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## Abstract

There has been a growing consensus that moderate consumption of alcohol is associated with a lower risk of mortality and that this association is probably causal. However, a recent review article has raised a serious challenge to this consensus. In short, it determined that most prior research in this area committed serious misclassification errors; furthermore, among those studies that were free of these misclassification errors, no support for a protective role of alcohol consumption was found. This article reexamines the issue using prospective data for more than 124,000 persons interviewed in the U.S. National Health Interview Surveys of 1997 through 2000 with mortality follow-up through 2002 using the Linked Mortality File. The study involves about 488,000 person-years. Controlling for a variety of covariates, this study finds that compared with nondrinkers, those who consume a moderate amount of alcohol have lower all-cause and CHD mortality. The fact that the current study has taken care to avoid the pitfalls of some earlier studies and still finds that those who consume a moderate amount of alcohol have lower all-cause mortality and CHD mortality lends credence to the argument that the relationship is causal.

## Introduction

At least since Pearl’s classic study in the United States in the 1920s (1926), empirical evidence has suggested that moderate alcohol consumption is associated with a lower risk of mortality. As more studies confirmed this basic finding, more researchers have concluded that the relationship is probably causal (e.g., Marmot 2001). Various refinements in methodology have been made since Pearl’s study. As discussed herein, however, recent research by Fillmore et al. (2006) has identified serious methodological shortcomings that remain in most of the previous research on the relationship between moderate alcohol consumption and mortality. The present study reexamines the relationship between moderate alcohol consumption and mortality in the United States, using recent nationally representative data, while attempting to avoid the methodological errors found in some previous studies.

## Previous Research

Most researchers credit Raymond Pearl with realizing that we must distinguish between heavy and moderate drinkers. Pearl wrote that “moderate drinking of alcohol beverage did not shorten life. On the contrary moderate steady drinkers exhibited somewhat lower rates of mortality, and greater expectation of life than did abstainers” (1926:226). This pattern—moderate drinkers having lower mortality than both abstainers and heavy drinkers—has often been referred to a U-shaped (or, sometimes, J-shaped) relationship (Emberson et al. 2005; Marmot et al. 1981). Pearl, however, was cautious in his conclusion; he noted that moderate drinking was “not harmful.” Klatsky (2001) suggested that Pearl’s caution might have been influenced in part by the social period in which he wrote—namely, during Prohibition in the United States.

Since 1926, many additional studies have found the U-shaped relationship between alcohol consumption and mortality. Many studies focus not just on all-cause mortality, but specifically on mortality attributable to cardiovascular disease or coronary heart disease. In 1984, Marmot (1984) prepared a major review of the literature on alcohol and mortality risk attributable to coronary heart disease (CHD). By 1984, a large literature based on aggregate international comparisons, aggregate time trends, case-control studies, and (most importantly) panel studies documented that moderate drinkers tend to have a lower risk of CHD mortality than do nondrinkers. Marmot (1984) clearly believed that there was likely a causal basis to the observed association. Marmot (2001:731) later clarified that he believed that although the relationship between alcohol consumption and all-cause mortality was U-shaped, it was never clear that the relationship between alcohol consumption and CHD mortality was U-shaped. That is, while moderate consumption of alcohol was associated with reduced risk of CHD mortality, it was not clear that heavy consumption of alcohol was associated with an increased risk of CHD mortality.

In 1988, Shaper et al. (1988) proposed a critique of previous research. They argued that the higher mortality of nondrinkers might be due to the inclusion of ex-drinkers who might have given up drinking alcohol because of ill health, disability, frailty, and/or medication use. They argued, therefore, that it is important to distinguish between former drinkers and lifelong abstainers. This critique has sometimes been called the “sick quitter” hypothesis (Rimm 2001). As a result of Shaper et al.’s (1988) critique, a common practice has been to either exclude former drinkers or include them as a group separate from lifetime nondrinkers.

Another critique of the early literature (pre-1984) was that not only the amount of alcohol consumed but also the pattern of drinking is important. For example, consuming one alcoholic beverage every day of the week might have a different effect than consuming seven alcoholic beverages on one day. Recent research has therefore typically included information about the pattern of drinking (Fillmore et al. 2006). While controlling for binge drinking does not appear to have become standard practice, several researchers imply that it would be important to do so (Klatsky 2001; Marmot 2001; Thun et al. 1997).

As the basic U-shaped relationship between moderate alcohol consumption and risk of mortality persisted after these methodological critiques were leveled and addressed, more researchers have concluded that this relationship between moderate alcohol consumption and mortality is a causal relationship. Marmot wrote, “My view of the causal nature of the association was strengthened by findings subsequent to 1984” (2001:730). Bovet and Paccaud stated that “current epidemiological research supports virtually irrefutably that light-to-moderate drinking substantially reduces the risk of CHD” (2001:734). Rimm et al. wrote, “The inverse association between moderate alcohol consumption and coronary heart disease is well established. Evidence for a causal interpretation comes from over 60 ecological, case-control, and cohort studies” (1996:731).

Should alcohol be recommended as a means to reduce coronary heart disease, a major killer in the United States and other industrialized countries? Bovet and Paccaud came close to suggesting exactly this: “… the evidence currently available is large enough to guide recommendations on alcohol consumption. A net health benefit can be expected in people aged at least 40 and drinking no more than 2–3 drinks a day” (2001:736). Klatsky (2001) gave his paper the provocative title, “Could abstinence from alcohol be hazardous to your health?” Although he seems to have come close to answering his question in the affirmative, he did point out that virtually all the evidence for the health benefits of moderate consumption of alcohol comes from correlational studies rather than controlled experiments. He further reminded us, as did Bovet and Paccaud (2001) and others, that there may be health risks from even moderate consumption of alcohol, most notably fetal alcohol syndrome and certain types of cancer.

## Contribution of This Study

Given the large amount of prior research on moderate alcohol consumption and mortality, it is reasonable to ask, what is the contribution of this study? One contribution is that whereas most prior studies have been on local communities (Fillmore et al. 2006:117–124), the present study is nationally representative. There have been several previous national studies in the United States, but they have some limitations. Inasmuch as both Liao et al. (2000) and Rogers et al. (2000) used National Health Interview Study data, their data are the most similar to my own. The current study uses data from a somewhat more recent time frame. Rogers et al. (2000) used data from the 1990 NHIS interviews, with follow-up through 1995; Liao et al. (2000) used data from the 1988 and 1990 NHIS interviews, with follow-up through 1995; and my study uses data from the NHIS interviews in 1997 through 2000, with follow-up through 2002. The current study is also based on a somewhat larger number of person-years than the study by Rogers et al. (2000) (about 488,000 vs. about 235,000). Liao et al. (2000) did not report the number of person-years studied. They did report that the number of cases analyzed is 43,695, and that there was “an average of 6 years of follow-up,” implying that about 260,000 person-years were involved in the study, which would be fewer than the number of person-years in my study. More significantly, although Rogers et al. (2000) used sex as a control variable, they did not analyze the two sexes separately, which is surprising because there are clearly sex differences in age-specific death rates and patterns of drinking, and likely sex differences in the effects of alcohol. Analyzing men and women separately is the norm for studies in this area, including that by Liao et al. (2000). And while Liao et al. (2000) analyzed both all-cause and CHD mortality, Rogers et al. (2000) studied all-cause mortality and circulatory mortality, which they defined as including “heart and cerebrovascular diseases, as well as hypertension” (2000:21). While Rogers et al. (2000) used both quantity of alcohol consumption and pattern of consumption, Liao et al. (2000) used only quantity of alcohol consumption in their analysis. The fact that Rogers et al. (2000) did not analyze males and females separately is a serious shortcoming. Also, the fact that Liao et al. (2000) did not take into account the pattern of alcohol use is a shortcoming. A more serious shortcoming in the analysis by Liao et al. (2000) is that although they included a variety of basic controls in the analysis of all-cause mortality, they included only age in the analysis of CHD mortality.

Interestingly, Rogers et al. (2000) did not find that moderate drinkers have a significantly lower risk of all-cause mortality. It is not clear whether analyzing the two sexes separately would have affected the results.

Another major national study of moderate alcohol consumption and mortality in the United States was that by Thun et al. (1997), based on the Cancer Prevention Study II. Their study pertained to an older time frame than mine; their initial data collection was in 1982, with follow-up through 1991. Their sample was larger (490,000 vs. 132,000) and had a longer follow-up period (nine years vs. two to six years); although they did not report the number of person-years reflected in their study, it is clearly considerably greater than the number in mine. Thun et al. mentioned some limitations of their study. One is that “[b]ecause the study subjects were recruited by American Cancer Society volunteers, they were also more likely than the general U.S. population to be college-educated, married, middle-class, and white” (1997:1706). Another limitation that they mentioned is “the lack of information on sporadic binge drinking” (p. 1713). The current study does not have these particular limitations.

As I suggest earlier, there seems to be an emerging consensus that moderate alcohol consumption is related to lower mortality and, indeed, the relationship is causative, but Fillmore et al. (2006) raised a serious challenge to this consensus. They tracked down virtually all the prospective studies of the association between alcohol use and all-cause and CHD mortality published from the 1950s until mid-2004. Fifty-four studies in 17 countries met their criteria for inclusion; all these studies examined all-cause mortality, and 35 also studied CHD mortality. Fillmore et al. (2006) found that many of these studies committed one or both of two misclassification errors: (1) failure to separate former drinkers from complete abstainers, and (2) failure to separate occasional drinkers (which I call “near abstainers”) from complete abstainers. These errors are potentially significant in light of the “sick quitters” hypothesis. They found that fully 48% of the studies made both types of errors; 39% made only the first type of error; and only 13% of the studies made neither type of error. Liao et al. (2000) did not make either type of error, but Rogers et al. (2000) made the second type of error, and Thun et al. (1997) made both types of errors. More importantly, when focusing on the small number of studies that contained neither type of error, Fillmore et al. (2006) found no significant differences between long-term abstainers and any of the categories of drinkers (former, occasional, light, moderate, and heavy) in terms of either all-cause mortality or CHD mortality.

In sum, Fillmore et al. (2006) found that the vast majority of studies had made at least one type of misclassification error, and the studies that did not make either type of error failed to find that those with moderate consumption of alcohol had a lower mortality rate than abstainers. This is a serious challenge to the emerging consensus that moderate alcohol consumption has a protective effect for all-cause mortality and/or CHD mortality. The goal of this article is to reexamine the relationship, attempting to avoid the errors that Fillmore et al. (2006) identified as well as errors that others have identified.

Although it is common to analyze men and women separately, an additional minor contribution of my study is that I include sex-interaction effects. This approach is useful because although separate analyses of men and women tell us whether alcohol use has an effect on mortality of men and of women, it does not directly test whether the effect is stronger for men or for women. The sex-interaction effects test that difference.

Studies of the effect of moderate alcohol consumption on mortality do not always analyze both CHD mortality and all-cause mortality, but it is useful to do so. If moderate drinking is protective of health, the effect probably operates primarily through a reduced risk of CHD mortality. However, moderate alcohol consumption is known to be associated with higher risks of mortality from some other causes (e.g., some types of cancer). The effect of moderate alcohol consumption on all-cause mortality might be viewed as a measure of the net effect of moderate alcohol consumption.

## Materials and Methods

### Data

The data used in this article derive from the National Health Interview Survey (NHIS), an annual cross-sectional survey of the noninstitutionalized population in the United States. The NHIS uses a multistage cluster design to select a nationally representative sample of households (National Center for Health Statistics 2003). The NHIS obtains some information about each member of the sample households as well as more detailed information about one “sample adult” from each sample household. This study relies on data from the “sample adult” portion of the NHIS for 1997 through 2000. The NHIS for these years is supplemented with the Linked Mortality File, which indicates, for each adult interviewed in the NHIS, whether they died at any time on or before December 31, 2002. If a respondent died, the date and cause of death are recorded.

For all-cause mortality, participants were followed until their date of death or December 31, 2002 (the end of the follow-up period), whichever came first; those who were alive at the end of the follow-up were censored on December 31, 2002. CHD mortality was followed up in the same way except that deaths from causes other than CHD were censored at their date of death.

The data set contains a weight variable that provides a post-stratification adjustment based on age, race/ethnicity, and sex, using the census population as the control. The weight variable is used in the analysis.

To maintain subject confidentiality, the NCHS Research Data Center linked the NHIS data to the mortality data and performed the computer analyses using SAS.1

#### Alcohol Consumption

Adults who reported having at least 12 drinks in their lifetime were asked, “In the past year, how often did you drink any type of alcoholic beverage?” The responses were coded in terms of the number of days per week that they had an alcoholic beverage; this could range from 0 to 7. Those who reported drinking in the past year were asked, “In the past year, on those days that you drank alcoholic beverages, on the average, how many drinks did you have?” I used the responses to these two questions to code respondents into one of nine categories. There are three categories of nondrinkers and six categories of drinkers.

The three categories of nondrinkers are (1) “lifetime abstainers”, who had fewer than 12 drinks in their lifetime; (2) “near abstainers”, who had 12 or more drinks in their lifetime, but not 12 in one year; and (3) “former drinkers”, who had 12 or more drinks in one year, but not in the past year.

“Drinkers”—those who had 12 or more drinks in the past year—are divided into six categories based on both the frequency of consuming alcohol and the number of drinks usually consumed on days when they do drink alcohol. Those who usually drink on zero days in a given week are considered infrequent drinkers; those who usually drink on one or two days in a given week are considered occasional drinkers. Those who drink on three or more days in a given week are considered frequent drinkers. Those who usually consume one or two drinks on days on which they consume alcohol are considered moderate drinkers, and those who usually consume three or more drinks on days on which they consume alcohol are considered heavy drinkers.

Combining frequency and amount of drinking produces six categories of drinkers: (4) “infrequent moderate drinkers” consume an average of one or two drinks on days when they drink, but usually consume alcohol zero days per week (recall that all “drinkers” consumed at least 12 drinks in the past year); (5) “occasional moderate drinkers” consume an average of one or two drinks per day, on one or two days per week (this is the reference category); (6) “frequent moderate drinkers” consume one or two drinks per day, three or more days per week; (7) “infrequent heavy drinkers” consume three or more drinks on days when they drink alcohol, but they usually consume alcohol zero days per week; (8) “occasional heavy drinkers” consume three or more drinks per day, one or two days per week; and (9) “frequent heavy drinkers” consume three or more drinks per day, on three or more days per week.

A separate question, used for some analyses, asked, “In the past year, on how many days did you have five or more drinks of any alcoholic beverage?”

Regarding the validity of self-reports of alcohol consumption, Lang et al. suggested that they “… are generally regarded as valid for classification of individuals into broad consumption bands” (2006:54). Marmot (1984) argued that any inaccuracies in alcohol reporting probably do not substantially affect the correlation between alcohol and CHD mortality.

There has been considerable discussion of whether the type of beverage (wine, beer, or liquor) affects the beneficial effects of alcohol. In an extensive and widely cited article that reviewed 57 studies and focused on precisely this question, Rimm et al. (1996:731) concluded, “Results from observational studies, where alcohol consumption can be linked directly to an individual’s risk of coronary heart disease, provide strong evidence that all alcoholic drinks are linked with lower risk.” Consistent with Rimm et al.’s conclusion, Paganini-Hill et al. (2007:207) “found no difference in the effects of wine, beer, or hard liquor on mortality.” Similarly, Klatsky (2001:741) stated the wine/beer/liquor issue is unresolved, but added, “There is evidence of benefit from each beverage type.” Furthermore, Marmot’s view is that “it is the alcohol in wine that is protective rather than other substances” (2001:731).

A related issue is that the amount of alcohol per ounce obviously varies across beverage types. Also, the size of a typical serving varies across beverage types. The net result is that the total alcohol content is roughly the same, if one consumes one glass of wine, one can or bottle of beer, or one shot of liquor (Bovet and Paccaud 2001).

A discussion of the biochemical explanations of why those who have moderate consumption of alcohol tend to have a lower risk for death, especially from coronary heart disease, is beyond the scope of this paper; for a review, see Agarwal (2002). Genetic factors affect individual variation in the rate of alcohol metabolism; there are three variations of the gene that affects the rate of alcohol metabolism (Hines et al. 2001). Hines et al. (2001) found that moderate alcohol consumption is associated with a decreased risk of myocardial infarction and increased HDL levels (“good cholesterol”), especially for those whose genes cause them to metabolize alcohol relatively slowly. In their discussion, Hines et al. (2001) presented several arguments as to why their findings lend support to the plausibility of a causal interpretation of the association between moderate alcohol consumption and the reduced risk of myocardial infarction.

#### Covariates

Covariates include age (14 categories: 18–24; five-year age groups for ages 25–29 through 80–84; and 85 or older), race/ethnicity (non-Hispanic white, non-Hispanic black, Hispanic, and other), education (no high school, some high school, high school graduate, some college, college graduate, and graduate or professional degree), marital status (currently married, cohabiting, widowed/divorced/separated, and never married), work status (worked last week, worked last year but not last week, and did not work last year), smoking status (current daily smoker [fewer than 20 cigarettes], current daily smoker [20 or more cigarettes], current smoker some days, former smoker, and never smoked), and income (11 categories, ranging from less than $5,000 to$75,000 and higher). Except for income, which was analyzed as a continuous variable, each covariate was entered as a series of categorical variables.2

Self-reported health is viewed as an important indicator of health and has been documented to be an important predictor of subsequent mortality, even controlling for known health risk factors, including data from medical records (Benjamins et al. 2004; Idler and Benyamani 1997; Mossey and Shapiro 1982). However, self-reported health is rarely used as a covariate in studies of the effect of moderate alcohol consumption on mortality; Fillmore et al. (2006) reported that only 24% of studies of all-cause mortality and 4% of studies of CHD mortality employ a measure of “general health” as a covariate. In this study, self-reported health is included as a covariate. In the NHIS, the self-reported health of sample adults is categorized as excellent, very good, good, fair, or poor. The responses were recoded so that poor = 1, and excellent = 5.

It seems likely that those who have previously been diagnosed with a heart condition would have a greater risk of CHD mortality. Thus, it is useful to control for whether a person has been given such a prior heart-related diagnosis. However, studies examining mortality as related to moderate alcohol consumption usually do not use a prior diagnosis of heart problems as a covariate; Fillmore et al. (2006) reported that only 24% of studies of all-cause mortality and 17% of studies of CHD mortality used “past heart problems” as a covariate. Sample adults in the NHIS were asked, in four separate questions, whether they had ever been told by a doctor or other health professional that they had (1) coronary heart disease, (2) angina (“also called angina pectoris”), (3) a heart attack (“also called myocardial infarction”), or (4) any (other) kind of heart condition or heart disease. A dummy variable was created in which all respondents who answered “yes” to any of these four questions were coded 1, and all others were coded 0. Inasmuch as coronary heart disease is a major cause of death, I included this variable (prior CHD diagnosis) as a covariate in the analyses of both CHD mortality and all-cause mortality.

Inasmuch as it is well established that binge drinking is harmful to health, it is useful to take into account binge drinking. Here, “binge drinking” is defined as consuming five or more alcohol drinks in one day. For the purposes of this article, anyone who engaged in binge drinking on three or fewer days in the 365 days prior to the interview is regarded as “rarely binge drinking.” In some analyses, I restrict the sample to those who rarely binge drink.

#### Mortality

For each respondent, I calculated the number of days between the interview and either the date of death or the end of the follow-up period (i.e., December 31, 2002). For the analysis for CHD-related deaths, I used deaths attributable to ischemic heart diseases (codes I20–I25 in ICD-10). This is coded as 058 through 063 in the Underlying Cause of Death Recode: 113 groups.3

### Analysis Plan

I use Cox proportional hazards models (Yamaguchi 1991) to examine the effect of patterns of alcohol consumption on all-cause and CHD mortality. Because the NHIS is based on a complex sample design, I use the Survival procedure in SAS-callable SUDAAN Release 10.0.0; this procedure takes the sample design into account in calculating the standard errors.

I analyze all available cases. However, because relatively few people aged 18–49 died during the observation period, I replicate the analyses restricting the sample to those aged 50 and older. To control for possible confounding effects of binge drinking, I also replicate the analyses for those who rarely binge drink.

## Results

Of the 131,731 sample adults interviewed as part of the NHIS in 1997 through 2000, the final mortality status was determined for a total of 124,483 persons. During 178,282,307 person-days of follow-up (488,110 person-years), there were a total of 5,846 deaths, including 1,221 deaths from coronary heart disease.

Table 1 shows the bivariate distribution of individuals across the nine categories of drinking status by various background characteristics.

As is well known, women tend to drink less than men; in particular, women are disproportionately likely to be found in three categories: lifetime abstainer, near abstainer, and infrequent moderate drinker.

Infrequent and occasional heavy drinkers tend to be relatively young (median age of 30 or 31 years). Infrequent and occasional moderate drinkers tend to be older than infrequent and occasional heavy drinkers (median age about 40). Nondrinkers tend to be somewhat older than the four categories just referred to (median age about 45 to 52).

Non-Hispanic whites tend to drink more than individuals in the other three categories of race/ethnicity. In particular, non-Hispanic whites are more likely than those in other race/ethnicity categories to be frequent heavy drinkers, and they are much less likely to be lifetime abstainers. Non-Hispanic whites are also more likely than non-Hispanic blacks and others to be occasional heavy drinkers. It may be advantageous to non-Hispanic whites that they are also more likely to be occasional or frequent moderate drinkers.

Those with less education (i.e., high school graduate or less) are more likely to be lifetime abstainers or near abstainers. Those who did not attend high school are also slightly more likely to be former drinkers. Those who have a college degree or advanced degree are somewhat more likely to be in any of the moderate drinker categories. High school dropouts, high school graduates, and those who completed some college are more likely to be heavy drinkers, usually infrequent or occasional heavy drinkers rather than frequent heavy drinkers.

Compared with those in other marital statuses, cohabiters are less likely to be lifetime abstainers. Cohabiters and the never married are more likely than the married and the previously married to be heavy drinkers (usually infrequent or occasional heavy drinkers, rather than frequent heavy drinkers).

The drinking patterns of those who worked last week are similar to the drinking patterns of those who did not work in the last year; by contrast, those who worked in the last year but not in the last week are less likely to be nondrinkers and are correspondingly more likely to be drinkers, especially infrequent or occasional heavy drinkers.

Compared with nonsmokers, current smokers are more likely to be heavy drinkers. Smokers and nonsmokers are roughly equally likely to be moderate drinkers. Those who never smoked are the most likely to be lifetime abstainers from alcohol.

The median family income for moderate drinkers (all three categories) tends to be higher than that for heavy drinkers (all three categories), which in turn tends to be higher than that of nondrinkers (all three categories).

Among drinkers, patterns of alcohol consumption are only weakly associated with self-reported health. However, nondrinkers tend to have poorer self-reported health than drinkers. Consistent with the “sick quitter” hypothesis, former drinkers have the poorest self-reported health.

Interestingly, compared with drinkers, nondrinkers are more likely to have reported a CHD-related diagnosis at the time of the interview. Again consistent with the “sick quitter” hypothesis, former drinkers are the most likely to have a prior CHD-related diagnosis. Heavy drinkers are least likely to report a prior CHD-related diagnosis.

### Mortality Effects for Females

The analyses of mortality related to coronary heart disease (“CHD mortality”) for females are shown in Table 2. As noted earlier, occasional moderate drinkers are defined as those who consume alcoholic drinks on one or two days per week and have one or two drinks on days when they drink.

The focus in this article is the comparison between occasional moderate drinkers and nondrinkers. The first nine coefficients in column 1 of Table 2 report the hazard ratios for women in various alcohol consumption categories, compared with their counterparts who are occasional moderate drinkers. All three of the groups of nondrinkers—lifetime abstainers, near abstainers, and former drinkers—have a significantly higher risk of CHD mortality than occasional moderate drinkers. The hazard ratios are fairly similar for the three categories of nondrinkers: 1.94, 2.15, and 2.09, respectively. In other words, the risk of CHD mortality is roughly twice as high for female nondrinkers as for their female counterparts who are occasional moderate drinkers. The “sick quitters” hypothesis suggests that former drinkers may have stopped drinking because of health problems, and this might explain their higher mortality. However, among women, lifetime abstainers and near abstainers also have a higher risk of CHD mortality, compared with occasional moderate drinkers. By definition, lifetime abstainers and near abstainers never quit drinking—for health reasons or any other reason. The fact that women who are occasional moderate drinkers have a lower risk of CHD mortality than comparable women who are lifetime abstainers or near abstainers is consistent with the idea that moderate drinking is protective of health. When we restrict our attention to those who (a) are aged 50 or older (column 3) or (b) rarely binge drink (column 5), the results are similar: that is, the respective hazard ratios are significant and of similar magnitude.

As expected, males have a significantly higher risk of CHD mortality; the hazard ratio is roughly 2.9 (Table 2, column 1, line 10). However, none of the sex interaction terms are significant, implying that the effect of alcohol consumption on CHD mortality is similar for males and females.

Turning to all-cause mortality among women, all three groups of nondrinkers have a significantly higher risk of all-cause mortality than do their female counterparts who are occasional moderate drinkers (Table 3). The hazard ratios are fairly similar for the three categories of nondrinkers: 1.61, 1.72, and 1.90, respectively. These hazard ratios are not quite as high as those found for CHD mortality. Nevertheless, among women, the net effect of occasional moderate consumption of alcohol seems to be beneficial. Looking again at those who (a) are aged 50 or older or (b) rarely binge drink, the results are similar: that is, the respective hazard ratios are significant and of similar magnitude. As was the case with CHD mortality, men have a higher risk of all-cause mortality; the hazard ratio is about 2.0 (Table 3, column 1, line 10). As I’ll discuss later, some of the sex-interaction terms are significant.

### Mortality Effects for Men

Turning to the effects of occasional moderate alcohol consumption on CHD mortality for males, the results are not as clear-cut as they are for females. The hazard ratios for lifetime abstainers (1.56) and for near abstainers (1.42) are significant, but the hazard ratio for former drinkers (1.34) is not significant at the conventional .05 level of significance (see Table 4). Among men who are aged 50 or older, the hazard ratio for lifetime abstainers is significant (1.46), but the hazard ratios for near abstainers (1.34) and for former drinkers (1.28) are not significant at the .05 level. Among those who rarely binge drink, the hazard ratios for lifetime abstainers and near abstainers are significant (1.56 and 1.45, respectively), but the hazard ratio for former drinkers (1.36) is not significant.

In other words, whether occasional moderate alcohol consumption has a significant effect on the risk of CHD mortality among males depends to some extent on the category of nondrinker and the subpopulation on which we focus. It is worth noting, however, that the hazard ratios for lifetime abstainers are significant for all cases and for both subpopulations, and that the hazard ratios for near abstainers are significant for all cases and for those who rarely binge drink. On the other hand, none of the three hazard ratios for former drinkers are significant. So, using conventional two-tailed tests at the .05 level, five of the nine hazard ratios are significant (the nine hazard ratios are for all three groups of nondrinkers for the full population and for both subpopulations). If one-tailed tests, rather than two-tailed tests, are used, two additional hazard ratios are significant (i.e., all cases for former drinkers [1.34] and former drinkers who rarely binge drink [1.36]).4 One-tailed tests might be justified because the literature clearly specifies the direction of the effect. The two nonsignificant hazard ratios are found among males aged 50 or older, where the risk of CHD mortality for near abstainers and former drinkers is not significantly different from that of occasional moderate drinkers, even with a one-tailed test.

Turning to all-cause mortality among men, shown in Table 5, the hazard ratios for near abstainers (1.30) and for former drinkers (1.33) are significant; the hazard ratio for lifetime abstainers (1.19) reaches borderline significance (p < .07). These three hazard ratios for all-cause mortality are smaller than the corresponding hazard ratios for CHD mortality. It may be surprising that the hazard ratio for all-cause mortality for former drinkers is significant while the hazard ratio for CHD mortality for the same group is not significant at conventional levels. The explanation probably lies in the fact that the number of CHD deaths is much smaller than the number of all-cause deaths, and hence the standard errors are larger in the analysis of CHD mortality.

Among men who (a) are aged 50 or older or (b) rarely binge drink, the hazard ratios for all three groups of nondrinkers are significant at the .05 level.

### Sex-Interaction Effects

As noted earlier, none of the sex-interaction terms for CHD mortality are significant, meaning that the effects of membership in any given alcohol consumption category are comparable for both males and females. However, for all-cause mortality, several of the sex-interaction terms are significant. Which terms are significant varies somewhat, depending on whether one considers the whole sample or one of the subsamples. In terms of the whole sample, all three sex-interaction terms for nondrinkers are significant. The magnitude of these sex-interaction terms (about 1.3 in Table 5) indicates that females who are either lifetime abstainers, near abstainers, or former drinkers have a higher risk of all-cause mortality, compared with their male counterparts. Focusing on those who are 50 or older, two of the sex-interaction terms for nondrinkers are significant; compared with their male counterparts, women aged 50 or older who are either lifetime abstainers or former drinkers have a higher risk of all-cause mortality. Focusing on those who rarely binge drink, all three sex-interaction terms for nondrinkers are significant.

### The Effects of Heavy Drinking

It is well known that excessive consumption of alcohol is an important health behavior factor related to mortality (Mokdad et al. 2004). Nothing in this article should be construed as challenging the consensus that excessive consumption of alcohol contributes to mortality. The focus of this article, by contrast, is to investigate the effect of moderate alcohol consumption. The attention has been on the contrast between occasional moderate drinkers and nondrinkers. But what about the effect of heavy drinking (i.e., consuming three or more alcoholic drinks on days on which one drinks)? Reviewing the hazard ratios for the three categories of heavy drinkers in Tables 2 through 5 shows two patterns: (1) the hazard ratios are usually greater than 1.0, implying that the risk of death for heavy drinkers is greater than the risk of death for their same-sex counterparts who are occasional moderate drinkers; but (2) these hazard ratios are usually not significant. In general, among drinkers, I find significant hazard ratios only among frequent heavy drinkers (those who usually drink three or more drinks per day, three or more days per week); even then, the significant hazard ratios are found only for all-cause mortality. Compared with occasional moderate drinkers, frequent heavy drinkers do face a higher risk of all-cause mortality; the hazard ratios are higher for women (about 2.0) than for men (about 1.25). This is consistent with the findings of other researchers that excessive consumption of alcohol is detrimental to health. It is noteworthy, however, that the risk of CHD mortality for heavy drinkers is not significantly higher than it is for occasional moderate drinkers (see Marmot 2001).

## Summary and Discussion

There has been a growing consensus that moderate consumption of alcohol is associated with a lower risk of mortality and that this association is probably causal. Fillmore et al. (2006) identified serious misclassification errors in most of the existing prospective studies of alcohol use and mortality, thereby casting doubt on this growing consensus. Using nationally representative data for the United States, the present study has attempted to avoid the methodological errors that the literature has identified. In particular, the present study avoids the misclassification errors identified by Fillmore et al. (2006); examines both all-cause and CHD mortality; incorporates a number of important covariates in the analysis of both all-cause and CHD mortality; takes into account not only the quantity of alcohol consumption but also the pattern of use; and examines the effect of alcohol use on mortality separately for men and women.

This study finds that compared with nondrinkers, women who consume a moderate amount of alcohol have lower all-cause and CHD mortality. Among men, the pattern is not quite as consistent. In most comparisons, however, the risk of both types of mortality is lower for males who are occasional moderate drinkers than it is for their male counterparts who are nondrinkers.

The sex-interaction terms for CHD mortality indicate that for nondrinkers, the risks of mortality are elevated by a similar amount for both males and females. The sex-interaction terms for all-cause mortality indicate that for nondrinkers, the risks of mortality are elevated to a greater extent for females than for males.

### Limitations

It seems likely that, in general, the health behaviors of lifetime abstainers, and even of near abstainers, may be better than those of drinkers (Fraser 1999; Kent and Worsley 2008; Minugh 1998). Although I control for smoking behavior, it would clearly be better to control for additional health behaviors as well. However, this suggests that my test of the effect of moderate alcohol consumption is a conservative test. That is, if I had controlled for more health behaviors, the likely effect is that the mortality difference between occasional moderate drinkers and abstainers would have been greater than that observed.

Another limitation is the relatively short follow-up period, only two to six years. A longer follow-up period would obviously yield a larger number of person-years and would likely yield a larger number of deaths, which in turn would likely lead to more precise estimates.

### Strengths

Although most prior studies of the effect of moderate alcohol consumption on mortality have used community samples, the analysis in this article is based on a large, nationally representative data set. Whereas not all previous studies in this area have examined both CHD mortality and all-cause mortality, this study analyzes both. Although some studies have categorized drinkers according to only the frequency or quantity of drinks, this study categorizes drinkers according to both the frequency and quantity of their drinking. And whereas most previous studies in this area have made classification errors with respect to nondrinkers, this study avoids such classification errors. In addition, a larger than usual number of covariates is included in the analyses. In particular, self-reported health and having a prior CHD-related diagnosis are included as covariates here, whereas neither one is typically included. Finally, in calculating the standard errors, I take into account the complex sample design.

This article presents strong evidence that occasional moderate alcohol consumption has a protective role in health. The fact that the current study has taken care to avoid the pitfalls of some earlier studies and still finds that those who consume a moderate amount of alcohol have lower all-cause mortality and CHD mortality lends credence to the argument that the relationship is causal.

## Acknowledgment

I would like to thank <NAME> for computational assistance on this paper.

## Notes

1

I use the restricted-use data set. There is a corresponding public-use data set. With the public-use data set, an analyst can obtain the data set to be analyzed at his or her own institution. Owing to confidentiality concerns, however, there are some disadvantages to using the public-use data set. First, the NCHS used “standard data perturbation techniques that introduce statistical noise into the data set” (Lochner et al. 2007:2). Second, “synthetic data were substituted for the actual date and underlying cause-of-death data for selected decedent records” (Lochner et al. 2007:2). Third, while the restricted-use data set reports date of death, the public-use data set reports quarter of death. Given the limitations of the public-use data set, I opted to use the restricted-use data set. For more details, see Lochner et al. (2007).

2

Not all families reported their income. To deal with missing data, the National Center for Health Statistics (NCHS) used multiple-imputation methodology to create five imputed estimates of family income for each family. As recommended in NCHS documentation, each of the analyses reported in this article was replicated five times, once using each imputation of family income, and the results were then combined. More details are provided by NCHS at http://www.cdc.gov/nchs/about/major/nhis/2000imputedincome.htm and the Technical Documentation linked to that site.

3

These are found in the document titled “Underlying and Multiple Causes of Death September 2006” located at http://www.cdc.gov/nchs/data/datalinkage/h1_underlying_and_multiple_causes_of_death.pdf.

4

Former drinkers who rarely binge drink are the same group as all former drinkers; however, the comparison groups are different (i.e., occasional moderate who rarely binge drink versus all occasional moderate binge drinkers).

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text: Narasaraopet I can’t call this much of a success; there may be an effect on my productivity but it’s certainly not very clear subjectively. I’ll chalk this up as a failure for modafinil and evidence for what I believed - day-time modafinil use does not work for me (even if it works for others). Brain functions smart wool Taking walks, or doing gentle, no-impact exercises like yoga, tai chi, or qi gong all provide powerful mind-body benefits. (23, 24, 25) Format: Abstract Acetylcholine Muscarinic Receptors Amazon Devices Submitted July 31, 2017 11:05AM Biohacking Smart drugs for enhancing performance have a long history. Amphetamines were used in the Berlin Olympics in the 1930s, and taken by Nazi leader <NAME>, seen here at the games. Hitler himself took the drugs. The Art Archive/REX/Shutterstock Computer Moga Moral of the story? Thanks in advance Tommy says: Facebook Oxford £21- 22k Anyone purchase from Herbadiet on Ebay? Common 2 - 3g 17. <NAME>., <NAME>., <NAME>., & <NAME>. (2002). Vitamin D insufficiency among free-living healthy young adults. Am J Med, 112(8), 659-662.  New Items (6) CAFFEINE  Share This * An independent encyclopedia on supplementation and nutrition. Exercise is the human condition. For much of our species’ history, we have been mobile [...] Huzurabad show hide Anabolic steroids Anti-inflammatories NSAIDs Antirheumatics Corticosteroids Muscle relaxants Bisphosphonates OLIGOS & qPCR PROBES » Know Your Neurotransmitters Management Audio Articles Fasoracetam is a racetam drug that is in clinical trials for vascular dementia and ADHD. Distortion of experience of time – closed my eyes on bed, and “a month/week” was experienced in 5m of clock time (second day). This experience was normal, that day. Anti-Inflammatory Diet Optimal Choline Complex $32.99 Despite your best intentions, you just can't concentrate. We've all been in this familiar, frustrating situation, and it's something that can really undermine our performance. January 15, 2018 at 5:05 am Low-dose lithium orotate is extremely cheap, ~$10 a year. There is some research literature on it improving mood and impulse control in regular people, but some of it is epidemiological (which implies considerable unreliability); my current belief is that there is probably some effect size, but at just 5mg, it may be too tiny to matter. I have ~40% belief that there will be a large effect size, but I’m doing a long experiment and I should be able to detect a large effect size with >75% chance. So, the formula is NPV of the difference between taking and not taking, times quality of information, times expectation: \frac{10 - 0}{\ln 1.05} \times 0.75 \times 0.40 = 61.4, which justifies a time investment of less than 9 hours. As it happens, it took less than an hour to make the pills & placebos, and taking them is a matter of seconds per week, so the analysis will be the time-consuming part. This one may actually turn a profit. How Did Yogananda Benefit India? Shipping 30mg: 7 - 9 January: 1 What should I do? factorization <- fa(productivity, nfactors=4); factorization Racetams affect the neurotransmitter acetylcholine, which is involved with learning and memory.7 The various different racetams can affect other neurotransmitters as well. Some, such as Aniracetam and Oxiracetam, affect dopamine and serotonin levels. Because of this, they can alleviate anxiety and depression. RELATED BULLETPROOF ARTICLES Get the most out of Medical News Today. Subscribe to our Newsletter to recieve: GPA Calculator Everytime, when I take my Acetyl-L-Carnitine, my poop changes to “soft“ and “fishy smelling“. Contrary to our prior hypothesis, the power of the study proved insufficient. Retrospective calculation indicated that the power to show the required difference of 3.5 points between groups in the Orgogozo scale at 4 weeks was 44%. The probability of a false-negative result in the study sample was thus 56%. Roger, Sydney/Australia Nicotine gum aevigenomicmedicine.gcs-web.com/static...

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text:
# Localizing a quotient ring $A/ \mathfrak{p}$

Let's assume $A$ is a commutative ring with $1$ and $\mathfrak{p} \subset A$ is a prime ideal. We shall consider $A/ \mathfrak{p}$ as an $A$-module, so there is a localization $(A/ \mathfrak{p})_\mathfrak{p}$.

What can we say about this? I know it is isomorphic to $A_\mathfrak{p} \otimes _A A/\mathfrak{p}$, but I was hoping to somehow directly relate it to a quotient of the $A$-module $A_\mathfrak{p}$ (if this is even possible).

-
Localization is exact: $$(A/\mathfrak{p})_\mathfrak{p}=A_\mathfrak{p}/\mathfrak{p}_\mathfrak{p}.$$ What do we know about $\mathfrak{p}_\mathfrak{p}$ as an ideal of $A_\mathfrak{p}$? – <NAME> Jan 4 '12 at 15:10
You also end up with a field, seeing as you invert everything outside the image of $\mathfrak{p}$ which is $(0)$... – <NAME> Jan 4 '12 at 15:13
I agree with Alex. Moding out by $\mathfrak p$ kills the prime ideals below $\mathfrak p$. Localizing with respect to $\mathfrak p$ kills the prime ideals above $\mathfrak p$. These two operations commute. – <NAME> Jan 4 '12 at 15:18
Dear @Alex: $A/\mathfrak p$ is an $A$-module. As such, it can be localized at $\mathfrak p$. We have $$(A/ \mathfrak{p})_\mathfrak{p}=(A/ \mathfrak{p})_{(0)}.$$ (Canonical isomorphism.) - But your whole point is a great one! – <NAME> Jan 4 '12 at 15:37

This is a consequence of the fact that localization is an exact functor (see the comment section for this and other helpful remarks).

Exactness implies that localization (at arbitrary multiplicative subsets) commutes with quotients, which in this case gives us $(A / \mathfrak{p})_\mathfrak{p} \cong A_\mathfrak{p} / \mathfrak{p}_\mathfrak{p}$. This (considered as a ring, not an $A$-module) is also a field.

For the sake of completeness, let $\mathfrak{a} \subset A$ be an ideal and $S \subset A$ some multiplicative subset. The exact sequence

$$0 \rightarrow \mathfrak{a} \rightarrow A \rightarrow A/\mathfrak{a} \rightarrow 0$$

localized at $S$ yields the exact sequence

$$0 \rightarrow S^{-1}\mathfrak{a} \rightarrow S^{-1}A \rightarrow S^{-1}(A/\mathfrak{a}) \rightarrow 0$$

which immediately gives $$S^{-1}(A/\mathfrak{a}) \cong S^{-1}A/S^{-1}\mathfrak{a},$$ as needed.

-


text:
Hide

# Fog Catchers

Image by <NAME> (Wikimedia Commons), CC BY-SA 2.0

For many people, the word “Peru” conjures up images of the Inca temple Machu Picchu and llamas. But for some visitors to the country, even more remarkable is the sight of fog-catching nets, or atrapanieblas, that Peru is using to harvest water from dense fogs. These nets capture tiny droplets from the fogs, and the water trickles down pipes into troughs that are used to irrigate crops and from which livestock drink. Well, not only livestock — the fog water is an ingredient in a local beer brand, too. According to The Economist, as early as the 1990s, some villages were capturing as much as $8\, 000$ litres of water daily. Today, certain regions in Peru are capable of producing $1\, 400$ litres per second, if the infrastructure is fully deployed.

Now, the weather-simulation consultancy that was hired by the Peruvian government has delivered a model of the fogs that roll in from the sea each day. Everything in the model is positioned relative to an $x$-$y$ coordinate system, with the $x$-axis at ground level, running roughly parallel to the coast (just a few miles inland), and the $y$-axis oriented straight up. According to the model, there are $n$ originator fogs, $F_1, F_2, \ldots , F_ n$. When $F_ i$ rolls in for the first time on day $d_ i$, it settles into a space that intersects the $x$-$y$ plane in an axis-aligned rectangular region with left coordinate $\ell _ i$, right coordinate $r_ i$, and height $h_ i$ — that is, the rectangular region $[\ell _ i, r_ i] \times [0, h_ i]$. Because of the periodic nature of the sea currents, each originator fog $F_ i$ gives rise to $m_ i$ fogs in total (including $F_ i$ itself), the $k$-th of which intersects the rectangular region $[\ell _ i + k\Delta x_ i, r_ i + k\Delta x_ i] \times [0, h_ i + k\Delta h_ i]$ on day $d_ i + k \Delta d_ i$, for $0 \leq k < m_ i$ (where the “change” values $\Delta x_ i$, $\Delta h_ i$, and $\Delta d_ i$ are specific to $F_ i$).

The nets that are erected to catch the fogs are also modelled as axis-aligned rectangular regions lying in the same $x$-$y$ plane (but not necessarily with lower height $0$, as is the case for the fogs). Since building a single rectangular net of sufficient length and height to catch all possible fogs would be prohibitively expensive, it was decided that for the best use of public money, the nets would be installed incrementally. Initially (i.e., on day $0$), there are no nets. Each day, after all the fogs have lifted, net maintainers determine how many fogs were “missed” that day – that is, how many fogs corresponded to rectangles that were not completely contained in the region of the $x$-$y$ plane covered by nets. The workers then add rectangular net “patches” of minimum total area so that the resulting array of nets would have caught all the fogs that day. The next day, the fogs roll in again, they lift, the workers add more patches (if necessary), and the cycle continues. Note that the portion of the $x$-$y$ plane covered by nets at any point in time is a union of axis-aligned rectangles, but in general does not constitute a single rectangular region.

Given a complete description of the $n$ originator fogs, count the total number of fogs that are missed.

## Input

The first line of input contains a positive integer $n$ $(n \leq 1\, 000)$, the number of originator fogs. This is followed by $n$ lines, the $i$-th of which contains the parameters of $F_ i$ as eight space-separated integers in this order:

${m_ i}$

– the number of fogs generated by $F_ i$

${d_ i}$

– the day $F_ i$ appears for the first time

${\ell _ i}$

– the leftmost $x$-coordinate of $F_ i$

${r_ i}$

– the rightmost $x$-coordinate of $F_ i$

${h_ i}$

– the height of $F_ i$

$\Delta d_ i$

– the number of days between consecutive fogs generated by $F_ i$

$\Delta x_ i$

– the distance to which each subsequent fog generated by $F_ i$ shifts to the right (if $\Delta x_ i$ is negative, the shift is to the left)

$\Delta h_ i$

– the change in height of each subsequent fog generated by $F_ i$

You can assume that

• $1 \leq m_ i \leq 100$

• $0 \leq d_ i \leq 10^8$

• $-10^8 \leq \ell _ i < r_ i \leq 10^8$

• $1 \leq h_ i \leq 10^8$

• $1 \leq \Delta d_ i \leq 10^6$

• $-10^6 \leq \Delta x_ i, \Delta h_ i \leq 10^6$

• $h_ i + (m_ i-1)\Delta h_ i \geq 1$

## Output

Output a single integer, the total number of fogs that are missed.

Sample Input 1 Sample Output 1
2
2 3 0 2 9 2 3 0
1 6 1 4 6 3 -1 -2

3

Sample Input 2 Sample Output 2
3
4 0 0 10 10 1 15 0
3 5 50 55 8 1 -16 2
3 10 7 10 4 1 8 -1

6

Sample Input 3 Sample Output 3
2
7 0 0 20 10 3 0 10
10 1 0 2 5 2 2 7

11

Sample Input 4 Sample Output 4
7
8 317 17 21 1000000 59872 5 100000
1 419421 21 22 324455 59872 1 -30993
2 359549 50 51 390820 59872 0 -18659
7 60189 50 51 276352 59872 0 31787
1 419421 50 51 307591 59872 0 10826
1 419421 50 51 492473 59872 0 45464
1 419421 50 51 319158 59872 0 -47232

15

CPU Time limit 4 seconds
Memory limit 1024 MB
Difficulty 5.8hard
Statistics Show


text:
# Choosing subsets of a set such that the subsets satisfy a global constraint

We have a set of items $I = \{i_1, i_2, ..., i_n\}$. Each of these items has what we call a p value, which is some real number. We want to choose a subset of $I$, call it $I'$, of size $m$ (for some $m$ with $1 \le m \le n$) such that the average of the p values of the items in $I'$ falls within some specified range, $[p_l, p_u]$. (For example, we might require an average p value between 0.70 and 0.74.) Moreover, we want to do this efficiently.

We hope to do this in O(n) time, but any polynomial time algorithm is good enough. We certainly do not want to just try every possible subset of I of size $m$ and then check whether it satisfies the average p-value constraint.

Finally, we will be doing this repeatedly and we want the subsets chosen to be a uniformly random distribution over all the possible such subsets.

Is there a way of doing this?

-
Your question might be better suited to stackoverflow.com or cstheory.stackexachange.com. –  Aryabhata Aug 24 '10 at 16:14
A duplicate of this question exists on cstheory.se. –  <NAME> Aug 25 '10 at 15:18

Assuming $m$ is an input, your problem is NP-Complete.

Subset sum can be reduced to it.

Given $A = \{x_{1}, ..., x_{n}\}$ for which we need to find a subset of sum $S$, we can create $n$ inputs to your algorithm, with input $A$, $m$ and $p_{L} = p_{U} = \frac{S}{m}$, for $1 \leq m \leq n$.

If $m$ is fixed then the brute force algorithm (which you don't want) is $O(n^m)$ and so has a polynomial time algorithm.

-

One solution I was considering was to choose items for I' successively such that the average p value of the items selected so far always falls within some upper and lower bound.

Obviously, we could just choose p_l and p_u as our lower and upper bounds, respectively, and this would satisfy the average p value constraint. But this would also be too restrictive. It could leave out a large number of possible I' where small p values might balance out high p values.

So I was considering letting the upper and lower bounds start out far apart when the first items are selected and then let them narrow down to p_l and p_u when the final mth item is selected. So we would have a cone of ranges that would become narrower as more items are picked.

More precisely, we would define two functions u and l such that the average of the first i items picked (call this p_i) would satisfy l(i) <= p_i <= u(i) for 0 <= i <= m.

I'm not really sure how to define these two functions, though. I know that l(m) = p_l and u(m) = p_u, but I don't know what l(0) or u(0) should be. Also, should the functions be linear?


text:
Kinetic energy dissipation by friction

1. Feb 17, 2012

NoobBR

Is the equation right ? How do i solve it ?

Thanks in advance and sorry about my poor english or something else

2. Feb 17, 2012

Staff: Mentor

Not really. That's not a force equation, but an energy balance one. By setting up such an energy balance equation, you could solve for the distance traveled. But that's not what's asked for.

What's the force of friction?

3. Feb 17, 2012

vivekrai

It is infact just a Kinematics 1D Problem. The body undergoes a constant retardation due to friction. So just use v = u + at .

4. Feb 17, 2012

NoobBR

hmm i formulated wrong. If the friction coeficient "u" is a nonlinear function, lets say, u = x^2 how it would be solved ?

5. Feb 17, 2012

vivekrai

Write force equation and solve the differential Equation.

We'll have $m\cdot \frac{dv}{dt} = \mu mg \implies v dv =k x^2g dx$, Since $\mu = kx^2$

6. Feb 17, 2012

NoobBR

Thank you very much for the help, you people are right and its a question about aceleration.

Greetz!


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# Finding the x- and y-intercepts of a line given the equation: Find the x-intercept and y-intercept of the line 4x - 5y = 20 Please list steps. Keep simple

Finding the x- and y-intercepts of a line given the equation:
Find the x-intercept and y-intercept of the line
$4x-5y=20$
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LilsGroolonip86
$4x-5y=20$

$4x-5\cdot 0=20$
$4x=20$

$4\cdot 0-5\cdot y=20$
$-5y=20$


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## Account Lifecycle

We have recently implemented automated processing of the final stages of a user account’s lifecycle within our account management system, ‘Prometheus’. [1] This is used to apply expiry (or ‘grace’) and suspension periods to an account, as described in our account closure policy. [2]

All user accounts have ‘roles’ and ‘entitlements’. These are used by our systems to grant access to services, e.g. possession of a particular entitlement would allow a user to log in to a specific machine. The introduction of full lifecycle management means that most roles and entitlements are preserved for a grace period once an account has expired.

At the beginning of the grace period, an automated mail will be sent to the user, indicating the expiry of their account. At the end of the grace period the account will be automatically disabled (and, subject to the suspension period, deleted).

Eligibility for a DICE account is determined by details in the school database, so it is important that this information is correct and up to date. This is particularly pertinent for short-term visitor accounts. If you are sponsoring a visitor, please ensure that Informatics HR are informed of any changes to visit dates.

## Virtual Appleton Tower

As we prepare to decant from Appleton Tower to Forrest Hill and Wilkie Building, I thought it might be useful to describe how we’re networking the buildings and why we’ve done it the way we have.

In short, both FH and Wilkie will be operated as virtual floors of Appleton Tower.  This makes it straightforward to move machines from one site to another, as we can just configure the ports in a user’s new location to match what they had before.  Machines and VoIP phones can then just plug in and work, for the most part, so minimising downtime and reconfiguration.  It also simplifies network installation and management, as we have all the surrounding infrastructure services already in place.

Each site connects back to our Appleton Tower core over a pair of 10Gbps fibre links.  This allows for load-sharing, as we are collapsing three sets of uplinks into one for each new site.  It also gives us an additional measure of resilience, as it means that one switch failure, either in AT or FH or Wilkie, will not affect the service for all the others. Network diagrams for Forrest Hill are linked from here, and the Wilkie diagram is here.

The disadvantage of this scheme is that it introduces inter-building dependencies, which we normally try to avoid.  In this case, however, it was felt that this would be outweighed by the simplification of the decant process, given that we expect to be in the buildings for only one academic year.

## Planned group space downtime

The disk array ifevo3 has a fault with its flash memory. Though it may be just about possible to replace the faulty memory without disrupting the file service, the recommendation is to shut down the the disk array to do the work. So this is what we plan on doing.

The data on ifevo3 is nearly all group space, plus some of our system/backup data. While ifevo3 is down, the group space listed below will be unavailable.

To do this work without affecting other files and home directories served by the same server, we need to unmount the affected partitions from the servers. This will mean a brief interruption to all files served by the those servers, once before the work starts, and once again after it is complete. These brief breaks should last no longer than 2 minutes, you may not even notice them at all.

We are planning to do the work on Tuesday 26th of May, between 9am and 10am. Please let us know now if this is going to cause you real problems.

The list of group areas that will be unavailable during the work is:

/group/admin/repadmin
/group/corpora/public
/group/infdb/infreports
/group/infdb/infthesis
/group/infdb/ug4projects
/group/project/dcspaul-diy
/group/support/projects
/group/teaching/cvscs1
/afs/inf.ed.ac.uk/group/appguarden2
/afs/inf.ed.ac.uk/group/bundy
/afs/inf.ed.ac.uk/group/corpora/restricted/sky_news
/afs/inf.ed.ac.uk/group/cstr/projects/corpus_1
/afs/inf.ed.ac.uk/group/cstr/projects/Felipe_Espic
/afs/inf.ed.ac.uk/group/cstr/projects/galatea/d03
/afs/inf.ed.ac.uk/group/cstr/projects/galatea/d04
/afs/inf.ed.ac.uk/group/cstr/projects/merritt_synthesis
/afs/inf.ed.ac.uk/group/cstr/projects/merritt_synthesis2
/afs/inf.ed.ac.uk/group/cup/data1
/afs/inf.ed.ac.uk/group/ICSA/beaches
/afs/inf.ed.ac.uk/group/msc-projects/s1355318
/afs/inf.ed.ac.uk/group/msc-projects/s1355708
/afs/inf.ed.ac.uk/group/pasta-private
/afs/inf.ed.ac.uk/group/project/ami5
/afs/inf.ed.ac.uk/group/project/arc_tools
/afs/inf.ed.ac.uk/group/project/biomedTM
/afs/inf.ed.ac.uk/group/project/common_sense
/afs/inf.ed.ac.uk/group/project/deca
/afs/inf.ed.ac.uk/group/project/dnn_tts
/afs/inf.ed.ac.uk/group/project/gpgpu
/afs/inf.ed.ac.uk/group/project/idea
/afs/inf.ed.ac.uk/group/project/img2txt
/afs/inf.ed.ac.uk/group/project/mast
/afs/inf.ed.ac.uk/group/project/mast/mast2
/afs/inf.ed.ac.uk/group/project/nst/bbcdata/ptn4
/afs/inf.ed.ac.uk/group/project/nst/bbcdata/ptn5
/afs/inf.ed.ac.uk/group/project/nst/bbcdata/ptn6
/afs/inf.ed.ac.uk/group/project/nst/bbcdata/ptn7
/afs/inf.ed.ac.uk/group/project/nst/bbcdata/ptn8
/afs/inf.ed.ac.uk/group/project/nst/bbcdata/raw
/afs/inf.ed.ac.uk/group/project/reellives
/afs/inf.ed.ac.uk/group/project/slmc
/afs/inf.ed.ac.uk/group/project/UKConnect
/afs/inf.ed.ac.uk/group/statgen
/afs/inf.ed.ac.uk/group/synproc
/afs/inf.ed.ac.uk/group/teaching/matlab-help
/afs/inf.ed.ac.uk/group/ug4-projects/s1040800
/afs/inf.ed.ac.uk/group/workshop/datascience
/afs/inf.ed.ac.uk/group/workshop/ml

Remember that any web space served from these areas will also be unavailable.

And for our own record, these are the actual mount points:

kraken:/vicepv /vicepw
huldra:/vicepd /vicepe /vicepf /vicepg /viceph /vicepi /vicepj /vicepk /vicepl /vicepm /vicept /vicepu
nessie:/vicept /vicepu /disk/rmirror20 /disk/rmirror21
lammasu:/vicepa /disk/ptn175 /disk/ptn176 /disk/ptn197 /disk/ptn198
yeti:/vicepu /vicepv
telford:/disk/data /disk/data2

Thanks for your understanding,

Neil

Posted in Uncategorized | 1 Comment

## Explanation of Yesterday directory

As happened today, “Yesterday” isn’t always yesterday! A brief explanation.

All AFS home directories (and some group areas) contain a Yesterday sub-directory. This directory contains a copy of your home directory from “Yesterday”, which can be useful if you accidentally delete a file.

The Yesterday directory is actually a by-product of our backup system. “Yesterday” usually means “from around 9pm”. But if the backups are running behind schedule, as can happen once a month when full backups are taken, then “Yesterday” could mean “from around 1am” or “11am” – it just depends.

This command line will tell you when your Yesterday was created:

/usr/sbin/vos exam fs lsmount ~/Yesterday | cut -f4 -d\' | tr -d \# | grep Creation

To recap, “Yesterday” is usually around 9pm the day before, but for operational reasons it could be as little as “a few seconds ago”.

Neil

## SAN firmware update April 2015

Our two Dothill SAN storage boxes in the Informatics Forum are due a firmware update. Due to their built-in redundancy, the upgrades are supposed to be safe to do without affecting their operation. In fact we’ve already done a similar device at KB (that we use for our off-site copy of user’s data) without issue.

However, given the potential disruption that would caused if they do go off-line during the update (between them they have 100TB of storage), we will do the update this weekend, one on Saturday starting at 9am, the other on Sunday at 9am. The bulk of AFS file space should be considered at risk between 9am – 1pm on both days.

Home directories on the Appleton Tower servers (naga, cetus, gorgon and minotaur) are not at risk. Use the “homedir” command to see which server you are on. eg:

neilb> homedir
neilb (<NAME>) : huldra/vicepa : /afs/inf.ed.ac.uk/user/n/neilb : free 234.2G (used 48%)

In this case my home directory is on “huldra”.

As I say, nothing should go wrong, and the update will be invisible, we are just being cautious.

Neil

## Changes to default apache configuration

A few weeks ago we rolled out some new sensible default apache configuration to all our web servers.

These configuration changes will affect all DICE web servers unless their manager has chosen to exclude or modify some of these settings. This includes the few web services where the servers are managed DICE machines, but authorized users have the ability to add to the apache configuration.

The changes were made to improve the security of apache, and came about as the result of a project to improve the security of our web servers .

This resulted in a list of all sorts of possible steps we could take to improve security. Some realistic and practical, others less so. The ones that were simply apache configuration changes are listed on https://wiki.inf.ed.ac.uk/DICE/SecuringWebServers, and made it in to our sensible header https://wiki.inf.ed.ac.uk/DICE/ApacheConfSensible, it is these settings that are now active on all our web servers.

Most of the changes should be benign to regular users of a web site, however the mod_security module can be over zealous, and some extra configuration is likely to be needed if your web site supports web form uploads.

If your website runs on a DICE managed server, and you notice a change in behaviour, then it is possible these changes have had an affect. The one that has cropped up most, is the default upload limit set by mod_security, which defaults to a small 13MB, but is easily changed.

Note that we expect that our list of sensible apache configuration will continue to grow and adapt, and updates to the current list will be released over time.

Neil

## Removal of RC4 from HTTPS Cipher Suite

In line with current best practice we will shortly be removing the RC4 stream cipher from our Apache HTTPS sites. Indeed we’ve already removed it from https://wiki.inf.ed.ac.uk without any apparent issues.

For more details see:

Modern browsers will connect via one of the various other SSL ciphers that we support. However, please do let support know if your web client has problems connecting to .inf.ed.ac.uk web sites after 26th of March.

The sort of browsers that might have problems, are old style candy-bar mobile phone browsers, eg on an 8 year old Nokia 6120 or if you are using Internet Explorer 6 on Windows XP. Slightly less old browsers can potentially use RC4, but will use a securer alternative in its absence.

Neil

## DICE upgrade to Scientific Linux 7

As reported in previous posts (Upgrade of DICE desktops to SL7, Seven), we have been working hard on preparing DICE for upgrade to Scientific Linux 7. We are on track to begin upgrading DICE desktops in May, completing the teaching labs by the start of academic year 2015/2016 and all desktops by Xmas 2015.

We are now in a position to invite some users to act as trailblazers.  If you are keen to upgrade early and are willing to accept that some software may not yet be available, please contact us using the normal support form.

An SL7 ssh login box sl7test.inf.ed.ac.uk is now available for people to check software versions etc.

Release notes summarising changes from SL6 will be produced in the next few weeks.

## Recently-completed network security projects

Last year I wrote about a couple of network security projects which were in their early stages of development.  As the last of these has recently completed, I thought it might be useful to summarise their outcomes.

We have had edge filtering in place for a long time, since we ran Solaris on Suns in fact, configured automatically from our machine configuration system (lcfg).  This has proved to be very successful in practice.  Our main edge routers typically reject a couple of million bogus packets per day, though this is still rather less than 0.5% of their total throughput.  We mostly don’t log this in detail, as there’s just too much of it and most of it isn’t very interesting, but we do have a couple of externally-visible machines which log more extensively.  These show several thousand scans per day, mostly for various Microsoft services, against individual IP addresses which have not been in use for several years.

The first of the projects I mentioned was “Scanning for Compromised Machines“.  After some investigation of our own, we learned that the University would be buying in to the ESISS scanning tool.  We now have this in use, regularly scanning all machines (managed and self-managed) with open firewall holes.  This has proved to be reasonably successful, and has thrown up a number of cases for further investigation.  Where these are with self-managed machines, we follow up with the machine’s manager to have any vulnerabilties closed down.

The other project was a pilot Intrusion Detection System.  This was a useful exercise, and the experience gained will certainly be helpful if we do later implement this as a full service, though overall the result was rather less useful than the “Scanning” project for reasons which are listed in more detail in the report.  In summary, though, the reports it produces are rather noisy due to our heterogeneous environment, and the rules we use are a couple of weeks or so behind the leading edge so we tend to hear about (and patch!) vulnerabilities through other routes before they start to show in the reports.  We’ll leave the pilot system running, so long as it doesn’t interfere with the proper functioning of our network, but there would still be quite a bit of work required to bring it up to production standard, and that effort just isn’t available at the moment as a result of the SL7 upgrades and the Appleton Tower decant.


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Nowadays, the stock market's prediction is a topic that attracted researchers in the world. Stock market prediction is a process that requires a comprehensive understanding of the data stock movement and analysis it accurately. Therefore, it needs intelligent methods to deal with this task to ensure that the prediction is as correct as possible, which will return profitable benefits to investors. The main goal of this article is the employment of effective machine learning techniques to build a strong model for stock market prediction. We evaluate HARGREAVES SERVICES PLC prediction models with Active Learning (ML) and Factor1,2,3,4 and conclude that the LON:HSP stock is predictable in the short/long term. According to price forecasts for (n+1 year) period: The dominant strategy among neural network is to Sell LON:HSP stock.

Keywords: LON:HSP, HARGREAVES SERVICES PLC, stock forecast, machine learning based prediction, risk rating, buy-sell behaviour, stock analysis, target price analysis, options and futures.

## Key Points

1. How do you know when a stock will go up or down?
2. Which neural network is best for prediction?

## LON:HSP Target Price Prediction Modeling Methodology

Data mining and machine learning approaches can be incorporated into business intelligence (BI) systems to help users for decision support in many real-life applications. Here, in this paper, we propose a machine learning approach for BI applications. Specifically, we apply structural support vector machines (SSVMs) to perform classification on complex inputs such as the nodes of a graph structure. We consider HARGREAVES SERVICES PLC Stock Decision Process with Factor where A is the set of discrete actions of LON:HSP stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4

F(Factor)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Active Learning (ML)) X S(n):→ (n+1 year) $\begin{array}{l}\int {r}^{s}\mathrm{rs}\end{array}$

n:Time series to forecast

p:Price signals of LON:HSP stock

j:Nash equilibria

k:Dominated move

a:Best response for target price

For further technical information as per how our model work we invite you to visit the article below:

How do AC Investment Research machine learning (predictive) algorithms actually work?

## LON:HSP Stock Forecast (Buy or Sell) for (n+1 year)

Sample Set: Neural Network
Stock/Index: LON:HSP HARGREAVES SERVICES PLC
Time series to forecast n: 23 Sep 2022 for (n+1 year)

According to price forecasts for (n+1 year) period: The dominant strategy among neural network is to Sell LON:HSP stock.

X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)

Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)

Z axis (Yellow to Green): *Technical Analysis%

## Conclusions

HARGREAVES SERVICES PLC assigned short-term B3 & long-term B1 forecasted stock rating. We evaluate the prediction models Active Learning (ML) with Factor1,2,3,4 and conclude that the LON:HSP stock is predictable in the short/long term. According to price forecasts for (n+1 year) period: The dominant strategy among neural network is to Sell LON:HSP stock.

### Financial State Forecast for LON:HSP Stock Options & Futures

Rating Short-Term Long-Term Senior
Outlook*B3B1
Operational Risk 4071
Market Risk3756
Technical Analysis6683
Fundamental Analysis3237
Risk Unsystematic6049

### Prediction Confidence Score

Trust metric by Neural Network: 77 out of 100 with 751 signals.

## References

1. <NAME>, <NAME>. 2017b. The state of applied econometrics: causality and policy evaluation. J. Econ. Perspect. 31:3–32
2. <NAME>, <NAME>. 2005. Regularization and variable selection via the elastic net. J. R. Stat. Soc. B 67:301–20
3. <NAME>, <NAME>, <NAME>, <NAME>. 2019. Ensemble methods for causal effects in panel data settings. NBER Work. Pap. 25675
4. <NAME>. (1989), "Conditional heteroscedasticity in time series of stock returns: Evidence and forecasts," Journal of Business, 62, 55–80.
5. <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, and <NAME>. Online marketing platform, August 17 2007. US Patent App. 11/893,765
6. <NAME> and <NAME>. Nash q-learning for general-sum stochastic games. Journal of Machine Learning Research, 4:1039–1069, 2003.
7. <NAME>, <NAME>, <NAME>. 2012. Imagenet classification with deep convolutional neural networks. In Advances in Neural Information Processing Systems, Vol. 25, ed. <NAME>, <NAME>, <NAME>, <NAME>, K<NAME>, pp. 1097–105. San Diego, CA: Neural Inf. Process. Syst. Found.
Frequently Asked QuestionsQ: What is the prediction methodology for LON:HSP stock?
A: LON:HSP stock prediction methodology: We evaluate the prediction models Active Learning (ML) and Factor
Q: Is LON:HSP stock a buy or sell?
A: The dominant strategy among neural network is to Sell LON:HSP Stock.
Q: Is HARGREAVES SERVICES PLC stock a good investment?
A: The consensus rating for HARGREAVES SERVICES PLC is Sell and assigned short-term B3 & long-term B1 forecasted stock rating.
Q: What is the consensus rating of LON:HSP stock?
A: The consensus rating for LON:HSP is Sell.
Q: What is the prediction period for LON:HSP stock?
A: The prediction period for LON:HSP is (n+1 year)


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# Figure 2

 Invariant-mass distributions of KK pairs for pp and the 0-5$\%$ most central Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV for the momentum ranges 0.5 < $p_{\mathrm{T}}$ < 0.8 GeV/$c$ (upper panel) and 10 < $p_{\mathrm{T}}$ < 13 GeV/$c$ (lower panel), respectively. In panels (a) and (c) the unlike charge KK invariant-mass distribution from the same event and normalized mixed event background are shown. In panels (b) and (d) the invariant-mass distribution after subtraction of the combinatorial background for $\phi$ is shown. The statistical uncertainties are shown by bars. The solid curves are the fits to the distributions and the red dashed curves are the components of those fits that describe the residual background.


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 Solving tetration for base 0 < b < e^-e Gottfried Ultimate Fellow Posts: 766 Threads: 119 Joined: Aug 2007 09/13/2009, 09:57 AM (This post was last modified: 09/13/2009, 09:59 AM by Gottfried.) (09/13/2009, 07:24 AM)mike3 Wrote: Why do you need to use a complex fixed point for $b = e^{-e}$? It converges to a real fixed point as the tower approaches infinity (namely, $\frac{1}{e}$). The problem with the real fixpoint is, that the triangular Bell-matrices have (alternating signed) units on its diagonal. This prevents the computation of a matrix-logarithm as well of the diagonalization - at least in my implementations. If I have no option for one of those, I can approximate tetration only via diagonalization of the square Bell-matrices (means: omitting the fixpoint-shifting). But here all coefficients depend on the size of the used matrix, they are in my view unpredictable and may only serve as rough approximations for a "first impression". But well, let's see. It's surely not the highest summit of wisdom... and we also have the Newton-binomial-formula and others... Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 02:00 AM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 06:56 AM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 07:20 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 07:40 AM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 07:47 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 08:07 AM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 08:35 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 08:50 AM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 03:48 PM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 09:04 PM RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 06:14 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/13/2009, 07:24 AM RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 09:57 AM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/13/2009, 11:23 AM RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 11:44 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/14/2009, 09:43 PM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/17/2009, 08:01 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/17/2009, 11:03 AM RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 01:34 PM RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 07:34 PM RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/14/2009, 02:02 PM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/13/2009, 08:08 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/13/2009, 09:49 AM RE: Solving tetration for base 0 < b < e^-e - by tommy1729 - 09/18/2009, 12:16 PM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/18/2009, 01:00 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Complex Tetration, to base exp(1/e) Ember Edison 7 3,031 08/14/2019, 09:15 AM Last Post: sheldonison Is bounded tetration is analytic in the base argument? JmsNxn 0 1,566 01/02/2017, 06:38 AM Last Post: JmsNxn Solving tetration using differintegrals and super-roots JmsNxn 0 2,141 08/22/2016, 10:07 PM Last Post: JmsNxn tetration base sqrt(e) tommy1729 2 3,673 02/14/2015, 12:36 AM Last Post: tommy1729 Explicit formula for the tetration to base $$e^{1/e}$$? mike3 1 3,281 02/13/2015, 02:26 PM Last Post: Gottfried tetration base > exp(2/5) tommy1729 2 3,448 02/11/2015, 12:29 AM Last Post: tommy1729 regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 Gottfried 7 10,132 06/25/2013, 01:37 PM Last Post: sheldonison tetration base conversion, and sexp/slog limit equations sheldonison 44 60,379 02/27/2013, 07:05 PM Last Post: sheldonison simple base conversion formula for tetration JmsNxn 0 3,491 09/22/2011, 07:41 PM Last Post: JmsNxn Does anyone have taylor series approximations for tetration and slog base e^(1/e)? JmsNxn 18 22,930 06/05/2011, 08:47 PM Last Post: sheldonison

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# Does the gravitational force of a gas change with its temperature? And why?

I have read the paragraph below, somewhere-

Consider a sphere filled with gas. It will generate a spherically symmetric gravitational field outside itself, of strength proportional to the total mass.  If we now heat the gas, the gas particles will have this increased (relativistic) mass, corresponding to their increased kinetic energy, and the external gravitational field will have increased proportionally.

Now:

$$1.$$ Does the gravitational force of the gas increase by heating the gas as claimed above?

$$2.$$ If the answer to my first question is yes. Then, is the explanation (increasing relativistic mass) correct?

It best to think of the increase here as an increase in the energy of particles of the gas, and consequently the gas as a whole has a larger energy in the reference frame where the gas as a whole is not in motion. So you have a notion of rest energy of the gas, given by: $$E = \sum_i \gamma_i m c^2$$ where the sum is over the molecules in the gas. This $$E$$ is the rest energy of the gas, and it increases with temperature. The rest mass of the gas is $$M = E/c^2$$.
A simple such model is the one called the interior Schwarzschild solution, where we treat a spherical 'star' whose density is constant, out to some finite radius $$r_0$$. This is not a precise model, but it serves to give an impression of the physics. In this case the orbits far from the star are those given by Newtonian physics if we assign to the star the mass $$M = \int \sqrt{|g_{00}|} (\rho c^2 + p) {\rm d}V$$ where $$\rho c^2$$ is proper energy density (the sum of rest energy and kinetic energy of everything at each location in the star), $$p$$ is pressure, and $${\rm d}V$$ is the proper volume element. In practice the contribution of pressure to this formula is insignificant for most stars, but the contribution of kinetic energy to the total energy density can be significant. For a treatment allowing a more realistic model of the density and pressure, the result goes by the names Tolman-Oppenheimer-Volkoff.