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IMR Press / CEOG / Volume 49 / Issue 10 / DOI: 10.31083/j.ceog4910219
Open Access Original Research
Optimal Cutoff Value of 1-Hour Postload Glucose to Identify Insulin Resistance in Women with Polycystic Ovary Syndrome
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1 Department of Obstetrics and Gynecology, Inje University College of Medicine, Haeundae Paik Hospital, 48108 Busan, Republic of Korea
2 Department of Internal Medicine, Gachon University College of Medicine, 21565 Incheon, Republic of Korea
*Correspondence: wooki1974@empal.com (Sungwook Chun)
These authors contributed equally.
Clin. Exp. Obstet. Gynecol. 2022, 49(10), 219; https://doi.org/10.31083/j.ceog4910219
Submitted: 20 June 2022 | Revised: 15 July 2022 | Accepted: 3 August 2022 | Published: 21 September 2022
This is an open access article under the CC BY 4.0 license.
Abstract

Background: Despite the active researches recently conducted into the relationship between 1-h postload glucose (1-h PG) during standard oral glucose tolerance test and future risk of type 2 diabetes, research regarding the clinical capacity of 1-h PG to assess insulin resistance in those with polycystic ovary syndrome (PCOS) is still insufficient. The purpose of this study was to investigate the optimal 1-h PG cutoff value to identify insulin resistance in women with PCOS. Methods: One hundred fifty-three women aged 18 to 35 years who were diagnosed with PCOS were enrolled in this study. Insulin resistance was defined as having abnormal insulin sensitivity or hyperglycemia. Spearman’s rank correlation coefficient and receiver operating characteristic (ROC) curve analyses were conducted to assess the relationship between 1-h PG and other parameters and to determine the optimal 1-h PG cutoff for identifying insulin resistance, respectively. Results: Significant correlations were observed between 1-h PG, 2-h PG and fasting glucose, and other fasting-state insulin sensitivity assessment indices, other than fasting insulin level. The optimal 1-h PG threshold value for identifying insulin resistance was 138.5 mg/dL. Categorization of patients based on the 1-h PG threshold showed significant differences for all laboratory variables related to insulin sensitivity/resistance, other than fasting insulin. Conclusions: Our results suggest that a 1-h PG value of $\geq$ 138.5 mg/dL may be a promising assessment index for identifying insulin resistance in women with PCOS.

Keywords
oral glucose tolerance test
insulin resistance
polycystic ovary syndrome
insulin sensitivity
1. Introduction

Polycystic ovary syndrome (PCOS) is the most common endocrine disorder in women of reproductive age [1, 2]. Insulin resistance and the resulting hyperinsulinemia play a crucial role in the pathogenesis of reproductive disorders such as PCOS [1, 2, 3, 4]. Indeed, PCOS is a leading risk factor for prediabetes and type 2 diabetes mellitus (T2DM) in reproductive-aged women [5]; moreover, up to 35% of women with PCOS exhibit impaired glucose tolerance (IGT) and up to 10% meet the criteria for T2DM. Approximately 80% of women with PCOS and 95% of obese women with PCOS have insulin resistance [6]. Therefore, some authors suggest referring to PCOS as “syndrome XX”, just as metabolic syndrome is alternatively termed “syndrome X” [5].

Insulin sensitivity reflects the opposite effect of insulin resistance [7]. However, there remains no universal testing modality for insulin resistance, and this lack of standardization makes the diagnosis of insulin resistance difficult [7]. While the hyperinsulinemic-euglycemic clamp is the gold standard method for assessing insulin sensitivity/resistance, it is difficult to apply in real-world clinical situations owing to its cost and various technical difficulties [7]. Fasting insulin concentration, homeostatic model assessment of insulin resistance (HOMA-IR), quantitative insulin sensitivity check index (QUICKI), and glucose-to-insulin ratio (GIR) are uncomplicated and inexpensive quantitative fasting-state (homeostatic) methods used to evaluate insulin sensitivity; therefore, these insulin sensitivity assessment indices (ISAIs) are currently the most common measures for evaluating insulin sensitivity and resistance [7].

The oral glucose tolerance test (OGTT) is another standard method used to evaluate insulin sensitivity/resistance because it assesses hyperinsulinemia and glucose tolerance. Hyperglycemia, which consists of prediabetes (increased risk of diabetes) and diabetes, can be assessed by measuring fasting glucose levels and postprandial or postload glucose levels after a glucose challenge [8]. A standard 2-h 75-g OGTT, rather than the measurement of fasting blood glucose levels alone, is recommended to screen for IGT and T2DM in women with PCOS [9, 10].

While postprandial glucose concentrations peak 60 min after a meal in the normal population, they generally do not peak until approximately 2 hours after a meal in patients with diabetes [11]. Thus, the measurement of glucose levels 2 hours after the start of a meal is practical in general [8] and 1-h postload glucose (1-h PG) level during OGTT has been overlooked thus far compared to fasting and 2-h postload glucose (2-h PG) levels, except in specific clinical conditions such as gestational diabetes [12]. Recently, however, some authors have suggested that 1-h PG can identify insulin resistance in the presence of normal glucose tolerance and is superior to fasting and 2-h PG levels as a predictor of T2DM and its associated complications [13, 14, 15, 16, 17, 18, 19, 20].

Despite active researches on the relationship between 1-h PG and future T2DM risk, research on the clinical capacity of 1-h PG to assess insulin resistance in patients with PCOS remains insufficient. The present study investigated the relationship between 1-h PG during the standard 75-g OGTT and a variety of parameters related to insulin sensitivity/resistance, including fasting glucose, 2-h PG, and other fasting ISAIs, and further identified the optimal threshold value of 1-h PG to predict insulin resistance (determined by ISAIs) in women with PCOS.

2. Materials and Methods
2.1 Subjects

This retrospective study recruited Korean women aged 18–35 years who first visited Inje University Haeundae Paik Hospital between January 2010 and December 2013 and were diagnosed with PCOS according to the Rotterdam diagnostic criteria [2]. Among these patients, this study enrolled only those who met the recently revised diagnostic criteria in the international consensus guidelines for PCOS [21]. The exclusion criteria were [22, 23]: patients previously diagnosed with diabetes, thyroid disease or hyperprolactinemia, had undergone ovarian surgery, or taking medications known to affect the level of any sex hormone or gonadotropin in the previous 6 months of enrollment (oral contraceptives, ovulation induction agents, glucocorticoids, or anti-androgens), or anti-diabetic drugs, including insulin sensitizers. This study was approved by the Institutional Review Board (IRB) of Inje University Haeundae Paik Hospital, which waived the requirement for written consent for subjects in the present study.

2.2 Measurement of Anthropometric Parameters and Ultrasound Examinations

Clinical anthropometric parameters were evaluated in all patients when they first visited the outpatient department. Pelvic ultrasound examinations (vaginal or rectal) were conducted in the early follicular phase using a Voluson LOGIQ S7 (GE Ultrasound Korea, Ltd., Seongnam, Korea) equipped with a microconvex intracavitary probe with a frequency range of 3.6–9.0 MHz. All ultrasound examinations were conducted by the same reproductive endocrinologist based on the international consensus on ultrasound assessment of PCOS [24].

2.3 Biochemical Measurements and Determination of Hyperglycemia

Blood samples were collected from all study participants following an overnight fast according to the guidelines of the Declaration of Helsinki. The sera were separated by centrifugation and used to evaluate glucose and insulin levels. Glucose levels during fasting and 60 and 120 min after glucose ingestion during the 2-h OGTT were measured using L-Type GluI (Wako Pure Chemical Industries, Ltd., Osaka, Japan). Fasting insulin levels were evaluated using an Elecsys insulin assay (Roche Diagnostics Corp.). Both the intra- and inter-assay coefficients of variation for all tests were $<$ 5%. In the present study, hyperglycemia, comprising prediabetes (high fasting glucose or IGT) and diabetes, were diagnosed based on American Diabetes Association (ADA) [8] as fasting glucose $\geq$ 100 mg/dL or 2-h PG $\geq$ 140 mg/dL.

2.4 Assessment of Insulin Sensitivity and Determination of Insulin Resistance

We assessed insulin sensitivity in patients with PCOS using four established fasting ISAIs: fasting insulin and three other indices derived from a combination of fasting insulin and glucose levels, as follows [22, 23]: HOMA-IR was calculated as glucose value (mg/dL) $\times{}$ insulin value ( $\mu$ U/mL)/405; GIR was calculated by dividing the glucose value (mg/dL) by the insulin value ( $\mu$ U/mL); and QUICKI was calculated as 1/{log[insulin value ( $\mu$ U/mL)] + log[glucose value (mg/dL)]}.

Patients with PCOS showing abnormal levels for at least one of the established ISAI criteria in previous studies of Asian women were defined as having abnormal insulin sensitivity: fasting insulin $\geq$ 15 $\mu$ IU/mL [25], HOMA-IR $\geq$ 2.64 [26], GIR $\leq$ 10.7, or QUICKI $\leq$ 0.34 [27].

In the present study, insulin resistance was determined as the presence of abnormal insulin sensitivity or hyperglycemia.

2.5 Statistical Analyses

Values are expressed as means $\pm$ standard deviation (SD). Correlation analysis was conducted to assess the relationships between 1-h PG and other parameters using Spearman’s rank correlation coefficients and linear regression analysis, with partial correlations used to control for the effects of other covariates. Data from all study participants were used to identify the optimal 1-h PG cutoff value for identifying insulin resistance based on receiver operating characteristic (ROC) curve analysis. The confidence intervals (CIs) for the areas under the ROC curves with sensitivity and specificity were also evaluated. The optimal cutoff value of 1-h PG for identifying insulin resistance was defined as the threshold value at which the value of sensitivity plus specificity reached a maximum. ROC curve analysis was performed for insulin resistance as defined by the criteria applied in this study (described above). Unpaired t-tests were used to compare continuous parameters between the two groups, which were defined by the cutoff value for 1-h PG. All statistical analyses were conducted using IBM SPSS Statistics for Windows, version 25.0 (IBM Corp., Armonk, NY, USA), with p $<$ 0.05 considered statistically significant.

3. Results

This study included 153 patients. Table 1 shows the baseline anthropometric characteristics and laboratory parameters of the study participants.

Table 1.Baseline clinical characteristics of the study participants.
 Characteristic Participants (n = 153) Age (years) 26.39 $\pm$ 5.18 Height (cm) 162.04 $\pm$ 5.32 Body weight (kg) 58.46 $\pm$ 14.44 Body mass index 22.23 $\pm$ 5.23 Waist to hip ratio 0.80 $\pm$ 0.07 Fasting glucose (mg/dL) 91.76 $\pm$ 13.42 Fasting insulin ( $\mu$ IU/mL) 9.24 $\pm$ 8.67 Values are mean $\pm$ standard deviation.

To evaluate the ability of the 1-h PG test to identify patients with insulin resistance, we first performed a correlation analysis between 1-h PG levels and established ISAIs (Table 2). The 1-h PG level during the 75-g OGTT was significantly related to fasting glucose (r = 0.302, p $<$ 0.001) and 2-h PG (r = 0.637, p $<$ 0.001) level (Fig. 1A).

Table 2.Correlations between 1-h postload glucose levels and other parameters related to glucose and insulin metabolism.
 r p r ${}^{a}$ p Fasting glucose (mg/dL) 0.302 $<$ 0.001 0.637 $<$ 0.001 2-h PG (mg/dL) 0.637 $<$ 0.001 0.786 $<$ 0.001 Fasting insulin ( $\mu$ IU/mL) 0.107 0.189 0.152 0.080 HOMA-IR (fasting) 0.271 0.001 0.468 $<$ 0.001 GIR (fasting) –0.210 0.009 –0.231 0.007 QUICKI (fasting) –0.269 0.001 –0.354 $<$ 0.001 r, Spearman’s rank correlation coefficient; and r ${}^{a}$ , partial correlation coefficient adjusted by age, body mass index and waist to hip ratio. 2-h PG, 2-hour postload glucose; GIR, glucose-to-insulin ratio; HOMA-IR, homeostasis model assessment of insulin resistance; QUICKI, quantitative insulin sensitivity check index.
Fig. 1.

Correlations of 1-h postload glucose concentration and other parameters related to glucose and insulin metabolism in women with polycystic ovary syndrome. (A) 2-h postload glucose level. (B) Homeostasis model assessment of insulin resistance.

Significant correlations were observed between the 1-h PG and other ISAIs, despite the 1-h PG level was not significantly correlated with fasting insulin level (r = 0.107, p = 0.189). Fig. 1B shows the significant relationship between 1-h PG and HOMA-IR (r = 0.271, p = 0.001). These results did not change even after controlling for the effects of variables such as age, BMI, and waist to hip ratio (Table 2).

We conducted ROC curve analysis to determine the optimal 1-h PG cutoff value to identify insulin resistance. Based on the criteria for insulin resistance in the presence of abnormal insulin sensitivity or hyperglycemia in the present study, a total of 54 patients with PCOS showed insulin resistance. The ROC curve analysis revealed an optimal 1-h PG cutoff of 138.5 g/dL to reflect insulin resistance (Fig. 2), which was close to the existing 2-h PG reference value of 140 mg/dL for IGT [8].

Fig. 2.

Receiver operating characteristic curves were used to determine the optimal cutoff value of 1-h postload glucose on a 75-g oral glucose tolerance test in women with polycystic ovary syndrome.

All patients were divided into two groups according to the 1-h PG cutoff value: group 1 (1-h PG $<$ 138.5 mg/dL) and group 2 (1-h PG $\geq$ 138.5 mg/dL). Table 3 shows the significant differences in all laboratory parameters except fasting insulin levels between groups 1 and 2. While the mean fasting insulin level of group 2 (10.29 $\pm$ 10.43 $\mu$ IU/mL) was higher than that of group 1 (8.45 $\pm$ 7.01 $\mu$ IU/mL), this difference was not statistically significant (p = 0.220). As shown in Table 3, the mean waist-to-hip ratio (WHR) of group 2 (0.81 $\pm$ 0.08) was significantly higher than that of group 1 (0.78 $\pm$ 0.06; p = 0.031). Neither body weight nor body mass index (BMI) differed between the two groups.

Table 3.Comparisons of clinical and biochemical parameters among patients with polycystic ovary syndrome and high or low 1-h postload glucose levels.
 Group 1 (n = 87) Group 2 (n = 66) p Age 26.17 $\pm$ 5.04 26.67 $\pm$ 5.38 0.560 Height (cm) 161.93 $\pm$ 5.01 162.18 $\pm$ 5.74 0.771 Body weight (kg) 57.42 $\pm$ 14.24 59.82 $\pm$ 14.69 0.311 Body mass index (kg/m ${}^{2}$ ) 21.88 $\pm$ 5.25 22.70 $\pm$ 5.22 0.335 Waist-to-hip ratio 0.78 $\pm$ 0.06 0.81 $\pm$ 0.08 0.031 Fasting glucose (mg/dL) 88.67 $\pm$ 5.62 95.85 $\pm$ 18.70 0.003 1-h PG (mg/dL) 104.37 $\pm$ 20.74 174.80 $\pm$ 45.93 $<$ 0.001 2-h PG (mg/dL) 96.06 $\pm$ 17.64 135.33 $\pm$ 52.71 $<$ 0.001 Fasting insulin ( $\mu$ IU/mL) 8.45 $\pm$ 7.01 10.29 $\pm$ 10.43 0.220 HOMA-IR (fasting) 1.57 $\pm$ 1.36 3.07 $\pm$ 3.23 0.001 GIR (fasting) 18.49 $\pm$ 10.90 13.29 $\pm$ 8.35 0.002 QUICKI (fasting) 0.37 $\pm$ 0.04 0.35 $\pm$ 0.04 $<$ 0.001 Values are mean $\pm$ standard deviation. Group 1 (1-h PG $<$ 138.5 mg/dL); and Group 2 (1-h PG $\geq$ 138.5 mg/dL). 1-h PG, 1-hour postload glucose; 2-h PG, 2-hour postload glucose; GIR, glucose to insulin ratio; HOMA-IR, homeostasis model assessment of insulin resistance; QUICKI, quantitative insulin sensitivity check index.
4. Discussion

Insulin resistance contributes to the pathophysiology of T2DM and is a cardinal characteristic of metabolic syndrome and many cardiovascular diseases [7]. Insulin resistance and compensatory hyperinsulinemia are critical components in the pathogenesis of PCOS [1, 22] and are involved in the dysfunction of ovarian steroidogenesis in PCOS [1]. While it is difficult to explain the causes of insulin resistance in patients with PCOS, the complexity and polygenic nature of PCOS suggest that more than one mechanism may be involved. Although the most common cause of insulin resistance is obesity, obesity cannot thoroughly explain the relationship between PCOS and insulin resistance [1, 6].

While the hyperinsulinemic-euglycemic clamp is considered the gold standard method to evaluating insulin sensitivity, clamp techniques and other methods requiring intravenous infusions and multiple blood samplings have no practical clinical application because of their costs, invasiveness, time-consuming nature, and dependence on experienced personnel [7, 28]. Accordingly, we assessed insulin resistance in this retrospective study based on fasting insulin level, HOMA-IR, QUICKI, and GIR, all of which are uncomplicated and inexpensive quantitative fasting-state (homeostatic) methods for evaluating insulin sensitivity. In particular, QUICKI is a simple, accurate, and reproducible method use to accurately predict changes in insulin sensitivity after both therapeutic interventions and diabetes onset [7].

In the normal population, postprandial glucose concentrations are known to peak 60 min after the start of a meal, and return to preprandial levels within 2–3 hours [11, 12]. Hulman et al. [29] reported that glucose curves varied greatly between classes, with peaks occurring after 32–61 min in clinically healthy participants. In contrast, in patients with diabetes, postprandial glucose levels generally peak approximately 2 h after the start of a meal and do not return to the control value for 4–6 hours [11, 12]. Hence, 2-h PG is generally more practical than 1-h PG [8]. However, recent studies have suggested that 1-h PG following the standard OGTT may be more effective than fasting glucose or 2-h PG in identifying people at high risk for the future development of T2DM and its complications [14, 16, 17, 18, 20, 30, 31]. Abdul-Ghani et al. [14] conducted a study of 1551 non-diabetic subjects from the San Antonio Heart Study to assess the use of insulin secretion/insulin resistance indices to predict the risk of future T2DM over 7–8 years of follow-up, reporting a significant difference in the area under the ROC curve between 1-h PG, with a cutoff value of 155 mg/dL (0.84; 75% sensitivity and 79% specificity), and 2-h PG, with a cutoff value of 140 mg/dL (0.79; 92% sensitivity and 51% specificity). They also suggested in their other studies that a 1-h PG cutoff point of 155 mg/dL plus the Adult Treatment Panel III criteria for metabolic syndrome could be used to identify groups at high risk for future T2DM among currently nondiabetic subjects [15, 16]. Bergman et al. [30] proposed that the measurement of 1-h PG might serve as a novel biomarker to detect dysglycemia earlier than the currently recommended screening criteria for glucose disorders and could potentially replace the conventional 2-h PG following OGTT in a clinical setting.

Despite recent research advances on the effectiveness of 1-h PG in predicting T2DM and its associated complications, research on the clinical utility of 1-h PG to assess insulin resistance in patients with PCOS remains lacking. To our knowledge, this is the first study in women with PCOS to assess the optimal threshold of 1-h PG to identify insulin resistance; in the present study, however, the optimal cutoff point of 1-h PG for insulin resistance in PCOS patients was 138.5 mg/dL, which was close to the existing 2-h PG reference value of 140 mg/dL [9].

Insulin resistance is regarded as the single major determinant of 1h-PG [32]. Manco et al. [13] conducted a cross-sectional analysis in study participants with normal glucose tolerance from the Relationship between Insulin Sensitivity and Cardiovascular Risk study and suggested that the optimal 1-h PG if 8.95 mmol/L ( $\fallingdotseq{}$ 161.26 mg/dL) on an OGTT to identify a subgroup of individuals with increased insulin resistance and $\beta{}$ -cell dysfunction. Abdul-Ghani et al. [14] suggested that the optimal cutoff value for predicting future T2DM was 155 mg/dL. Our calculated optimal cutoff value of 1-h PG for predicting insulin resistance through the OGTT differed from those of previous well-validated studies [13, 14]. The optimal 1-h PG threshold values in these two studies differed from ours. Although the discrepancy in cutoffs between these two studies and ours may be attributable to differences in factors, including subject race/ethnicity, sex, study design, blood samples (serum vs. plasma), and the criteria for determining insulin resistance, it may also suggest the need for a lower 1-h PG cutoff in patients with PCOS to predict insulin resistance. On the contrary, two studies to be mentioned below suggested 1-h PG cutoff values for identifying insulin resistance and predicting prediabetes which is similar to ours. Tricò et al. [33] reported that a 1h-PG concentration $\geq$ 7.4 mmol/L ( $\fallingdotseq{}$ 133 mg/dL) during an OGTT is associated with a worse clinical and metabolic phenotype, and Marcovecchio et al. [34] suggested that a 1h-PG $\geq$ 132.5 mg/dL was able to identify those with impaired insulin sensitivity in overweight/obese Caucasian youth with normal glucose tolerance, and the suggested 1-h PG cutoff values of both studies were in agreement with ours.

In this study, WHR was the only anthropometric parameter that differed significantly between the two groups defined by the 1-h PG cutoff. Waist circumference is an important component of the diagnostic criteria for insulin resistance syndrome, as central adiposity is a cardinal characteristic of the syndrome [35] and WHR is a validated anthropometric indicator related to insulin resistance [36, 37]. Given the significant relationship between obesity and insulin resistance, we expected that BMI would differ between the two groups in our study. Bianchi et al. [20], however, reported that patients with normal glucose tolerance with 1-h PG $>$ 155 mg/dL showed a significant difference in waist circumference but not in BMI compared with those with 1-h PG $\leq$ 155 mg/dL, which was strongly in agreement with our results. In another study, obesity did not affect the insulin response to oral glucose in PCOS-affected women with normal glucose tolerance [38].

Kulshreshtha et al. [38] reported amplified insulin response to glucose and that the difference between 1-h and 2-h post-glucose insulin decreased as glucose tolerance worsened in women with PCOS. Saxena et al. [3] noted that the 2-h postprandial insulin level was a good indicator of insulin resistance. In the present study, we only assessed the fasting insulin level and other ISAIs through a combination of fasting insulin and glucose levels; For accurate evaluation in this study, we should conduct an assessment of the postload insulin levels at 1 and 2 h following OGTT; however, an estimation of postprandial insulin levels is not in general included in the routine screening tests for those with PCOS, so we could not analyze the estimates of insulin sensitivity (e.g., Matsuda index) during the OGTT in this retrospective study, which leads to a major limitation of the present study. Furthermore, the sample size in this study was not large enough to conduct subgroup analysis according to the different specific PCOS phenotypes, which may be an additional drawback of our study.

5. Conclusions

In conclusion, the 1-h PG level during the standard 75-g OGTT was significantly correlated with other verified insulin sensitivity/resistance-related parameters. The 1-h PG value may be a promising alternative for the assessment of insulin sensitivity/resistance in women with PCOS, and the optimal calculated cutoff value reflecting insulin resistance was 138.5 mg/dL. Further large-scale prospective trials on predicting the future incidence of T2DM, with an additional analysis of postload/postprandial insulin levels, are needed to clarify these findings.

Author Contributions

These should be presented as follows. All authors—conceptualization; All authors—data curation; All authors—formal analysis; All authors—methodology; SC—project administration; SC—visualization; SC—writing–original draft; SL—writing–review & editing.

Ethics Approval and Consent to Participate

The study was conducted in accordance with the guidelines of the Declaration of Helsinki. This study was approved by the Institutional Review Board (IRB) of Inje University Haeundae Paik Hospital (IRB No. 129792-2014-035), which waived the requirement for written consent for subjects in the present study.

Acknowledgment

Not applicable.

Funding

This research was funded by the Research Year of Inje University in 2019, grant number 20190014.

Conflict of Interest

The authors declare no conflict of interest.

Publisher’s Note: IMR Press stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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# Introduction

As planning for the next semester kicks into full gear, students are asking an ever-increasing number of questions on the University of Illinois at Urbana-Champaign’s subreddit (/r/uiuc). Some of the questions asked should be squarely directed to an advisor, who is paid to provide guidance on a student’s progress and schedule. Alas, many students opt not to talk with advisors for whatever the reason. Thus, the community has adopted a rallying call by responding to such questions with “ask your advisor” when they arise.

On November 13th, 2018, there was even a Reddit thread that wondered about the number of instances for the phrase “ask your advisor”. The user was a bit curious as a promotional flyer for Engineering Career Services (ECS) Advising said that, “95% of students would recommend ECS Advising to other students.” As a result, my interest was peaked and this post was born.

The post is then split into two sections:

1. analysis that answers the question
2. details behind how created the query that obtained the data from Google’s BigQuery service

For those only interested in the answer, well… There were only 566 uses of the phrase “Ask your advisor” over the years. The majority came from the /u/IDKAskYourAdvisor account created in December 8, 2016. The top posters of the phrase with at least four posts are:

/u/cleverdragon1 11
/u/Mobius118f 8
/u/pissblasta3 8
/u/theillini19 8
/u/[deleted] 7
/u/IlliniTy 6
/u/Mosquite_Leaf 6
/u/CertainTackle 5
/u/DragonZaid 5
/u/uiucrower 5
/u/csdude007 4
/u/GenjoKodo 4
/u/jeffgerickson 4
/u/JRDSandstorm 4
/u/mathuiuc 4
/u/MrAcurite 4
/u/ProgramTheWorld 4
/u/schreiberbj 4
/u/TheFearlessChuaEater 4
/u/UIUCEngineering 4
/u/WUTDO11231235 4

# Data Background

Reddit data was compiled and published by Redditor /u/Stuck_In_the_Matrix in the post _”I have every publicly available Reddit comment for research. ~ 1.7 billion comments @ 250 GB compressed. Any interest in this?“_ on /r/datasets. These data sets were then uploaded onto Google’s BigQuery by Felipe Hoffa (/u/fhoffa), who is a Google Cloud Developer Advocate. He’s written up a nice overview of the data on Medium.

With this being said, we’re interested primarily in looking at the comments portion of the Reddit data. This data is contained under the Shared Data projects of category of fh-bigquery within the reddit_comments. Depending on the year, the data is organized differently since more users came onto the platform leading to more data being generated.

• From 2005 - 2014, the comment data is stored in a table coded by year.
• For example, the table 2007 gives comment data collected for the entire 2007 year.
• From 2015 - Present, the data is broken up by year and the month it was harvested in.
• For example, the table 2015_01 gives comment data collected in January of 2015.

For more details about table structure and naming, please see the appendix section.

If this kind of data is interesting to you, consider joining the /r/bigquery community.

# The Query

The query we’re interested in crafting obtains all comments posted to the /r/UIUC community that contain the “ask your advisor” phrase (regardless of case). Once we harvest all the comments, we can run other analytics on the data including counting observations.

In short, the query we would like to run can be given as.

SELECT author, body, score, downs, created_utc
FROM fh-bigquery.reddit_comments.20*
WHERE subreddit = 'UIUC'

## Understanding the Query

Our focus is largely on obtaining comments with a phrase. To identify and capture comments with a specific phrase requires the use of regular expressions to parse through the unstructured comment text. Under BigQuery’s Standard SQL (and not Legacy SQL), we can filter comments using REGEX_CONTAINS(), which uses re2 library. The patten we want to detect is then:

From here, we want to look at all comments from over the years. This means we’ll be processing slightly over ~974.36 GB of data when run and, thus, we will only be able to run the query once-per month as Google BigQuery has a 1TB analysis quota. Now, you can run this more often, but it quickly becomes pricy as each query is about 1TB that cost ~\$5. Referencing all comments over the years can be done using an asterisk inside the FROM declaration, e.g.

fh-bigquery.reddit_comments.20*

Now, I should be mention that we can optimize this query a bit by restricting the tables iterated over to just the time after Thu Aug 7 08:16:29 2008, which is when /r/UIUC was created. Though, the total savings would be less than 1 GB. So, for the sake of simplicity, we’re just going to use the asterisk.

## Appendix

Extra analysis can be found at: https://github.com/coatless/bigquery-reddit

At a later point, I’ll look into writing a more in-depth blog post.

All of the Reddit comment data tables can be viewed at:

Generally, all the tables have the same schema. Later tables gain one additional field. The schema for 2015_01 is given here.

Field Name Data Type Mode
body STRING NULLABLE
score_hidden BOOLEAN NULLABLE
archived BOOLEAN NULLABLE
name STRING NULLABLE
author STRING NULLABLE
author_flair_text STRING NULLABLE
downs INTEGER NULLABLE
created_utc INTEGER NULLABLE
subreddit_id STRING NULLABLE

format: plain


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# Adjusting Grid Size in YOLO?

I was going through the YOLO Object Detection Paper by Joseph Redmon.

The authors use a grid size of $S = 7$. If I am not wrong, the network architecture has carefully been curated for this specific grid size (Since the output of the final conv layer has dimensions $7 \times 7 \times 1024$).

Thus my question is, is there any clear way to adjust the network architecture for different values of $S$? The authors do not mention anything about this in their paper.


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# Fractal plane continuum with order $\aleph_0$?

Continuum means compact and connected.

Define the order of a point $$x$$ in a continuum $$X$$ to be the least cardinal $$\alpha$$ such that $$X$$ has a neighborhood base of open sets at $$x$$ with no more than $$\alpha$$ points their boundaries.

The Sierpinski triangle has three points of order $$2$$, countably many points of order $$4$$ (the vertices of the other triangles), and all other points are of order $$3$$.

The Sierpinski carpet has order $$\mathfrak c=|\mathbb R|$$ at each of its points.

I am looking for something to go between the Sierpinski triangle and the Sierpinski carpet.

Question 1. Is there a fractal plane continuum which has order $$\aleph_0$$ at each of its points?

Fractal can be loosely interpreted here to mean "self-similar", "simple recursive construction", or "intersection of an easily definable nested sequence of plane domains".

A slight variation on Question 1:

Question 2. Is there a fractal plane continuum which has a basis of open sets with countably infinite boundaries?

• When your title said "order $\omega$" I was expecting some sort of ordinal invariant. If you had said "order $\aleph_0$" I would have expected a cardinal, as you indeed explain. – Gerald Edgar May 1 at 18:16
• @GeraldEdgar Thanks for pointing that out. There is also something known as "rim-type" of a continuum which is expressed in ordinals. My property depends on cardinality only. – D.S. Lipham May 1 at 18:42

• There is a problem at the top and bottom "endpoints" which can be easily resolved. As it stands, these points only have order 1. But the order becomes $\aleph_0$ everywhere if we squeeze the top and bottom Cantor sets to a single point. – D.S. Lipham Jun 2 at 20:01


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# Neural Networks

Jump to: navigation, search
 Revision as of 20:55, 22 April 2011 (view source)Ang (Talk | contribs)← Older edit Revision as of 20:57, 22 April 2011 (view source)Ang (Talk | contribs) Newer edit → Line 129: Line 129: example of a '''feedforward''' neural network, since the connectivity graph example of a '''feedforward''' neural network, since the connectivity graph does not have any directed loops or cycles. does not have any directed loops or cycles. - %We will write [itex]\textstyle s_l[/itex] to denote the - %number of units in layer [itex]\textstyle l[/itex] of the network (not counting the bias unit).


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# A farmer has a rectangular property that needs to be fenced on three sides (a river surrounds the fourth. If he has 2400 feet of fencing material available, what maximum area will he be able to enclose?

May 8, 2017

The dimensions that give the maximum area are $600$ feet by $1200$ feet (that's to say, the side parallel to the river will measure $1200$ feet).

#### Explanation:

Start by tracing a diagram.

We now have:

$2 x + y = 2400$

If we solve for $y$, we get:

$y = 2400 - 2 x$

Now, we know that $A = x y$. Therefore,

$A = \left(2400 - 2 x\right) x$

$A = - 2 {x}^{2} + 2400 x$

Now differentiate with respect to $x$.

$\frac{\mathrm{dA}}{\mathrm{dx}} = - 4 x + 2400$

Find critical numbers.

$0 = - 4 x + 2400$

$x = 600$

Since $y = 2400 - 2 x$, we have that $y = 2400 - 2 \left(600\right) = 1200$

Therefore, the dimensions the give the maximum area are $600$ by $1200$ feet. The maximum area is therefore $7 , 200 , 000$.

We know that this is a maximum because the function $A = - 2 {x}^{2} + 2400 x$ opens down and therefore has a maximum and no minimum.

Hopefully this helps!


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# Cell Sensing, Implementation in CPM Code

## Overview

Cells in a group communicate with one another in order to sense a gradient. We use a minimal adaptive model based on local excitation and global inhibition (LEGI). The network looks like the following

$S$ is the signaling molecule representing the EGF gradient, $X$ is the local reporter, $Y$ is the global reporter, and $R$ is the downstream readout.

### Reactions for a specific cell

$s_k$ is the local number of signaling molecules near cell $k$, $x_k$ is the number of local reporter molecules in cell $k$ and $y_k$ is the number of global reporter molecules. As well as being produced by the signaling molecule, $y_k$ can also be exchanged between its neighbors. $% %]]>$ represents the set of all cells neighboring cell $k$. The rate $\gamma$ at which cells exchange $y$ depends on the size of the cell-cell contact.

$R_k$ is the difference between the local and global reporters. A positive value of $R_k$ reinforces cell $k$’s polarity vector in the direction of motion whereas a negative $R_k$ does the opposite.

## Chemical Concentration and Signal

There is a space dependent chemical concentration field. The chemical concentration has a constant gradient.

The average signal from the chemical concentration that cell $k$ feels is given as $\bar{s}_k$. Diffusion is Poissonian so the variance in the measured signal $s_k$ is equal to the average $\bar{s}_k$.

In the code this will be implemented by sampling values of $s_k$ from a Gaussian distribution with the variance equal to the mean. Found a function that does this here (in module ran_mod).

Implementation of Gaussian sampler works, above is an example of a 1000 numbers sampled from a distribution with a mean and variance of 9. The function is defined as normal(mean,sigma) in the module sensing.

We can place one cell in a chemical concentration with a linear gradient and see if sampling its measured signal yields a normal distribution of values.

The distribution is not quite Gaussian anymore because values less than zero are not allowed. If the function getCellSignal( meanSignal) outputs a negative number then the signal value is set to zero. If this constraint is lifted, a Gaussian distribution is recovered.

## Local Species

The local species $x_k$ is the local reporter of the chemical signal that cell $k$ measures. The dynamics of the local reporter satisfy the stochastic equation

$\xi_i$ are unit Gaussian variables that make-up the noise $\eta_{x_k}$ in the local reporter. In steady-state we can solve for $x_k$ and $\bar{x}_k$.

Similar to the chemical concentration signal we can sample $x_k$ from a distribution. This is implemented in the function getLocalX( meanSignal, signal). This function takes a sampled signal value $s_k$ and then samples values for $\xi_i$ in order to calculate $x_k$.

Here is an example of the distribution in values of $x_k$ given some distribution of $s_k$. Again, $x_k$ is restricted to be non-negative values only.

## Global Species

The global species $y$ is the global reporter of the chemical concentration across all cells in the group. The number of the global species in cell $k$ is given as $y_k$. The dynamics of the global species is more complicated than the local one since it can diffuse to and from different cells.

The first two terms are the production and degradation rates of $y_k$, same as in the case for $x_k$. The first summation term accounts for the loss of $y_k$ due to the movement of the global reporter into neighboring cells. The notation $% %]]>$ represents all nearest neighbor pairs. Similarly, the second summation term accounts for the gain in global reporter moving into cell $k$ from neighboring cells.

The movement of $y$ in and out cells depends on the size of the boundary overlap between nearest neighbors and so $% } %]]>$ must account for that. We choose that the magnitude of $% } %]]>$ be proportional to the size of the boundary overlap.

Note that $\gamma_{j,k}$ has a few interesting properties.

It is also useful to know the sum of all the contributing exchanges between cell $k$ and all the other cells and define that to be $\Gamma_k$.

The steady-state solution can be written in terms of vectors.

$M$ is a square, symmetric matrix governing degradation and exchange of the global reporter in all cells.

As in the local species case, $\xi_i$ and $\chi_{j,k}$ are unit Gaussian variables that contribute to the noise in the global reporter. In order to compute $\eta_{y_k}$ we need to know the average number $\bar{y}$ in every cell.

Using this we can then solve for the actual measured value of the global reporter in each cell $\vec{y}$.

### Implementation

All possible values of $\gamma_{j,k}$ are stored in an array gNN, such that gNN(j,k) corresponds to $\gamma_{j,k}$. Below is a list of subroutines/functions that implement the above dynamics.

• Subroutine makeMtrxGamma( gNN, N, rSim, sigma, x) calculates all $\gamma_{j,k}$ values.
• Subroutine makeMtrxM( gNN, M, N) calculates the values of all matrix elements $M_{j,k}$.
• Subroutine getMeanY( meanSignal, M, meanY, N) calculates the vector $\vec{\bar{y}}$.
• Subroutine getEtaY( etaY, gNN, meanSignal, meanY, N) calculates the vector $\vec{\eta}_y$.
• Subroutine getSpeciesY( etaY, M, N, signal, y) calculates the population of $y$ in each cell.

Here is an example of the distribution in values of $x_k$ and $y_k$ given some distribution of $s_k$ in a simulation involving only one cell. The chemical concentration profile has the same gradient as in the previous examples, but the off-set has been increased.

Once the values of $x_k$ and $y_k$ are calculated for all cells involved we can measure the downstream output $R_k$.

Below is the result over many instances (1000) of a simulation involving a chain of 10 cells sitting parallel to the chemical gradient. Each data point represents the mean value of $R$ at each cell, and the errors bars represent $\pm$ one standard deviation.

The figure on the left is representative of simulations with a relatively large gradient whereas the figure on the right is of simulations with a shallow gradient. As you can see the larger the gradient the less noisy the output becomes.

## Polarization and Bias

The cell sensing and signaling network will influence the polarization of the individual cells which will in turn affect the bias term in the CPM simulations.

### Polarization

It is the downstream output $R_k$ which will contribute to the change in the cell’s polarization vector. The change in the polarization vector of cell $k$ at every Monte Carlo time step is given as

$R_0$ is the expected signaling molecule difference across the whole cluster of cells. The purpose in dividing by $R_0$ is to attempt to normalize $R_k$ so that $\epsilon$ may be used as a tuning parameter on the order of 1 in order to vary the strength of cell-cell communication.

## Bias

The bias is modified in order to eliminate the need for the parameter $P$. With the above expression for $\Delta\vec{p}_k$ the term

### Issues with this Model of Polarization & Bias

This model produces unrealistic results. Although cells properly sense their environment, this does not translate into relatively quick, coherent motion in the direction of increasing signal concentration as desired. Even in the case of a steep gradient, cells do not behave as expected.

In this video each of the 6 cells is colored to indicate their $R_k$ value. Hot colors represent large, positive values whereas cool color represent smaller/negative values. The chemical gradient increases linearly from left to right.

As you can see cell movement does not look coordinated and the polarization vectors change erratically. Cells are properly measuring and communicating the signal as indicated by the right-side of the group generally having the largest values for the downstream readout. This means that the problem in the model lies in translating the various values of $R_k$ to the dynamics of each cell which is done through the polarization and the bias.

I believe that the problem is most likely caused by the calculation of the change in polarization. Say that a cell at the very right edge of the group has both $\vec{p}_k$ and $\Delta\vec{x}_k$ pointing perpendicular to the gradient then its positive readout $R_k$ would only reinforce movement perpendicular to the gradient. Other problems also occur when a cell becomes disconnected form the group.

## Updated Polarization Implementation

These problems stem from the fact that the influence of sensing on polarization occurs through scaling $\Delta\vec{x}_k$. Whereas it should depend on where the cell is located in the group. I propose that changes in polarization obey the following equation

The vector $\vec{q}_k$ points away from all cell $k$’s neighbors.

Using this implementation of updating the polarization vector yeilds results which are much more in-line with expectations.

Here are two preliminary simulation videos.

Qualitatively, the behavior is good but parameters need fine-tuning in order to get cells of desired sizes/shapes. The chemical gradient increases linearly from left to right, and there is about a +100 increase in the chemical concentration initially, between the cells.

Julien Varennes

Written with StackEdit.

Written on July 10, 2015


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In mathematics, given a linear space , a set is radial at the point if for every there exists a such that for every , .[1] Geometrically, this means is radial at if for every a line segment emanating from in the direction of lies in , where the length of the line segment is required to be non-zero but can depend on .

The set of all points at which is radial is equal to the algebraic interior.[1][2] The points at which a set is radial are often referred to as internal points.[3][4]

A set is absorbing if and only if it is radial at 0.[1] Some authors use the term radial as a synonym for absorbing, i. e. they call a set radial if it is radial at 0.[5]

## References

1. Jaschke, Stefan; Küchler, Uwe (2000). "Coherent Risk Measures, Valuation Bounds, and ()-Portfolio Optimization".
2. Nikolaĭ Kapitonovich Nikolʹskiĭ (1992). Functional analysis I: linear functional analysis. Springer. ISBN 978-3-540-50584-6.
3. Aliprantis, C.D.; Border, K.C. (2007). Infinite Dimensional Analysis: A Hitchhiker's Guide (3 ed.). Springer. pp. 199–200. doi:10.1007/3-540-29587-9. ISBN 978-3-540-32696-0.
4. John Cook (May 21, 1988). "Separation of Convex Sets in Linear Topological Spaces" (pdf). Retrieved November 14, 2012.
5. Schaefer, Helmuth H. (1971). Topological vector spaces. GTM. 3. New York: Springer-Verlag. ISBN 0-387-98726-6.
This article is issued from Wikipedia - version of the 12/5/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.


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# Review of Progress in Quantitative Nondestructive

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### Home > APCALC > Chapter 8 > Lesson 8.3.3 > Problem8-132

8-132.

Multiple Choice: The equation of the line normal to the curve $y = x^4 + 3x^3 + 2$ at the point where $x = 0$ is:

1. $y = x$

1. $y = 13x$

1. $y = 0$

1. $y = x + 2$

1. $x = 0$

A 'normal line' is perpendicular to a 'tangent line' at the point of tangency. So first find the equation of the tangent line, then manipulate its slope.