULTS A total of 72,597 patients starting ART, including 19,758 (27.2%) on ZDV, were analyzed. Patients on ZDV had higher CD4+ cell counts (150 vs.128 cells/μl) and hemoglobin level (12.0 vs. 11.0 g/dl) at baseline, and were less likely to be women than those on other regimens. Adjusted differences in CD4+ cell counts between regimens containing and not containing ZDV were -16 cells/μl [95% confidence interval (CI) -18 to -14] at 1 year and -56 cells/μl (95% CI -59 to -52) at 5 years. Impaired immunological recovery was more likely with ZDV compared to other regimens (odds ratio 1.40, 95% CI 1.22-1.61). CONCLUSION In southern Africa, ZDV is associated with inferior immunological recovery compared to other backbones. Replacing ZDV with another nucleoside reverse transcriptase inhibitor could avoid unnecessary switches to second-line ART.

Accelerometry and Energy Expenditure in Obese Adults and Normal Weight Controls

Objective: To evaluate a new triaxial accelerometer device for prediction of energy expenditure, measured as VO2/kg, in obese adults and normal-weight controls during activities of daily life. Subjects and methods: Thirty-seven obese adults (Body Mass Index (BMI) 37±5.4) and seventeen controls (BMI 23±1.8) performed eight activities for 5 to 8 minutes while wearing a triaxial accelerometer on the right thigh. Simultaneously, VO2 and VCO2 were measured using a portable metabolic system. The relationship between accelerometer counts (AC) and VO2/kg was analysed using spline regression and linear mixed-effects models. Results: For all activities, VO2/kg was significantly lower in obese participants than in normalweight controls. A linear relationship between AC and VO2/kg existed only within accelerometer values from 0 to 300 counts/min, with an increase of 3.7 (95%-confidence interval (CI) 3.4 - 4.1) and 3.9 ml/min (95%-CI 3.4 - 4.3) per increase of 100 counts/min in obese and normal-weight adults, respectively. Linear modelling of the whole range yields wide prediction intervals for VO2/kg of ± 6.3 and ±7.3 ml/min in both groups. Conclusion: In obese and normal-weight adults, the use of AC for predicting energy expenditure, defined as VO2/kg, from a broad range of physical activities, characterized by varying intensities and types of muscle work, is limited.

Impact of Baseline Renal Function on Tenofovir-containing Antiretroviral Therapy Outcomes in Zambia

Background. Although tenofovir (TDF) use has increased as part of first-line antiretroviral therapy (ART) across sub-Saharan Africa, renal outcomes among patients receiving TDF remain poorly understood. We assessed changes in renal function and mortality in patients starting TDF- or non-TDF-containing ART in Lusaka, Zambia. Methods. We included patients aged ≥16 years who started ART from 2007 onward, with documented baseline weight and serum creatinine. Renal dysfunction was categorized as mild (eGFR 60-89 mL/min), moderate (30-59 mL/min) or severe (<30 mL/min) using the CKD-EPI formula. Differences in eGFR during ART were analyzed using linear mixed-effect models, the odds of developing moderate or severe eGFR decrease with logistic regression and mortality with competing risk regression. Results. We included 62,230 adults, of which 38,716 (62%) initiated a TDF-based regimen. The proportion with moderate or severe renal dysfunction at baseline was lower in the TDF compared to the non-TDF group (1.9% vs. 4.0%). Among patients with no or mild renal dysfunction, those on TDF were more likely to develop moderate (adjusted OR: 3.11; 95%CI: 2.52-3.87) or severe eGFR decrease (adjusted OR: 2.43; 95%CI: 1.80-3.28), although the incidence of such episodes was low. Among patients with moderate or severe renal dysfunction at baseline, renal function improved independently of ART regimen and mortality was similar in both treatment groups. Conclusions. TDF use did not attenuate renal function recovery or increase mortality in patients with renal dysfunction. Further studies are needed to determine the role of routine renal function monitoring before and during ART use in Africa.

Heart rate variability in response to pain stimulus in VLBW infants followed longitudinally during NICU stay.

The objective of this longitudinal study, conducted in a neonatal intensive care unit, was to characterize the response to pain of high-risk very low birth weight infants (<1,500 g) from 23 to 38 weeks post-menstrual age (PMA) by measuring heart rate variability (HRV). Heart period data were recorded before, during, and after a heel lanced or wrist venipunctured blood draw for routine clinical evaluation. Pain response to the blood draw procedure and age-related changes of HRV in low-frequency and high-frequency bands were modeled with linear mixed-effects models. HRV in both bands decreased during pain, followed by a recovery to near-baseline levels. Venipuncture and mechanical ventilation were factors that attenuated the HRV response to pain. HRV at the baseline increased with post-menstrual age but the growth rate of high-frequency power was reduced in mechanically ventilated infants. There was some evidence that low-frequency HRV response to pain improved with advancing PMA.