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Maternal morbidities constitute a significant burden than maternal mortality in developing countries. Community-based estimates of maternal morbidity in developing countries ranges from 16.5 pregnancy-related complications to more than 100 acute complications for every maternal death.1,2 Nevertheless, as most of the community-based estimates of maternal morbidities were based only on recall by women, the validity of the estimates was questionable.3–5 We had reported one of the first prospectively measured community-based estimates of maternal morbidities in women who had delivered at home from rural Gadchiroli, India. These observations in which the incidence of maternal morbidities during labor and puerperium was 52.6% (17.7% during labor and 42.0% during puerperium) were from the first year (1995-96) of the field trial of home-based newborn care (HBNC) in Gadchiroli.6 In the third year (1997-98) of the trial, newborn mortality rate (NMR), which was the primary outcome of the trial, decreased by 62% in comparison to the control area.7 Hence the HBNC interventions were continued as a service program in the 39 villages uninterruptedly since then, further reducing the NMR and the infant mortality rate (IMR) to 25.2 and 31.1 respectively by 2001 – 03.8

To study whether these interventions also impacted maternal health, specifically adverse maternal health conditions, we analyzed the data from the Gadchiroli field trial and the subsequent service program in 39 intervention villages from 1995 – 96 to 2008 with the objective a) to evaluate the association between HBNC interventions and the incidence of maternal health conditions including the need for emergency obstetric care and b) to estimate the longitudinal trend of the incidence of maternal health conditions in 39 villages.

# Methods

## Area and population

The field trial of HBNC was conducted in the Gadchiroli district in Maharashtra state in India during 1993-98 by SEARCH (Society for Education, Action, and Research in Community Health).9 The area (figure 1), population characteristics, prevailing healthcare, the background work of SEARCH, the methods of data collection, the quality and the validation of the data, the definitions, and the incidence of maternal health condition during the first year of the intervention (1995-96) have all been extensively reported.6,7,10

Since traditional birth attendants (TBAs) used to conduct most deliveries in rural Gadchiroli at home, SEARCH had trained the TBAs in the area in 1988-89, including those in the 39 intervention villages. They were trained to distribute iron-folic acid and calcium tablets during pregnancy, provide vitamin A supplements if a woman complained of night blindness in the last trimester, and use gentian violet to treat vaginal discharge. They were also trained in handwashing; using gloves, antiseptic lotion, clean blade and thread during delivery; the importance of antenatal checkups and early referral when certain danger signs were present.11

The sources of maternal health care were the clinic of SEARCH located outside the intervention villages, run by an obstetrician (RB), the government district hospital located in the centre of the intervention area and few private doctors. The families used to call on unqualified private practitioners to inject oxytocin to expedite home deliveries.

## Interventions

In the first year of the intervention phase (1995-96) of the field trial of HBNC 39 female community health workers (CHWs) were introduced, one in each intervention village. These were married women residents of the village with 5 to 10 years of schooling. Their training and job description in the first year of the trial has been described in detail.7,9,10,12–14

After the maternal and neonatal conditions were prospectively observed and recorded in the first year of the field trial,6,12 the CHWs were trained and home-based newborn care interventions were incrementally introduced.7 In the third and final year of the trial (1997-98) and subsequently, during the service program (1998 – 2008), CHWs provided the interventions described in Panel 1. The CHWs were part-time workers of SEARCH, and their payment was based on a mix of fixed payment (1/3) and performance-based evaluation (2/3).

CHWs worked in close collaboration with the family, TBA and supervisory physician (SB), and later with the two field supervisors who were upgraded CHWs. The supervisors visited each village once every 15 days to check the findings and the quality of interventions of the CHW, but the supervisors themselves did not provide any treatment directly.

The clinic of SEARCH, located outside the intervention area, provided the facilities for an antenatal checkup; detection of risk factors; management of anemia, medical illnesses and reproductive tract infections; and, especially in the case of risk factors, advising the mothers to seek hospital delivery, usually at the government district hospital which was the only source of caesarian section delivery and blood transfusion. SEARCH as well as the government hospital provided free or subsidized ambulance service.

## Maternal knowledge and practices

We had studied maternal knowledge and practices through key informant interviews (with TBAs) and focused group discussions with mothers and grandmothers during the pre-intervention period.15 These had revealed the following harmful beliefs and behaviors: 1) A mother should not eat adequately during pregnancy or consume iron tablets, lest a large fetus would lead to a difficult delivery. 2) Pregnant women should not consume meat, milk, eggs (‘hot foods’) or certain leafy vegetables or fruits (‘papaya’ may cause abortion, guava or banana may cause ‘cough’). 3) Pregnancy and delivery are natural events, hence there is no need for medical checkups or interventions. 4) Breast feeding was often not started before the third day. This is because the colostrum was considered impure milk and hence discarded. 5) Delivery rooms were dirty and without toilet facilities. 6) A mother could not step out of the delivery room for five to seven days after delivery. 7) To minimize their toilet needs during this period, mothers reduced their food and fluid intake.

Panel 1.Interventions in Home Based Newborn Care
1. Keeping a list of women who could become pregnant and registering pregnancy in the fourth or fifth month of pregnancy.
2. Making three home visits during pregnancy to collect information about maternal health and giving appropriate advice for seeking care from a TBA or doctor. If necessary, they would accompany the woman to a medical clinic.
3. Giving health education – to individual women twice during pregnancy, by using a flip chart which gave messages about diet, care during pregnancy, antenatal checkup, iron-folic acid supplements, tetanus toxoid, night blindness, birth preparedness, danger signs during pregnancy, delivery and postpartum period and seeking medical care, safe home delivery, breastfeeding and the care of newborns.
4. Being present at home delivery, to observe the TBA conducting the delivery, to assist her and to encourage her to follow the instructions about safe and clean delivery and to record the events and timings.
5. Recommending referral when necessary and helping the family make the proper decision.
6. Providing care to the newborn immediately at birth.
7. Examining the newborn and mother on the first day within 6 hours after birth.
8. Encouraging early and exclusive breastfeeding.
9. Revisiting the baby and the mother on days 2,3,5,7,15,21,28. During these home visits she inquired about the presence of certain complaints, examined mother and newborn, gave health education to the mother using a flipchart, helped the mother in breastfeeding and in keeping the baby warm, managed newborn sicknesses and advised referral when necessary.
10. In addition to treating sicknesses in newborns and pneumonia in under-five year children, she also treated minor illnesses in children and adults.

These insights were used to design the health education messages imparted by the CHWs at home using a flip chart, twice during pregnancy and once during the newborn / postpartum period. Additionally, group health education for pregnant women and mothers-in-law was organized in the village every four months. The CHW interviewed the mothers using a questionnaire to assess their knowledge fifteen days after the group health education session. CHW also observed the mothers’ health behaviors and had recorded the same in a printed mother- newborn record during her home visits.

## Statistical analysis

The definitions used to diagnose maternal health conditions in this field setting are in Panel 2 and have also been published earlier.6

Some women used to move temporarily to their parents’ home for delivery. We included the events in the village where they actually occurred (‘de-facto method’) irrespective of where the women came from. The total number of deliveries, stillbirths (completed 28 weeks of gestation) and child deaths in the intervention and control villages were regularly recorded by an independent system of vital statistics collection using male community health workers. This system has been operational since 1988. Recording of adult deaths, including maternal deaths, was not part of the vital statistics collection system. This system had been assessed to be 98% complete.12 The proportion of mothers and deliveries observed (coverage) by female CHW and included in this study was estimated by comparing them with these vital statistics data on total deliveries in the area. Percent difference was calculated by dividing the absolute difference for that variable by percent incidence of that variable in the first year.

In table 2 (interventions), the mean percent coverage was calculated by calculating the mean of coverage of all eight indicators for each year. In Tables 3, 4 and 5, the data collection for certain conditions was started at a later period than the baseline, and the denominator was taken accordingly. Data collection on the prolonged rupture of membranes and abnormal behavior was stopped in the years 1998 – 2002, and was restarted immediately after. The abnormal presentation was recorded in home deliveries only when the CHW was present at the time of delivery.

Data of two successive years were combined to increase the robustness of the data except for the 1st year of the data collection (1995 – 96), which was considered the baseline period for this analysis. Significance was calculated on the basis of percent reduction. P value for overall change from 1995 to 2008 was calculated using Chi-square test. Analysis was done using statistical package R (version 3.6.2).

Panel 2.Definitions of maternal health condition
1. Edema: Bipedal edema observed by CHW in last trimester.
2. Vaginal discharge: Excessive and abnormal vaginal discharge as perceived by woman in last trimester.
3. Night blindness: Reported by woman using a very specific local term, “Chalanyaandhar” in last trimester.
4. Fever: History of fever in the last week before delivery in last trimester.
5. Skin infection: Boil, ulcer, pustule, abscess, pyoderma in last trimester.
6. Itching of Skin: Infected scabies, itching on body in last trimester
7. Burning of urine: History of burning of urine in last 24 hours in last trimester
8. Antepartum hemorrhage: Vaginal bleeding/spotting in last trimester
9. Prolonged rupture of membranes: more than 24 hours between loss of water and onset of labor pain [excluding caesarian cases]
10. Abnormal presentation: Presenting part during delivery being face, hand, shoulder, leg or breech (in presence of CHW).
11. Retained placenta: Placenta did not come out for more than one hour after baby’s birth [excluding caesarian cases]
12. Primary postpartum hemorrhage (PPH): Excessive bleeding on first day (as above) and an objective evidence of circulatory stress, either mother hypothermic (35.0°C) or unconscious.
13. Secondary postpartum hemorrhage: five days after delivery, mother used more than five pads a day or increased vaginal bleeding after bleeding had decreased or stopped; or any increase in use of pads (by at least 2) after it was less or none.
14. Puerperal fever: Temperature >37.8°C on any day during 2-28 days after delivery.
15. Puerperal Infection of genital tract: Foul smelling vaginal discharge and fever; or foul smelling vaginal discharge and secondary PPH.
16. Fits: Mother had convulsions during or after labor on any day within a month after delivery.
17. Abnormal behavior: Abnormal speech or behavior on any day within a month after delivery.
18. Insomnia: Inability to sleep but behavior is normal on any day within a month after delivery.
19. Breast problems: Retracted or cracked nipple (day one); or painful lumps in breast after delivery; or difficulties in breastfeeding on any day within a month after delivery.
20. Need of emergency obstetric care: Presence of any one of the following
a) Primary PPH
b) Retained placenta
c) Fits
21. Need of medical attention (non-emergency): Presence of any one of the following
a) Abnormal presentation
b) Puerperal infection
c) Abnormal behavior
d) Secondary PPH
e) Breast problems with fever

# Results

The characteristics of the mothers studied, their place of delivery, the source of obstetrical care and the change from 1995 – 96 to 2006 – 2008 are described in Table 1. A total of 10780 deliveries took place over 13 years in the 39 villages, out of which 10208 (94.7%) deliveries were observed. Similarly, a total of 10208 mothers were observed and served over 13 years. The proportion of literate mothers increased significantly by 135%, from 39.1% to 92.1%. The mean parity decreased from 1.5 to 0.7, as well as the percentage of multi-parous women (parity more than 3). The mean age of first pregnancy decreased from 23.9 years to 22.4 years. The proportion of women with past history of stillbirth or newborn death reduced significantly by 44.55%. The proportion of home deliveries decreased by 27.75%, whereas the proportion of institutional deliveries increased from 5.2% to 31.2%. The proportion of the deliveries attended by TBA reduced by 22.61%, whereas the proportion of deliveries conducted by Nurse / Doctor increased by 137.5%. The rate of caesarian section deliveries increased significantly from 0.5% at the baseline to 7.3% in 2006 – 08. The proportion of home deliveries involving visits of a local medical practitioner, usually untrained, remained almost the same. Nevertheless, as the overall proportion of home deliveries decreased significantly, the proportion of deliveries attended by local medical practitioners probably increased.

Table 1.Characteristics of Women and the Sources of Obstetrical Care in Community Based Program of Rural Gadchiroli (1995-2008, n = 10208 **)
 Characteristics 1995-96 (n=772) 1996-98 (n=1631) 1998-2006 (n=6265) 2006-08 (n=1540) Absolute change in percentage point (1995-96 vs 2006-08) P value for overall change % % % % Age years, mean(SD) 23.9 (4.60) 23.8 (4.02) 23.11 (3.40) 22.41 (2.91) <0.001 Literate women (percent) 39.1 43.2 69.9 92.1 53.02 <0.001 Parity Primiparous 30.1 30.5 39.0 46.9 16.83 <0.001 1-3 61.3 63.0 58.0 52.7 -8.61 <0.001 More than 3 8.7 6.6 3.0 0.5 -8.22 <0.001 Mean Parity (SD) 1.52 (1.48) 1.28 (1.31) 0.97 (1.1) 0.72 (0.84) <0.001 Past history of still birth or neonatal death 17.1 17.5 13.6 9.5 -7.62 <0.001 Place of delivery Home 94.8 96.2 81.9 68.5 -26.31 <0.001 Facility delivery 5.2 3.7 18.1 31.2 26.05 <0.001 On the way to hospital 0.0 0.0 0.0 0.3 0.26 0.0296 Missing 0.0 0.1 0.0 0.0 0.00 0.5948 Who conducted delivery (exclusive categories) TBA 88.2 94.3 83.6 68.2 -20.03 <0.001 Relatives 3.9 1.4 1.6 2.6 -1.29 0.0003 Nurse / doctor # 7.9 4.0 9.1 18.8 10.86 <0.001 TBA + Nurse/doc 0.0 0.0 5.1 8.4 8.44 <0.001 CHW 0.0 0.1 0.6 1.9 1.95 <0.001 Missing information 0.0 0.2 0.0 0.1 0.06 0.3547 Caesarian section delivery. 0.5 0.7 3.8 7.3 6.82 <0.001 Doctors visit at home during labor $27.3 25.1 28.4 27.1 -0.25 0.0003 All incidence are calculated for all mothers excluding twin births # Including home and hospital deliveries. Those visiting during home deliveries are usually unqualified medical practitioners$ Doctors visited home for any complication / problem during labor
** n based on all years between 1995 and 2008.

The coverage of HBNC interventions on eight selected indicators is described in Table 2. The coverage according to each of the eight indicators, as well as the mean coverage increased progressively and significantly from the first to the third year (1997 – 98) and then was maintained subsequently throughout the period of the continued service program. The increase in the coverage was the steepest during the years of trial, reaching saturation point during the service program. The antenatal medical consultation seeking increased during the second and third year of the trial and subsequently from 2002 – 04. The proportion of women visited by the CHW increased from 74.2 in 1995 – 96, reaching 89.2 by the end of the trial (1997 – 98), and peaking by 1998 – 2000, after which it remained around the same level. Health education was introduced only in the third year of trial and had continued later on.

The incidence of maternal health conditions during the last trimester of pregnancy, the change over time and the mean number of maternal health conditions per 100 mothers is shown in Table 3. There was a significant reduction in swelling on feet, excessive vaginal discharge, night blindness, fever, and burning in urine. No significant difference was observed in the incidence of skin infection, itching of the skin and ante-partum hemorrhage. Nevertheless, the incidence of these conditions was minuscule. Overall during pregnancy, the maximum percentage reduction was observed in night blindness (88.4%), followed by excessive vaginal discharge (87.34%), while the least reduction was observed in swelling over feet (32.97%). The proportion of mothers with any adverse maternal health condition during pregnancy reduced by 44.76%, while the mean number of conditions per 100 mothers reduced from 51 in 1995 – 96 to 26 in 2006 – 08, a total reduction of 49%.

The incidence of maternal health conditions during labor, the difference over time and the mean number of maternal health conditions per 100 mothers are shown in Table 4. During labor, the incidence of primary postpartum hemorrhage (the most, by 87.47%), abnormal presentation and retained placenta reduced significantly. There was no reduction in the incidence of prolonged rupture of membranes (PROM). Overall, the proportion of women with any adverse maternal health condition during labor decreased from 12.31% to 6.82%, a reduction of 44.59%. Similarly, the mean number of maternal health conditions per 100 mothers decreased from 13 to 7, a reduction of 46%.

The incidence of maternal health conditions during postpartum period, totally during pregnancy, labor and postpartum, the change over time, as well as the mean number of maternal health conditions per 100 mothers, are shown in Table 5. During puerperium, the incidence of most of the adverse maternal health conditions, namely secondary postpartum hemorrhage (PPH), puerperal fever, suspected puerperal infection, fits during puerperium, insomnia, breast problems and skin infection reduced significantly. Although the incidence of abnormal behavior did not reduce significantly, it was present in a very small proportion of women, 0.26% in 1995 – 96 and 0.06 in 2006 – 08. The maternal health conditions with the highest incidence at the baseline were breast problems (18.39%), secondary PPH (15.16%), puerperal fever (12.05%) and suspected puerperal infection (8.42%), all of which demonstrated significant reduction of 73.17%, 86.29%, 88.68% and 100% respectively. Overall, the proportion of mothers with any adverse maternal health condition during puerperium reduced by 77.82% and the mean number of conditions per 100 mothers reduced from 74 in 1995 – 96 to 11 in 2006 – 08, a total reduction of 85%.

Overall, the mean number of adverse maternal health conditions per 100 mothers during pregnancy, labor and puerperium decreased from 140 in 1995 – 96 to 44, a total reduction of 69%. The proportion of women with any adverse maternal health condition during pregnancy, labor and puerperium decreased from 67.1 to 35.39, a 42.26% reduction. Additionally, we had classified the primary PPH, retained placenta and fits as maternal health conditions requiring emergency obstetric care. The total incidence of these conditions decreased significantly by 78.83%.

After the health education was introduced in the third year of interventions, many women demonstrated correct knowledge and behaviors relevant to maternal health commensurate with the health education messages delivered. For example, when questioned, 84.4% of mothers responded that they should eat adequately during pregnancy and in the postpartum period, 78.7% responded that the family should make preparations for delivery, 84.4% said that hand washing is necessary during delivery and during baby care, and 85% told that the delivery room should be clean.

Mothers’ self-reported behavior showed that 93.9% mothers ate adequately during pregnancy, 39.1% sought antenatal/medical care during pregnancy, 11.8% consumed iron/calcium tablets during the last trimester of pregnancy and 78.9% ate adequately after delivery*. The CHW also observed that the delivery room was clean in 75.8% deliveries.

# Discussion

This analysis showed that when the trained CHWs provided home-based newborn care interventions in 39 intervention villages over 13 years, various adverse maternal health conditions during pregnancy, labor and puerperium decreased significantly. The reduction was broad, occurring in most of the conditions, including night blindness, vaginal discharge, fever, suspected puerperal infections, primary and secondary postpartum hemorrhage, breast problems, and insomnia. Moreover, the need for emergency obstetric care as well as non-emergency medical attention also decreased significantly.

Was the diagnosis of maternal health conditions valid? Due to the inherent limitations of the setting, the home deliveries and the postpartum period were not completely witnessed by a physician or accompanied by laboratory tests. The observations on the health of the mothers were recorded by the CHWs, and the quality of their data was regularly checked by a visiting physician. As reported earlier, their data showed 94.8% agreement with the parallel data collected by the physician on 18 maternal variables in a sub-sample.6 Similarly, the diagnosis was made by a computer program using certain defined criteria as described in Panel 2, and the same criteria were consistently applied over the entire thirteen years period.

Table 2.Maternal Care Interventions and their Percent Coverage during Different Years of Trial and Service Program (1995-2008, n=10208**)
 1995-96 (n=772) 1996-98 (n=1631) 1998-2006 (n=6265) 2006-08 (n=1540) Absolute change in percentage point (1995-96 vs 2006-08) P value for overall change % % % % incidence Selected indicators of the interventions A 1. Tetanus toxoid received at least once (out of three) during pregnancy. 79.0 95.5 98.7 99.5 20.5 <0.001 2. Seen by doctor during pregnancy 14.0 25.3 49.7 40.5 26.5 <0.001 3. Percent deliveries at home conducted by trained TBA 85.7 97.1 95.9 95.7 5.8 <0.001 B 4. Home visits and observation by CHW 74.2 89.2 99.2 99.5 25.5 <0.001 5. CHW present at the time of delivery at home 77.6 79.7 85.2 84.5 8.0 <0.001 C 6. Exclusive breast feeding started within 6 hours (excluding caesarian cases) 57.7 87.8 95.7 98.8 38.4 <0.001 7. CHW advised and assisted mother in newborn care at home - 89.2 99.2 99.5 10.5 <0.001 D 8. Health education at least twice by home visits. NR NR 81.7 84.8 18.7 <0.001 Mean percent coverage on the 8 indicators 48.5 70.5 86.2 87.1 38.6 <0.001

All incidence are calculated for all mothers excluding twin births
NR : Not Recorded
** n based on all years between 1995 and 2008.

Table 3.Incidence of Maternal health conditions during Pregnancy in rural Gadchiroli (1995-2008, n=10208**)
 Type of maternal health condition 1995-96 (n=772) 1996-98 (n=1631) 1998-06 (n=6265) 2006-08 (n=1540) Absolute change in percentage point (1995-96 vs 2006-08) P value for overall change % % % % Swelling on feet 23.1 20.8 18.0 15.5 -7.6 <0.001 Excessive vaginal discharge. 12.3 9.3 3.6 1.6 -10.7 <0.001 Night blindness. 8.8 7.2 3.5 1.0 -7.8 <0.001 Fever 7.0 6.1 3.0 2.6 -4.4 <0.001 Skin infection* NA NA 0.5 0.5 -0.2 0.2621 Itching of skin* NA NA 2.4 3.3 0.9 0.2405 Burning in urine# NA NA 2.1 1.2 -2.0 0.0050 Antepartum hemorrhage (APH)# NA NA 0.3 0.4 0.1 0.9319 Any condition during pregnancy 40.7 34.8 25.7 22.5 -18.2 <0.001 Mean no. of conditions per 100 mother 51 43 31 26 -25.0 <0.001

All incidence are calculated for all mothers excluding twin births
* : Starting year is 2002-03
# : Starting year is 2001-02
NR: Not Recorded
** n based on all years between 1995 and 2008.

Table 4.Incidence of Maternal health conditions during Labor in Rural Gadchiroli (1995-2008, n=10208**)
 Type of maternal health condition 1995-96 (n=772) 1996-98 (n=1631) 1998-06 (n=6265) 2006-08 (n=1540) Absolute change in percentage point (1995-96 vs 2006-08) P value for overall change % % % % Prolonged rupture of membranes 5.2 4.7 4.4 4.5 -0.7 0.9162 Prolonged labor 9.8 7.9 20.1 17.9 8.1 <0.001 Abnormal presentation $4.2 2.0 2.2 2.3 -1.9 <0.001 Retained placenta 1.8 2.1 0.6 0.9 -0.9 <0.001 Primary post-partum hemorrhage 3.1 1.4 0.8 0.4 -2.7 <0.001 Any Maternal health condition during labor 16.8 13.1 11.2 18.4 1.6 <0.001 Any Maternal health condition during labor (excluding Prolonged labor) 12.3 9.3 5.3 6.8 -5.5 <0.001 Mean no. of maternal health conditions per 100 mother 23 15 15 24 1.0 0.7695 Mean no. of maternal health conditions per 100 mother (excluding Prolonged labor) 13 10 6 7 -6.0 <0.001 All incidence are calculated for all mothers excluding twin births$: Denominator is the deliveries where CHW is present
** n based on all years between 1995 and 2008.

Table 5.Incidence of Maternal health conditions during Puerperium and Overall Period in Rural Gadchiroli (1995-2008, n=10208**)
 Type of maternal health condition 1995-96 (n=772) 1996-98 (n=1631) 1998-06 (n=6265) 2006-08 (n=1540) Absolute change in percentage point (1995-96 & 2006-08) P value for overall change % % % % During puerperium Secondary postpartum hemorrhage 15.2 9.9 2.5 2.1 -13.1 <0.001 Puerperal fever 12.0 6.2 2.2 1.4 -10.7 <0.001 Suspected Puerperal infection 8.4 3.8 0.5 0.0 -8.4 <0.001 Fits during puerperium 1.2 0.6 0.1 0.0 -1.2 <0.001 Abnormal behavior 0.3 0.4 0.3 0.1 -0.2 0.5382 Insomnia 7.4 3.1 2.6 2.3 -5.0 <0.001 Breast problems 18.4 10.7 5.9 4.9 -13.5 <0.001 PNC- Skin infection 2.2 1.1 0.8 0.5 -1.7 <0.001 Any condition during puerperium 43.9 25.3 12.1 9.7 -34.2 <0.001 Mean no. of maternal health conditions per 100 mother during puerperium 74 35 14 11 -63.0 <0.001 Overall Mean no. of maternal health conditions per 100 women during pregnancy, labor and puerperium 148 93 60 61 -87.0 <0.001 Mean no. of maternal health conditions per 100 women during pregnancy, labor and puerperium (excluding Prolonged labor) 140 89 45 44 -96.0 <0.001 Any maternal health conditions during pregnancy, labor or puerperium. 70.1 56.0 42.3 41.3 -28.8 <0.001 Any maternal health condition during pregnancy, labor or puerperium (excluding Prolonged labor) 67.1 54.9 36.4 35.4 -31.7 <0.001 Emergency maternal health conditions 14.9 11.6 11.3 17.1 2.2 <0.001 Emergency maternal health conditions (excluding Prolonged labor) 5.8 4.0 2.8 1.2 -4.6 <0.001 Non-Emergency maternal health conditions 21.6 13.7 4.5 4.0 -17.7 <0.001

All incidence are calculated for all mothers excluding twin births
** n based on all years between 1995 and 2008.

Many conditions, especially during pregnancy, or which require a physician’s presence or laboratory investigations for diagnosis such as pregnancy-induced hypertension, pre-eclampsia, urinary tract infection, glycosuria and, proteinuria were not studied. Moreover, not all women who had delivered in these 39 villages were visited by the CHWs, especially during the first two years of the program, when the percentage coverage was 74.2 and 84.6, respectively. The unstudied women may have had more health problems than in the women studied.

Can the observed reduction in maternal health conditions be attributed to the home-based newborn care? A major limitation of this evaluation was the lack of a control group. As stated above, the primary outcome of the Gadchiroli trial and the subsequent service program was not to assess the effect on maternal conditions (but newborn mortality), and hence these were not observed and recorded in the control area. In any event, in a community setting, it would have been difficult and unethical to observe and record health conditions without providing any intervention for thirteen years. The CHWs had observed and recorded maternal health conditions with minimum intervention in the first year and then with incremental home-based interventions in the second and third years of the trial as well as during the subsequent years of the service program. This allowed for the comparison of the incidence of maternal health conditions during the first and the last two years of interventions.

Another possible confounding is the change in the nature and availability of obstetrical care in the area over 13 years. There was a significant increase in institutional deliveries and caesarean section deliveries. In addition, the proportion of deliveries conducted by nurses or doctors and antenatal consultation by mothers increased significantly. Nevertheless, the maternal interventions of the HBNC itself may have significantly contributed to the change in the healthcare-seeking behavior of women leading to positive changes such as seeking antenatal medical consultation and seeking a referral for institutional delivery through better preparedness. Similarly, though there was an increase in institutional deliveries, this change mostly happened in the last 2 years, when the government launched the Janani Suraksha Yojana (JSY) and picked up.

Moreover, a very striking dose-response relationship was observed in the intervention area. The coverage of various interventions in the HBNC package progressively increased (table 2 and Fig. 2), with the mean percent score on eight indicators reaching 87.1% in 2006 – 08 (p<0.001). The health condition burden per 100 women demonstrated a matching trend of reduction of 47.26% (p<0.001) by 2006 – 08 compared to the baseline. The primary outcome of the HBNC trial and service program, the newborn mortality rate, also decreased during these thirteen years from 62 in 1993 – 95 to 25.8 (p<0.005) in 2006 – 08. Because of this strength of association and temporal relationship, it is reasonable to attribute the reduction in adverse maternal health conditions to HBNC.

Figure 2.Home-based Newborn Care package showed progressively increasing coverage

Women’s clinic and trained TBAs were in operation since 1988-89, and hence were part of the baseline scenario. Training of TBAs alone has not convincingly shown to reduce adverse maternal health conditions, but the knowledge of, and by a small degree, seeking referral for, has been found to have increased in a meta-analysis.16 An effect of larger degree is observed in our study, which can be attributed to the addition of a semi-skilled CHW to the pre-existing set-up of TBAs and the women’s clinic. It might have contributed in the following ways:

1. Changed the maternal knowledge and behaviors. Another study from India has also shown that community-based behavior change management intervention for essential newborn care can significantly improve maternal health equity and outcomes including knowledge of danger signs, care practices, self-reported complications, and timely care-seeking from trained providers.17

2. Delivery and care practices of the TBAs are expected to have improved because an independent worker (CHW) now was observing and recording (Hawthorne effect).

3. Increased care seeking from a doctor during pregnancy, from 14% in 1995-96 to 40.52% in 2006 – 08 (table 2). Even one prenatal visit late in pregnancy has been shown to confer benefits.18

4. Early initiation of excusive breastfeeding (table 2).

5. Social and emotional support to mother due to the presence of a trained woman from her own village and culture. Studies in developed as well as developing countries have shown beneficial effects of a companion.19,20

The reduction in edema and night blindness could have occurred due to the changes in diet or increased care seeking during pregnancy due to health education. Reduction in vaginal discharge, infections and fever could be because of increased hand washing and better hygiene during delivery and the postpartum period or increased antenatal care seeking resulting in the treatment of reproductive tract infections. Considering that primary PPH is a major cause of maternal mortality, significant reduction observed in it is an important gain. It may have decreased due to better delivery practices by TBAs, institutional deliveries or due to initiation of early breast feeding (Fig. 2). Reduced PPH due to increased uterine contractions induced by early suckling is also plausible, though never proved by controlled trials.21,22

Secondary PPH could have decreased due to reduced puerperal infections and increased breastfeeding. Social and emotional support as well as help in the management of newborn may have reduced the incidence of insomnia. Breast problems could have decreased due to heath education, support in breastfeeding and actively managing breastfeeding problems such as breast engorgement, cracked or inverted nipples or the inability of a premature/septic newborn to suck. Earlier studies have shown that frequent home visits by a health worker improve breastfeeding.5

A significant proportion of women in developing countries still deliver at home. Even those who deliver in hospitals are discharged within 24 to 48 hours.21 Thus, most women spend the postpartum period at home. The postpartum period remains a relatively neglected period though it contributed 61% of maternal deaths in developing countries23 and has a high incidence, 43%, of adverse maternal conditions.6 Some 23 – 50% of women perceive that they had health problems during this period,21 yet only a small proportion of women receive a postpartum home visit. The National Family Health Survey in India from 1998 – 99 had reported that only 17% of the home-delivered women received a postpartum visit by a health worker within two months of delivery.24

The WHO group on postpartum care had recommended that “since many births do take place outside the health system, caregivers at community level should be trained. Discharge from a health facility within 24 hours after birth with just one or two home visits may be hardly adequate”.21 A Cochrane review focusing on the assessment of the effectiveness of community-based intervention packages in reducing maternal and newborn morbidity and mortality and improving neonatal outcomes also concluded that in addition to the importance of skilled delivery and facility-based services for maternal and newborn care, there is evidence to consider the integration of maternal and newborn care in community settings. This can allow several interventions to be packaged effectively for delivery through community health workers and health promotion groups.25

Our study supports these recommendations and shows that such an approach was associated with reduced maternal health conditions by 44.76% during pregnancy, 44.59% during labor and 77.82% during postpartum period. Home-based postpartum care and newborn care hence can neatly fit together.

# Conclusions

It is generally believed that improving maternal care will improve newborn health as well. However, since the health and the health care of mother and baby are inseparable, it should not be surprising if this relationship operates in another way, improving newborn health care may improve maternal health. This study revealed such a phenomenon.

This is the first report of its kind, hence this cannot be considered a definitive answer. Though, as the adverse maternal health conditions decreased during pregnancy and postpartum period, this study should pave the way for more studies to confirm these findings. Even in the settings where significant mothers are delivering in institutions, as these mothers are discharged soon after the delivery, most of the postpartum /newborn period is spent at home. Hence an integrated package of home-based care for the mother and newborn is logical. Such a package can provide avenues for other health care actions such as the provision of birth planning through a continuum of care and therefore can be considered as an immediate possibility. In the specific context of India, where a large (more than 0.8 million) number of female community health workers are already functional in most of the states and providing home visits to the newborns as part of the national strategy of implementation of home-based newborn care, such possibility has concrete implications and immediate feasibility for national scaling up.

## Acknowledgements

The authors would like to thank the women, traditional birth attendants, community health workers and the village community leaders in the 39 intervention villages as well as the communities of the 47 control villages. The study would have been impossible without them.

## Ethical approval

This study analyses past data from the published trial of home-based newborn care (1995 – 98) and the subsequent service program continued by SEARCH. The services provided were completely free of cost and every beneficiary mother was explained all the interventions in vernacular language. Individual mother – newborn’s identities are not revealed. SEARCH has kindly permitted the authors to use this data for publication.

## Funding

Financial support for conducting the study was provided by The John D and Catherine T. MacArthur Foundation, Chicago, and The Ford Foundation, New Delhi. The funding sources had no involvement in the study.

## Authorship contributions

AAB analyzed the data and wrote the manuscript. ATB designed the study, trained the health workers, monitored the progress of the trial and reviewed the manuscript. RB trained the traditional birth attendants and reviewed the manuscript. MD monitored the data collection and did statistical analysis. KS did the statistical analysis. SB supervised the health workers in the field and provided field training/education. All authors have read and approved the final manuscript.

## Competing interests

The authors completed the Unified Competing Interest form at http://www.icmje.org/disclosure-of-interest/ (available upon request from the corresponding author) and declare no conflicts of interest.

## Correspondence to:

Abhay T Bang
[email protected]
Society for Education, Action and Research in Community Health (SEARCH), Shodhgram, Post-Chatgaon, Taluka-Dhanora, District-Gadchiroli, Maharashtra 442605, India


text:
## Manifolds with minimal radial curvature bounded from below and big volume.(English)Zbl 0970.53023

This paper deals with compact Riemannian manifolds $$M^n$$ with radial curvature $$\geq 1$$ (with some base point), as a general assumption. In a previous paper by the author and S. Mendonca [Indiana Univ. Math. J. 48, 249-274 (1999; Zbl 0959.53013)] it was shown that for sufficiently small $$\varepsilon>0$$ the additional assumption of a lower bound $$\pi-\varepsilon$$ for the radius implies that $$M$$ is homeomorphic to the sphere $$S^n$$ and that the Gromov-Hausdorff distance between $$M^n$$ and $$S^n$$ tends to 0 as $$\varepsilon$$ tends to 0. In the present paper the following is shown: If the Gromov-Hausdorff distance between $$M^n$$ and $$S^n$$ is smaller than $$\varepsilon$$ then the volume of $$M^n$$ converges to the volume of $$S^n$$ as $$\varepsilon$$ converges to 0. Furthermore under the additional assumption $$\text{vol}(M^n) \geq\text{vol} (S^n)-\varepsilon$$ the Gromov-Hausdorff distance between $$M^n$$ and $$S^n$$ tends to 0 as $$\varepsilon$$ tends to 0. As a corollary, under the general assumption above, a convergence in the Gromov-Hausdorff distance turns out to be equivalent to a volume convergence.

### MSC:

 53C20 Global Riemannian geometry, including pinching 53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces

### Keywords:

comparison theorem; Gromov-Hausdorff distance

Zbl 0959.53013
Full Text:

### References:

 [1] Jeff Cheeger, Critical points of distance functions and applications to geometry, Geometric topology: recent developments (Montecatini Terme, 1990) Lecture Notes in Math., vol. 1504, Springer, Berlin, 1991, pp. 1 – 38. · Zbl 0771.53015 [2] Teodora Cosma, Généralisations métriques des espaces absolus, Proceedings of 23rd Conference on Geometry and Topology (Cluj-Napoca, 1993) ”Babeş-Bolyai” Univ., Cluj-Napoca, 1994, pp. 40 – 46 (French). · Zbl 0996.54510 [3] I. Gottlieb and S. Vacaru, A. Moor’s tensorial integration in generalized Lagrange spaces, Lagrange and Finsler geometry, Fund. Theories Phys., vol. 76, Kluwer Acad. Publ., Dordrecht, 1996, pp. 209 – 216. [4] Tobias H. Colding, Ricci curvature and volume convergence, Ann. of Math. (2) 145 (1997), no. 3, 477 – 501. · Zbl 0879.53030 [5] Karsten Grove and Peter Petersen, A radius sphere theorem, Invent. Math. 112 (1993), no. 3, 577 – 583. · Zbl 0801.53029 [6] Karsten Grove and Katsuhiro Shiohama, A generalized sphere theorem, Ann. of Math. (2) 106 (1977), no. 2, 201 – 211. · Zbl 0341.53029 [7] Yoshiroh Machigashira, Manifolds with pinched radial curvature, Proc. Amer. Math. Soc. 118 (1993), no. 3, 979 – 985. · Zbl 0788.53025 [8] Yoshiroh Machigashira, Complete open manifolds of non-negative radial curvature, Pacific J. Math. 165 (1994), no. 1, 153 – 160. · Zbl 0818.53055 [9] V. Marenich, S. J. X. Mendonça, Manifolds with minimal radial curvature bounded from below and big radius, Indiana Univ. Math. J. 48 (1999). CMP 2000:04 · Zbl 0959.53013 [10] Yoshiroh Machigashira and Katsuhiro Shiohama, Riemannian manifolds with positive radial curvature, Japan. J. Math. (N.S.) 19 (1993), no. 2, 419 – 430. · Zbl 0804.53059 [11] B. N. Apanasov, Bending and stamping deformations of hyperbolic manifolds, Ann. Global Anal. Geom. 8 (1990), no. 1, 3 – 12. · Zbl 0705.53013 [12] Neculai Papaghiuc, Some results on normal semi-invariant submanifolds with semi-flat normal connection in Sasakian space forms, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 32(80) (1988), no. 3, 263 – 272. · Zbl 0657.53031 [13] Takao Yamaguchi, Collapsing and pinching under a lower curvature bound, Ann. of Math. (2) 133 (1991), no. 2, 317 – 357. · Zbl 0737.53041
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.

format: plain


text: dc.creator Wang, Fang en_US dc.creator Steimle, Timothy C. en_US dc.date.accessioned 2012-07-09T19:33:43Z dc.date.available 2012-07-09T19:33:43Z dc.date.issued 2012 en_US dc.identifier 2012-FC-11 en_US dc.identifier.uri http://hdl.handle.net/1811/52471 dc.description Author Institution: Department of Chemistry and Biochemistry; Arizona State University; Tempe, Arizona 85287-1604; U.S.A en_US dc.description.abstract Gas-phase metal-containing molecules serve as ideal venues for testing computational methodologies being developed to predict chemical properties of simple molecules. The most accurate determination of molecular properties comes from the analysis of pure rotational spectra, which for metal containing molecules can be difficult to obtain. One powerful method for recording pure rotational spectrum is to use the PPMODR technique which couples the sensitivity of optical detection with the precision of molecular beam microwave spectroscopy. Here we report on the application of PPMODR to the study of tungsten carbide, WC , and platinum carbide, PtC. The $J=1\rightarrow2$ pure rotational transitions in the $X^3\Delta_1(v=0)$ state of $^1^8^6$W$^1^2$C and $^1^8^4$W$^1^2$C reveal a small splitting, an analysis of which provides accurate determination of the rotational and $\Omega$-doubling parameters for the $X^3\Delta_1(v=0)$ state, which are critical to the proposed electron electric dipole moment experiments (eEDM) $^,$$^,$. The implications for the proposed eEDM measurements will be presented. We also report on the $J=0\rightarrow1$ and $J=1\rightarrow2$ rotational transitions of PtC for the $X^1\Sigma^+(v=0)$ state. The $^1^9^5$Pt(I=1/2) nuclear spin-rotation interaction parameter, C$_I^e^f^f$ , was determined to be 0.138(6) MHz. A comparison with other Pt-containing molecules and a proposed molecular orbital correlation diagram is given. en_US dc.language.iso en en_US dc.publisher Ohio State University en_US dc.title PUMP/PROBE MICROWAVE-OPTICAL DOUBLE RESONANCE (PPMODR) STUDY OF TUNGSTEN CARBIDE (WC) AND PLATINUM CARBIDE (PtC) en_US dc.type Article en_US dc.type Image en_US dc.type Presentation en_US


text:
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Instantly share code, notes, and snippets.

# andrewharvey/generate-map-previews.sh

Created Dec 20, 2011
HTML pages for my dev/demo site.
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I'm in my mid 20's, living in Sydney and having completed a bachelor of Science (Computer Science) degree at the University of New South Wales I am currently employed at a geospatial solution delivery company in a presales and solution delivery capacity.

I have an interest in the geospatial field, being involved in a collaborative community effort to build a free worldwide map; through the OpenStreetMap project, with a brief involvement in the fosm.org project.

I have an interest in cartography and the visualisation of geospatial data having produced a few special purpose maps.

Most of the development work I do these days resolves around front-end and back-end web development, with the odd Perl scripting and Debian based Linux sysadmin work.

I admire people who can give good presentations, so I'm always keen to give it a go myself, like I did when I gave my Sydney Georabble presentation.

I enjoy working with data (and have become quite familiar with ABS census data by building the asgs2pgsql and abs2pgsql tools).

I am supportive of free and open source software and free culture in general. I release source code for hobby projects I work on via github. I also contribute to Debian.

In my youth I wrote extensive guides to several high school subjects and licensed these under a Creative Commons license which still prove to be useful to others to date.

My current computing environment resolves around Debian, XMonad, Vim and the Dvorak keyboard layout. It took me quite a while to slowly piece together this setup and get used to the environment, but well worth the steep learning curve.

In my free time I like to explore the natural environment by bushwalking, cycling or visiting the beach. Sometimes I post photos from my explorations.

You can get in touch with me via email at andrewharvey4@gmail.com. I accept OpenGPG encrypted or signed email, but unfortunately I haven't met anyone offering to sign my key so I am not included in the web of trust.

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 #!/bin/sh # dimensions of the preview images WIDTH=400 HEIGHT=200 # the spot we use for the OSMT preview OSMT_X=151.12508 OSMT_Y=-34.04459 OSMT_Z=16 # OSMT Overlay # https://gist.github.com/andrewharvey/1290744 mapnik_render_static_map.py \ --mapfile /usr/share/stylesheets/osmt.xml \ --centrex $OSMT_X \ --centrey$OSMT_Y \ --zoom $OSMT_Z \ --width$WIDTH \ --height $HEIGHT \ --output tianjara.net/img/osmt.png # AGRI Base for OSMT # https://gist.github.com/andrewharvey/3736925 tiles2staticmap.pl \ --lat$OSMT_Y \ --lon $OSMT_X \ --zoom$OSMT_Z \ --width $WIDTH \ --height$HEIGHT \ --tileBase http://agri.openstreetmap.org/{z}/{x}/{y}.png \ --output tianjara.net/img/agri-osmt.png convert -quality 85 tianjara.net/img/agri-osmt.png tianjara.net/img/agri-osmt.jpg rm -f tianjara.net/img/agri-osmt.png
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 default : about-me.html about-me.html : about-me.html.header about-me.html.content about-me.html.footer cat $^ >$@ about-me.html.content : about-me.md markdown < $^ >$@ clean : rm -f about-me.html about-me.html.content
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text:
# How do you solve and write the following in interval notation: x>2?

Mar 9, 2017

$\left(2 , + \infty\right)$

#### Explanation:

$x > 2 \text{ is in solution form}$ and tells us that x cannot equal 2 but can take values greater than 2.

$\text{this is expressed in interval notation as } \left(2 , + \infty\right)$

The parenthesis on both ends of the interval indicates that x cannot equal $2 \text{ or } + \infty$ but any value in between them.

$\text{If the solution was "x>=2" then}$

$\left[2 , + \infty\right)$ would be the solution in interval notation.

$\text{the "[" indicates can equal the value at this end.}$


text:
#fra-introduction

#### 3.1.2.2. Other Comprehensive Income

Comprehensive income includes all items that impact owners’ equity but are not the result of transactions with shareowners. Some of these items are included in the calculation of net income, and some are included in other comprehensive income (OCI). Under IFRS, when comprehensive income is presented in two statements, the statement of comprehensive income begins with the profit or loss from the income statement and then presents the components of other comprehensive income. Although US generally accepted accounting principles (US GAAP) indicate a preference for this type of presentation when a single statement of comprehensive income is not presented, they permit companies to present the components of other comprehensive income in the statement of changes in equity.5

Exhibit 6 presents the statement of comprehensive income of the Volkswagen Group from its Annual Report 2009.

Exhibit 6. Statement of Comprehensive Income of the Volkswagen Group for the Period 1 January to 31 December
€ million2009 2008
Profit after tax911 4,688
Exchange differences on translating foreign operations:
Fair value changes recognized in other comprehensive income917 –1,445
Transferred to profit or loss57
Actuarial gains/losses–860 190
Cash flow hedges:
Fair value changes recognized in other comprehensive income683 1,054
Transferred to profit or loss–908 –1,427
Available-for-sale financial assets (marketable securities):
Fair value changes recognized in other comprehensive income200 –330
Transferred to profit or loss71 100
Deferred taxes216 145
Share of profits and losses of equity-accounted investments recognized directly in equity, after tax30 –188
Other comprehensive income406 –1,901
Total comprehensive income1,317 2,787
Of which attributable to
Shareholders of Volkswagen AG1,138 3,310
Minority interests179 –523

Exhibit 6 shows that other comprehensive income, although smaller in absolute terms than profit after tax (net income), had a significant effect on total comprehensive income. In 2009, other comprehensive income represented approximately 31 percent of total comprehensive income and was approximately 45 percent of the size of profit after tax (net income). In 2008, other comprehensive income was negative (a loss) and was approximately 41 percent of the size of profit after tax (net income) in absolute terms. The statement of comprehensive income will be discussed in greater detail in a later reading. The next section briefly describes the statement of changes in equity.

If you want to change selection, open original toplevel document below and click on "Move attachment"


text:
Symptom Distress Analysis

03/13/2021

## [1] "/private/var/folders/_c/rdymbdms14j05zp8ml7dj5lw0000gn/T/RtmpgVXlBJ/Rinst6b72fd732f2/TestGardener"

Introduction

In this vignette we run through an analysis of a typical rating scale, the Symptom Distress Scale used by the nursing profession to assess the level of distress of a hospitalized patient. The scale has a description of 13 distressing experiences, and the intensity or frequency of each is rated using the integers 0, 1, 2, 3 and 4. There are 473 respondents.

The vignette can serve as a template for the analysis of any rating scale or Likert type scale. It can also serve for tests scored using pre-assigned weights to assess the quality of the answer on something other than just “right/wrong.”

There are five distinct stages to the processing of the data: 1. Reading in the data. 2. Using the data to set up a named list object containing the information essential to their analysis. 3. The actual analysis 4. Producing desired graphs and other displays. 5. Simulating data in order to assess the accuracy of estimated quantities.

Here the data required for the analysis are entered. There are up to five objects to enter:
- a title for the analysis - the choice data - the right answer key - a character string for each item or question to display in plots - a character string for each option choice within each item The two essential objects are the choice data and the right answer key. The other three are given default values.

The choice are an N by n matrix called U in the code. The rows of U correspond to examinees and the column to items or questions. Each number in U is the index of the option or answer that the examinee has chosen using the number 1 to M where M is the number of answers available for choice. The number of choices M can vary from one item to another. We call this data structure index mode data.

The choice indices may also be stored in a dataframe where all variables are of the factor type. We have avoided this level of sophistication since the only operations on U are summing and retrieving values and, given the potential size of U, it can be worthwhile to place additional restrictions on the structure such being in integer mode.

Note! Missing or illegal values in the matrix are treated as if they are an actual option or answer, and must be assigned the index M itself. If these are present, then the actual designed answers are numbered from 1 to M-1; otherwise M for an item is a proper answer choice. TestGardener treats missing or illegal choices in exactly the same way as it treats choices of actual answers, since whether or not an proper answer was chosen is itself information about the ability or status of the examinee.

Note again: The raw data provided to a test analyzer are often in what we call score mode where the value indicates the score or value assigned to that choice. This is often the case where the data are binary right/wrong values that are scored either 1 or 0, and is also often the case for rating scales. The test analyzer will have to convert these scores to indices before submitting U to TestGardener. In the binary data 1/0 case, this conversion just involves adding 1 to all the scores. The same is the case for rating scale scores that are 0 to some larger integer.

However, the data in the Symptom Distress Scale are already in index mode. Added to the five possible responses is a sixth choice for missing or illegal responses, of which there are many for all symptoms.

Finally, our example here is only one of many possible ways to construct a matrix U, since choice data can be read in from many types of files. The easiest case is the “.csv” file that consists of comma-separated values. Here we read in data supplied as rows of values not separated at all, and we treat these rows as single strings.

The key object is not needed for rating scale type questions, and we set it to NULL.

The reader may find it helpful to consult man pages for the functions used using the command help("filename") to obtain more detail and see example code.

First we will set up a title for the data to be used in plots:

titlestr  <- "Symptom Distress"

We use the basic scan()’ command to read the 473 lines in the file like this:

U         <- scan("SDS.txt","o")
# U         <- scan(paste(getwd(),"/data/SDS.txt",sep=""),"o")
U         <- matrix(U,473,2,byrow=TRUE)
U         <- U[,2]
N         <- length(U) # Number of examinees
Umat      <- as.integer(unlist(stringr::str_split(U,"")))
n         <- length(Umat)/N # Number of items
U         <- matrix(Umat,N,n,byrow=TRUE)

We use the stringr package to break the each 13 character string into separate characters and then convert these characters to 13 integers. The result is an integer vector of length 13 times 6 with each set of 13 stacked on top of each other. The number of questions n is this length divided by the number of examinees.

However, we have also set up both U and key objects as .rda compressed files that are automatically loaded if library(TestGardener) has been entered.

There are many other ways in R to achieve the same result, of course, and this is unlikely to be viewed as the most elegant.

The right answer key is not needed, and is set to NULL here.

key <- NULL

Setting up the analysis

Now we turn to computing objects using these data that are essential to the analysis of the data.

All questions for these 24 questions in the test have four answers, but in case there are questions whether there are are missing or illegal answers for a question, we’ll use this code to add the last wastebasket option where needed.

noption <- matrix(5,n,1)
for (i in 1:n)
{
if (any(U[,i] > noption[i]))
{
noption[i]  <- noption[i] + 1 # Add one option for invalid responses
U[U[,i] >= noption[i],i] <- noption[i]
}
}

These data encode missing or illegal choices for each item as choices for the last option, which is added on to the options coding legitimate choices. We call this option the garbage option, , which is named grbg in the code. Here we indicate which option this is.

grbg <- noption

Now we turn to code that sets up objects that are essential to the analysis but that the analyst may want to set up using code rather than inputting. The first of these is a list vector of length n where each member contains a numeric vector of length M containing the designed scores assigned to each option. For multiple choice tests, that is easily done using the following code:

optScore <- list() # option scores
for (item in 1:n){
scorei <- c(0:4,0)
optScore[[item]] <- scorei
}

Note that the last option for each item is the garbage option, and we assign a designed score of zero to it.

There is also the possibility of inputting strings for each question and each option within each question. We won’t use this feature in this analysis.

Here we define labels for the 13 forms of distress

itemVec <- c("Inability to sleep", "Fatigue", "Bowel symptoms", "Breathing symptoms",
"Coughing", "Inability to concentrate", "Intensity of nausea",
"Frequency of nausea", "Intensity of pain", "Frequency of pain",
"Bad outlook on life", "Loss of appetite", "Poor appearance")

The ratings for each option, including “blank” for missing, are defined.

optVec <-c("0", "1", "2", "3", "4", " ")
optLab <- list()
for (i in 1:n)
{
optLab[[i]] = optVec
}

Next, we set up a named list called optList that contains ScoreList and the item and option strings:

optList <- list(itemLab=itemVec, optLab=optLab, optScr=optScore)

The maximum sum score possible would be 4 times 13 = 52. But in reality the highest sum score is only 37, but lots of people scored 0. We’ll set for our plotting of sum scores and expected sums the upper limit at 37.

scrrng = c(0,37)

We’re now finished with the data input and setup phase. From these objects we have a function make_dataList that completes the set up:

SDS_dataList <- TestGardener::make.dataList(U, key, optList, grbg, scrrng=scrrng)

The result is a named list with many members whose values may be required in the analysis phase. Consult the documentation using help("make.dataList.R").

One default option requires a bit of explanation. Function make.dataList() computes sum scores for each examinee, which in the multiple choice case are simply counts of the number of correct answer choices. The analysis phase does not use these sum scores directly. Instead, it uses the rank orders of the sum scores (ordered from lowest to highest) divided by N and multipled by 100, so that the scores now look like percentages, and we refer to them as “percent ranks.”

A problem is that many examinees will get the same rank value if we order these ranks directly. We cannot know whether there might be some source of bias in how these tied ranks are arranged. For example, suppose male examinees for each rank value are followed by female examinees with that rank value. We deal with this problem by default by adding a small random normally distributed number to each tied rank that is too small to upset the original rank order. This within-rank randomization is called “jittering” in the statistics community, and its tends to break up the influence of any source of bias. This is the default, but can be turned off if desired.

These jittered percent ranks are used to provide initial values for a cycled optimization procedure used by TestGardener.

Let’s make our first plot a display of the histogram and the probability density function for the sum scores.

hist(SDS_dataList$scrvec, SDS_dataList$scrrng[2], xlab="Sum Score",
main=titlestr)

We see that, on the whole, most patients do not experience great distress. A patient who rated all symptoms as 1 would be at about the 75% level, for example. The histogram indicates that the most popular score is 8, which is about half-and-half 0 and 1. The distribution is rather highly skewed in the positive direction.

From here on, the commands and text are essentially the same as those for the SweSAT math data, except for comments what we see in the figures.

The next steps are optional. The analysis can proceed without them, but the analyst may want to look at preliminary results that are associated with the the objects in the set up phase.

First we compute item response or item characteristic curves for each response within each question. These curves are historically probability curves, but we much prefer to work with a transformation of probability, “surprisal = - log(probability),” for two reasons: (1) this greatly aids the speed and accuracy of computing the curves since they are positive unbounded values, and (2) surprisal is in fact a measure of information, and as such has the same properties as other scientific measures. It’s unit is the “bit” and what is especially important is that any fixed difference between two bit values means exactly the same thing everywhere on a surprisal curve.

The initializing of the surprisal curves is achieved as follows using the important function Wbinsmth():

theta     <- SDS_dataList$percntrnk thetaQnt <- SDS_dataList$thetaQnt
WfdResult <- TestGardener::Wbinsmth(theta, SDS_dataList)
# Wbinsmth <- function(theta, dataList, WfdList=dataList$WfdList, # thetaQnt=seq(0,100, len=2*nbin+1), wtvec=matrix(1,n,1), # iterlim=20, conv=1e-4, dbglev=0) { # WfdResult <- Wbinsmth(theta, SDS_dataList) One may well want to plot these initial surprisal curves in terms of both probability and surprisal, this is achieved in this way: WfdList <- WfdResult$WfdList
meanHvec <- AnalyzeResult$meanHvec Displaying the results of the analysis cycles Plot meanHsave and choose cycle for plotting The mean fitting values in meanHvec should decrease, and then level off as we approach optimal estimations of important model objects, such as optimal percent ranks in numeric vector theta and optimal surprisal curves in list vector WfdList. Plotting these values as a function of cycle number will allow us to choose a best cycle for displaying results. cycleno <- 1:ncycle plot(cycleno,meanHvec[cycleno], type="b", lwd=2, xlab="Cycle Number") This plot shows a nice exponential-like decline in the average fitting criterion meanHvec over ten iterations. It does look like we could derive a small benefit from a few more iterations, but the changes in what we estimate using super precision in the minimization will be too small to be of any practical interest. Here we choose to display results for the last cycle: icycle <- 10 SDS_parListi <- parList[[icycle]] The list object SDS_parListi contains a large number of objects, but in our exploration of results, we will only need these results: WfdList <- SDS_parListi$WfdList
theta      <- SDS_parListi$theta Qvec <- SDS_parListi$Qvec
binctr     <- SDS_parListi$binctr arclength <- SDS_parListi$arclength
alfine     <- SDS_parListi$alfine • WfdList: List object of length n that contains information about the surprisal and probability curves • theta: A vector of length N of values of what we call “score index”, which are real numbers between 0 and 100. These values are used for computing various score values such as expected sum scores. • Qvec: Values within the range 0 to 100 below which these percentages of examinees fall: 5, 25, 50, 75 and 95. • binctr: The surprisal curves are estimated by first binning the values in vector theta and then using the surprisal values within each bin. binctr contains the values at the centres of the bins. • arclength: This is the total length of the curve traced out by the surprisal scores as theta moves from 0 to 100. alfine: An equally spaced set of values along this space curved, used for plotting purposes. Plot surprisal curves for test questions Well, here we just plot the probability and surprisal curves for just symptom eight as an illustration, namely Frequency of nausea. If argument plotindex is omitted, curves for all questions would be plotted. TestGardener::Wbinsmth.plot(binctr, Qvec, WfdList, SDS_dataList, Wrng=c(0,3), plotindex=8) Let’s make a few observations on what we see in these two plots. When probability goes up to one, surprise declines to zero, as we would expect. The probability a rating 0 is high and the surprisal is low if the respondent is in the bottom 25%, as we would expect. But, for some reason that is also the case if patient is near the 75% mark. Perhaps if the distress for other factors is that high, nausea considered of minor importance. Or, if one is that sick, nausea is relieved by a treatment. A mild distress rating of 1 appears at the 50% level. The probability of higher ratings is rare, and it seems that few patients at the upper end of the scale worry about this symptom. (We convert 6-bits into 2-bits by multiplying 3 5-bits by 2.585, the value of the logarithm to the base 2 of 6.) It is the speed of an increase or decrease in the surprisal curve that is the fundamental signal that an examinee should be boosted up and dragged down, respectively, from a given position. The sharp increase in surprise for rating 0 at the 40% level signals that an examinee in that zone should be increased. Of course the examinee’s final actual position will depend, not only on the five surprisal curves shown here, but also on those for the remaining 12 questions. We call the rate of increase or decrease the “sensitivity” of an option. We have a specific plot for display this directly below. The dots in the plot are the surprisal values for examinees in each of the 20 bins used in this analysis. The points are on the whole close their corresponding curves, suggesting that 473 examinees gives us a pretty fair idea of the shape of a surprisal or probability curve. Plot the probability density of percentile ranks The density of the percentile ranks will no longer be a flat line. This is because examinees tend to cluster at various score levels, no matter how the score is defined. Certain groups of items will tend to be correctly answered by the middle performance folks and other by only the top performers. Among the weakest examinees, there will still be a subset of questions that they can handle. We want to see these clusters emerge. ttllab <- paste(titlestr,": percent rank", sep="") scrrng <- c(0,100) theta_in <- theta[theta > 0 & theta < 100] indden10 <- TestGardener::scoreDensity(theta_in, scrrng, ttlstr=ttllab) Sure enough, there are four distinct clusters of score index values. Within each of these clusters there are strong similarities in examinee’s choice patterns, whether right or wrong. We have only plotted score indices which are away from the two boundaries, because there are significant tendencies to have estimated score index values at 0 and 100. Compute expected test scores and plot their density function for all examinees The expected score for an examinee are determined by his value theta for the question and by the score values assigned by the test designer to each option. We use a plotting interval defined by the range of the sum scores, but as a rule the density of expected scores is positive only over a shorter interval. mu <- TestGardener::testscore(theta, WfdList, optList) ttllab <- paste(titlestr,": expected score", sep="") muden <- TestGardener::scoreDensity(mu, SDS_dataList$scrrng, ttlstr=ttllab)

The expected score distribution is much more compressed than the sum score ratings, with 10 being the favourite rating. But there is a cluster of ratings at the side of the distribution of 20, which corresponds to 6 ratings of 1 and 7 ratings of 2. Being in a hospital is never great, but it’s nice to know that it is not unbearable, either. Or perhaps the nurses in Winnipeg, Manitoba where the data were collected are especially effective.

But at the top end, the best examinees lose heavily in average score terms. There are no average scores above 21, even though there are plenty of examinees with score indices of nearly or exactly 100. This effect is due to the fact that a few questions are faulty in the sense of not getting close to probability one or surprisal 0 at score index 100. We found, for example, that one question did not have any answer that could be judged correct by serious mathematical standards. And another question seemed to suffer from some teachers having overlooked covering the topic of “percent increase.”

Plot expected test scores and expected test score over mesh

indfine <- seq(0,100,len=101) mufine <- TestGardener::testscore(indfine, WfdList, optList)

TestGardener::mu.plot(mufine, SDS_dataList$scrrng, titlestr) It is typical that lower expected test scores are above the diagonal line and higher ones below. The process of computing an expected score compresses the range of scores relative to that of the observed test scores. Compute the arc length of the test effort curve and plot the curve We have 119 curves simultaneously changing location simultaneously in both probability and surprisal continua as the score index moves from 0 to 100. We can’t visual such a thing, but we are right to think of this as a point moving along a curve in these two high dimensional spaces. In principle this curve has twists and turns in it, but we show below that they are not nearly as complex as one might imagine. What we can study, and use in many ways, is the distance within the curve from its beginning to either any fixed point along it, or to its end. The curve is made especially useful because it can be shown that any smooth warping of the score index continuum will have no impact on the shape of this curve. Distance along the curve can be measured in bits, and a fixed change in bits has the same meaning at every point in the curve. The bit is a measure information, and we call this curve the test information curve. The next analysis and display displays the length of the curve and how it changes relative to the score index associated with any point on the curve. print(paste("Arc length =", round(arclength,2))) # [1] "Arc length = 28.21" TestGardener::ArcLength.plot(arclength, alfine, titlestr) The relationship is surprisingly linear with respect to the score index theta, except for some curvature near 0 and 100. We can say of the top examinees that they acquire nearly 69 2-bits of information represented in the test. That is, the probability of getting to the highest arclength is equivalent to tossing 69 heads in a row. (We convert 6-bits into 2-bits by multiplying 26.58 by 2.585]). Display test information curve projected into its first two principal components The test information curve is in principle an object of dimension Wdim, but in most cases almost all of its shape can be seen in either two dimensions or three. Here we display it in two dimensions as defined by a functional principal component analysis. Result <- TestGardener::Wpca.plot(arclength, WfdList, SDS_dataList$Wdim, titlestr=titlestr)

There is a strong change in the direction of this curve at the 50% marker point. Given what we saw in the density plots, this seems to be the point where the patient experiences distress that would no longer be called normal.

Display the sensitivity and power curves

The position of an examinee on the percentile rank continuum is directly determined by the rate of change or the derivative of the surprisal curve. An option becomes an important contributor to defining this position if it deviates strongly from zero on either side. This is just as true for wrong answers as it is for right answers. In fact, the estimated percentile rank value of an examinee is unaffected by what option is designated as correct. It is not rare that a question actually has two right answers, or even none, but such questions can still contribute to the percentile rank estimation.

TestGardener::Sensitivity.plot(WfdList, Qvec, SDS_dataList, titlestr=titlestr, plotindex=8)

The peaks and valleys in these curves are at the positions of the four clusters that we saw in the plot of the density of the score index theta.

The sensitivities of options can be collected together to provide a view of the overall strength of the contribution of a question to identifying an examinee’s percentile rank. We do this by, at each point, adding the squares of the sensitivity values and taking the square root of the result. We call this the item power curve. Here is the power curve for question 9:

Result <- TestGardener::Power.plot(WfdList, Qvec, SDS_dataList, plotindex=9, height=0.3)
# Warning: Removed 1 rows containing missing values (geom_point).

We see only a small amount of power everywhere over the score index continuum except at the highest level of distress. The power integrated over the score index is among the lowest.

Now let’s look at a question that has a great deal of power, question 8.

Result <- TestGardener::Power.plot(WfdList, Qvec, SDS_dataList, plotindex=8, height=0.3)

##Investigate the status of score index estimate by plotting H(theta) and its derivatives

An optimal fitting criterion for modelling test data should have these features: (1) at the optimum value of theta fit values at neighbouring values should be larger than the optimum; (2) the first derivative of the fitting criterion should be zero or very nearly so, and (3) the second derivative should have a positive value.

But one should not automatically assume that there is a single unique best score index value that exists for an examinee or a ratings scale respondent. It’s not at all rare that some sets of data display more than one minimum. After all, a person can know some portion of the information at an expert level but be terribly weak for other types of information. By tradition we don’t like to tell people that there are two or more right answers to the question, “How much do you know?” But the reality is otherwise, and especially when the amount of data available is modest.

If an estimated score index seems inconsistent with the sum score value or is otherwise suspicious, the function Hfuns.plot() allows us to explore the shape of the fitting function H(theta) as well as that of its second derivative.

Here we produce these plots for the first five respondents. Each illustrates something important in the shapes of these curves.

TestGardener::Hfuns.plot(theta, WfdList, U, plotindex=1:5)

# theta 1 . Press [enter] to continue

# theta 2 . Press [enter] to continue

# theta 3 . Press [enter] to continue

# theta 4 . Press [enter] to continue

# theta 5 . Press [enter] to continue
# [[1]]

#
# [[2]]

#
# [[3]]

#
# [[4]]

#
# [[5]]`

Respondent 1 (ratings: 1 0 0 0 0 0 0 0 0 0 0 0 0) is clearly virtually free of distress, having all ratings 0 except for a single rating of 1 for the first question, since curve H has a unique global minimum just next to 0.

Respondent 2 (2 2 1 0 0 1 1 1 1 1 3 0 0) is unquestionably in some distress, with a clear minimum at a score index value of about 85.

Respondent 3 (4 3 2 0 0 1 1 2 3 2 4 3 1) is, effectively, off the chart, with a minimum value very nearly at the upper boundary.

Respondent 4 (0 0 0 0 1 1 0 1 0 0 1 0 0) presents two minimum values, of which the first is exactly on the boundary value 0. The fact that the slope of the curve is still going down at 0 and the second derivative is strongly positive indicates that the best minimum location is indeed 0.

Respondent 5 (1 2 0 2 0 0 0 1 1 3 1 1 0) has two minimum locations, both at higher levels of distress. Our estimated score index value at 66.8 satisfies the criteria, but so does the even lower minimum at about 82. It can justly be argued that TestGardener underestimated the distress level in this case.


text:
• R K Swarnkar

Articles written in Bulletin of Materials Science

• Zn/ZnO core/shell nanoparticles synthesized by laser ablation in aqueous environment: Optical and structural characterizations

Zn/ZnO core/shell nanoparticles are synthesized by pulsed laser ablation (PLA) of Zn metal plate in the aqueous environment of sodium dodacyl sulfate (SDS). Solution of nanoparticles is found stable in the colloidal form for a long time, and is characterized by UV-visible absorption, transmission electron microscopy (TEM), photoluminescence (PL) and Raman spectroscopic techniques. UV-visible absorption spectrum has four peaks at 231, 275, 356, and 520 nm, which provides primary information about the synthesis of core-shell and elongated nanoparticles. TEM micrographs reveal that synthesized nanoparticles are monodispersed with three different average sizes and size distributions. Colloidal solution of nanoparticles has significant absorption in the green region, therefore, it absorbs 514.7 nm light of Ar+ laser and emits in the blue region centred at 350 and 375 nm, violet at 457 nm and green at 550 nm regions. Raman shift is observed at 300 cm-1 with PL spectrum, which corresponds to ${}^{3}$𝐸2N and 𝐸3L mode of vibrations of ZnO shell layer. Synthesis mechanism of Zn/ZnO core/shell nanoparticles is discussed.

• Effect of aging on copper nanoparticles synthesized by pulsed laser ablation in water: structural and optical characterizations

Effect of aging on copper nanoparticles synthesized by pulsed laser ablation of copper plate in water was studied. By characterization studies of the aged nanoparticles, it is found that copper nanoparticles converted into Cu@Cu2O nanostructure. The synthesized nanomaterial is characterized with UV-Visible absorption, transmission electron microscopy (TEM), X-ray diffraction (XRD), Fourier transform infrared (FTIR) and Raman and photoluminescence (PL) spectroscopic techniques. TEM image shows that the aged nanoparticles get assembled into cactus like structure and are spherical in shape with average diameter 7 nm and dispersion 2 nm. XRD and FTIR spectrum confirm the formation of Cu@Cu2O in the aged sample. Raman spectrum also confirms the presence of Cu2O nanoparticles. PL spectrum of the aged nanoparticles shows a direct allowed transition with bandgap energy of 2.24 eV. The mechanism for synthesis of core-shell nanoparticles and formation of self-assembly of nanoparticles is also discussed.

• # Bulletin of Materials Science

Current Issue
Volume 42 | Issue 6
December 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019


text:
## Rong, Yongwu

Compute Distance To:
 Author ID: rong.yongwu Published as: Rong, Yongwu
 Documents Indexed: 26 Publications since 1991 Reviewing Activity: 7 Reviews Co-Authors: 15 Co-Authors with 14 Joint Publications 283 Co-Co-Authors
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### Co-Authors

 9 single-authored 3 Helme-Guizon, Laure 2 Liang, Chunlei 2 Luse, Kerry M. 2 Yang, Jingjing 1 Chen, Li 1 Chmutov, Michael 1 Chmutov, Sergei V. 1 Evans, Christina 1 Jasso-Hernández, Edna F. 1 Kofman, Ilya 1 Lickorish, William Bernard Raymond 1 McDaniel, Michael 1 Przytycki, Józef Henryk 1 Wang, Guanyu 1 Wang, Shi Cheng 1 Yen, David W. 1 Zeng, Chen
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### Serials

 4 Topology and its Applications 3 Journal of Knot Theory and its Ramifications 2 Computers and Fluids 2 International Journal of Production Research 2 Kobe Journal of Mathematics 2 Algebraic & Geometric Topology 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Fundamenta Mathematicae 1 Indiana University Mathematics Journal 1 Journal of the London Mathematical Society. Second Series 1 Pacific Journal of Mathematics 1 Topology 1 Transactions of the American Mathematical Society 1 European Journal of Combinatorics 1 Discrete and Continuous Dynamical Systems. Series S
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### Fields

 21 Manifolds and cell complexes (57-XX) 6 Combinatorics (05-XX) 6 Algebraic topology (55-XX) 3 Operations research, mathematical programming (90-XX) 2 Numerical analysis (65-XX) 2 Computer science (68-XX) 2 Fluid mechanics (76-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

21 Publications have been cited 132 times in 91 Documents Cited by Year
A categorification for the chromatic polynomial. Zbl 1081.05034
Helme-Guizon, Laure; Rong, Yongwu
2005
Degree one maps between geometric 3-manifolds. Zbl 0758.57016
Rong, Yongwu
1992
Torsion in graph homology. Zbl 1105.57012
Helme-Guizon, Laure; Przytycki, Józef H.; Rong, Yongwu
2006
Some knots not determined by their complements. Zbl 0837.57009
Rong, Yongwu
1993
Maps between Seifert fibered spaces of infinite $$\pi_ 1$$. Zbl 0815.57002
Rong, Yongwu
1993
Degree one maps of Seifert manifolds and a note on Seifert volume. Zbl 0844.57001
Rong, Yongwu
1995
A categorification for the Tutte polynomial. Zbl 1128.57010
Jasso-Hernández, Edna F.; Rong, Yongwu
2006
The Kauffman polynomial and the two-fold cover of a link. Zbl 0718.57004
Rong, Yongwu
1991
A 2$$D$$ parallel high-order sliding and deforming spectral difference method. Zbl 1390.76664
Zhang, Bin; Liang, Chunlei; Yang, Jingjing; Rong, Yongwu
2016
Knight move in chromatic cohomology. Zbl 1139.57009
Chmutov, Michael; Chmutov, Sergei; Rong, Yongwu
2008
Link polynomials of higher order. Zbl 0903.57002
Rong, Yongwu
1997
Digital topological method for computing genus and the Betti numbers. Zbl 1214.68425
Chen, Li; Rong, Yongwu
2010
The preimages of submanifolds. Zbl 0777.57010
Rong, Yongwu; Wang, Shicheng
1992
Khovanov type homologies for graphs. Zbl 1286.05072
Helme-Guizon, Laure; Rong, Yongwu
2012
Examples of knots with the same polynomials. Zbl 1100.57009
Luse, Kerry; Rong, Yongwu
2006
Mutation and Witten invariants. Zbl 0823.57011
Rong, Yongwu
1994
A high-order flux reconstruction method with adaptive mesh refinement and artificial diffusivity on unstructured moving/deforming mesh for shock capturing. Zbl 1390.76662
Yang, Jingjing; Zhang, Bin; Liang, Chunlei; Rong, Yongwu
2016
Graph-based set-up planning and tolerance decomposition for computer-aided fixture design. Zbl 1060.68650
Zhang, Y.; Hu, W.; Rong, Y.; Yen, David W.
2001
Approximating Jones coefficients and other link invariants by Vassiliev invariants. Zbl 0998.57033
Kofman, Ilya; Rong, Yongwu
2000
A categorification for the Penrose polynomial. Zbl 1213.57019
Luse, Kerry; Rong, Yongwu
2011
On derivatives of link polynomials. Zbl 0927.57008
Lickorish, W. B. R.; Rong, Y.
1998
A 2$$D$$ parallel high-order sliding and deforming spectral difference method. Zbl 1390.76664
Zhang, Bin; Liang, Chunlei; Yang, Jingjing; Rong, Yongwu
2016
A high-order flux reconstruction method with adaptive mesh refinement and artificial diffusivity on unstructured moving/deforming mesh for shock capturing. Zbl 1390.76662
Yang, Jingjing; Zhang, Bin; Liang, Chunlei; Rong, Yongwu
2016
Khovanov type homologies for graphs. Zbl 1286.05072
Helme-Guizon, Laure; Rong, Yongwu
2012
A categorification for the Penrose polynomial. Zbl 1213.57019
Luse, Kerry; Rong, Yongwu
2011
Digital topological method for computing genus and the Betti numbers. Zbl 1214.68425
Chen, Li; Rong, Yongwu
2010
Knight move in chromatic cohomology. Zbl 1139.57009
Chmutov, Michael; Chmutov, Sergei; Rong, Yongwu
2008
Torsion in graph homology. Zbl 1105.57012
Helme-Guizon, Laure; Przytycki, Józef H.; Rong, Yongwu
2006
A categorification for the Tutte polynomial. Zbl 1128.57010
Jasso-Hernández, Edna F.; Rong, Yongwu
2006
Examples of knots with the same polynomials. Zbl 1100.57009
Luse, Kerry; Rong, Yongwu
2006
A categorification for the chromatic polynomial. Zbl 1081.05034
Helme-Guizon, Laure; Rong, Yongwu
2005
Graph-based set-up planning and tolerance decomposition for computer-aided fixture design. Zbl 1060.68650
Zhang, Y.; Hu, W.; Rong, Y.; Yen, David W.
2001
Approximating Jones coefficients and other link invariants by Vassiliev invariants. Zbl 0998.57033
Kofman, Ilya; Rong, Yongwu
2000
On derivatives of link polynomials. Zbl 0927.57008
Lickorish, W. B. R.; Rong, Y.
1998
Link polynomials of higher order. Zbl 0903.57002
Rong, Yongwu
1997
Degree one maps of Seifert manifolds and a note on Seifert volume. Zbl 0844.57001
Rong, Yongwu
1995
Mutation and Witten invariants. Zbl 0823.57011
Rong, Yongwu
1994
Some knots not determined by their complements. Zbl 0837.57009
Rong, Yongwu
1993
Maps between Seifert fibered spaces of infinite $$\pi_ 1$$. Zbl 0815.57002
Rong, Yongwu
1993
Degree one maps between geometric 3-manifolds. Zbl 0758.57016
Rong, Yongwu
1992
The preimages of submanifolds. Zbl 0777.57010
Rong, Yongwu; Wang, Shicheng
1992
The Kauffman polynomial and the two-fold cover of a link. Zbl 0718.57004
Rong, Yongwu
1991
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### Cited by 113 Authors

 8 Rong, Yongwu 6 Sazdanović, Radmila 6 Wang, Shi Cheng 4 Kanenobu, Taizo 3 Derbez, Pierre 3 Helme-Guizon, Laure 3 Ichihara, Kazuhiro 3 Ito, Tetsuya 3 Liang, Chunlei 3 Przytycki, Józef Henryk 3 Soma, Teruhiko 3 Stošić, Marko 2 Boileau, Michel Charles 2 Chandler, Alex 2 İs, Melih 2 Karaca, Ismet 2 Kegel, Marc 2 Kofman, Ilya 2 Lidman, Tye 2 Lowrance, Adam M. 2 Miyazawa, Yasuyuki 2 Saito, Toshio 1 Abe, Tetsuya 1 Audoux, Benjamin 1 Baker, Kenneth L. 1 Baranovsky, Vladimir 1 Beck, Andrea D. 1 Borrell, Guillem 1 Buck, Dorothy 1 Buckingham, Paul Richard 1 Bychkov, Boris Sergeevich 1 Cha, Jae Choon 1 Champanerkar, Abhijit 1 Chen, Haimiao 1 Chen, Kuangxu 1 Chen, Wenqian 1 Cheng, Zhiyun 1 Chmutov, Michael 1 Chmutov, Sergei V. 1 Cooper, Benjamin 1 Dancso, Zsuzsanna 1 Deruelle, Arnaud 1 Ding, Chi 1 Dürrwächter, Jakob 1 Evako, Alexander V. 1 Everitt, Brent 1 Goodall, Andrew J. 1 Hayat-Legrand, Claude 1 Hillman, Jonathan Arthur 1 Hogancamp, Matthew 1 Hom, Jennifer 1 Huang, Hong 1 Jasso-Hernández, Edna F. 1 Jeong, Myeong-Ju 1 Jin, Xian’an 1 Jong, In Dae 1 Ju, Yaping 1 Karakurt, Çağrı 1 Kazakov, Alexander Andreevich 1 Kempf, Daniel 1 Kirk, Paul A. 1 Kopper, Patrick 1 Krushkal, Vyacheslav S. 1 Kurz, Marius 1 Lei, Ziyi 1 Li, Youlin 1 Licata, Anthony M. 1 Lickorish, William Bernard Raymond 1 Litjens, Bart 1 Livingston, Charles 1 Loebl, Martin 1 Lozano-Durán, Adrián 1 Luse, Kerry M. 1 Malek Jafarian, Seyyed Majid 1 Masai, Hidetoshi 1 Matignon, Daniel 1 Miyazaki, Katura 1 Moffatt, Iain 1 Mollaei, Mehdi 1 Moriuchi, Hiromasa 1 Motegi, Kimihiko 1 Munz, Claus-Dieter 1 Neofytidis, Christoforos 1 Ni, Yi 1 Pabiniak, Milena D. 1 Paoluzzi, Luisa 1 Park, Chan-Young 1 Porti, Joan 1 Ravelomanana, Huygens C. 1 Regts, Guus 1 Reid, Alan W. 1 Sabourau, Stéphane 1 Scofield, Daniel 1 Summers, Victor 1 Sun, Hongbin 1 Tagami, Keiji 1 Talalaev, Dmitry V. 1 Tao, Zhixiong 1 Vafaee, Faramarz 1 Vena, Lluís ...and 13 more Authors
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### Cited in 42 Serials

 17 Journal of Knot Theory and its Ramifications 10 Topology and its Applications 9 Algebraic & Geometric Topology 4 Proceedings of the American Mathematical Society 3 Computers and Fluids 3 Geometriae Dedicata 3 Transactions of the American Mathematical Society 2 Discrete Applied Mathematics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Advances in Mathematics 2 Fundamenta Mathematicae 2 Journal of Algebra 2 Osaka Journal of Mathematics 2 Communications in Contemporary Mathematics 1 Journal of Computational Physics 1 Theoretical and Mathematical Physics 1 ACM Transactions on Mathematical Software 1 Annales de l’Institut Fourier 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Journal of Combinatorial Theory. Series A 1 Kodai Mathematical Journal 1 Mathematische Annalen 1 Memoirs of the American Mathematical Society 1 Tokyo Journal of Mathematics 1 European Journal of Combinatorics 1 Bulletin of the Korean Mathematical Society 1 Graphs and Combinatorics 1 The Electronic Journal of Combinatorics 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 International Journal of Computational Fluid Dynamics 1 Geometry & Topology 1 Acta Mathematica Sinica. English Series 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of the Australian Mathematical Society 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Journal of Algebra and its Applications 1 Journal of Homotopy and Related Structures 1 Journal of Topology and Analysis 1 Quantum Topology 1 Applied General Topology 1 Journal of Linear and Topological Algebra
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### Cited in 19 Fields

 75 Manifolds and cell complexes (57-XX) 18 Combinatorics (05-XX) 14 Algebraic topology (55-XX) 7 Fluid mechanics (76-XX) 5 Differential geometry (53-XX) 5 Numerical analysis (65-XX) 4 Group theory and generalizations (20-XX) 3 Computer science (68-XX) 2 Associative rings and algebras (16-XX) 2 Partial differential equations (35-XX) 2 Geometry (51-XX) 2 Biology and other natural sciences (92-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Category theory; homological algebra (18-XX) 1 Topological groups, Lie groups (22-XX) 1 Convex and discrete geometry (52-XX) 1 Statistics (62-XX)