OPTIMAL QUANTIZATION FOR DISCRETE DISTRIBUTIONS

In this paper, we first determine the optimal sets of n-means and the nth quantization errors for all 1 ≤ n ≤ 6 for two nonuniform discrete distributions with support the set {1, 2, 3, 4, 5, 6}. Then, for a probability distribution P with support { 1 n : n ∈ N} associated with a mass function f, given by f(x) = 1 2k if x = 1 k for k ∈ N, and zero otherwise, we determine the optimal sets of n-means and the nth quantization errors for all positive integers up to n = 300. Further, for a probability distribution P with support the set N of natural number associated with a mass function f, given by f(x) = 1 2k if x = k for k ∈ N, and zero otherwise, we determine the optimal sets of n-means and the nth quantization errors for all positive integers n. At last we discuss for a discrete distribution, if the optimal sets are given, how to obtain the probability distributions

Optimal quantization for discrete distributions

In this paper, we first determine the optimal sets of $n$-means and the $n$th quantization errors for all $1\leq n\leq 6$ for two nonuniform discrete distributions with support the set $\{1, 2, 3, 4, 5, 6\}$. Then, for a probability distribution $P$ with support $\{\frac 1n : n\in \mathbb N\}$ associated with a mass function $f$, given by $f(x)=\frac 1 {2^k}$ if $x=\frac 1 k$ for $k\in \mathbb N$, and zero otherwise, we determine the optimal sets of $n$-means and the $n$th quantization errors for all positive integers up to $n=300$. Further, for a probability distribution $P$ with support the set $\mathbb N$ of natural number associated with a mass function $f$, given by $f(x)=\frac 1 {2^k}$ if $x=k$ for $k\in \mathbb N$, and zero otherwise, we determine the optimal sets of $n$-means and the $n$th quantization errors for all positive integers $n$. At last we discuss for a discrete distribution, if the optimal sets are given, how to obtain the probability distributions

Potential Economic Impact of a Coordinated Home Visitation Program: Preventing Adverse Birth Outcomes

Background and Purpose Evidence about the efficacy of healthy pregnancy home visitation programs is needed in California’s underserved Hispanic population, where preterm birth rates are higher than nonHispanic Whites. This study describes birth outcome data in a sample of families participating in the MOMS Orange County home visitation program. Methods: A descriptive comparative design was used. Birth outcome data for 1,102 women who participated in MOMS Orange County and had a live birth in 2010 were compared with data from the county of Orange (N = 38, 237) and the state of California (N = 509, 979) for the same time period, derived from county and state birth and death reports. Measures included social background, birth outcomes, and potential cost savings. Results: Although MOMS program mothers were less educated and had a higher level of poverty compared to both county and state samples, they had significantly fewer preterm births compared with the countywide and statewide samples. It was estimated that the provision of a home visitation program both countywide and statewide would result in a potential cost saving that $1.1 and$ 2.1 million, respectively. Conclusion: This coordinated prenatal program may improve birth outcomes among communities of impoverished women at potentially reduced costs

International burden of cancer deaths and years of life lost from cancer attributable to four major risk factors: a population-based study in Brazil, Russia, India, China, South Africa, the United Kingdom, and United States

Background: We provide a comprehensive view of the impact of alcohol consumption, tobacco smoking, excess body weight, and human papillomavirus (HPV) infection on cancer mortality and years of life lost (YLLs) in Brazil, Russia, India, China, South Africa, the United Kingdom (UK), and United States (US). Methods: We collected population attributable fractions of the four risk factors from global population-based studies and applied these to estimates of cancer deaths in 2020 to obtain potentially preventable cancer deaths and their 95% confidence intervals (CIs). Using life tables, we calculated the number and age-standardised rates of YLLs (ASYR). Findings: In Brazil, Russia, India, China, South Africa, the UK, and the US in 2020, an estimated 5.9 million (3.3 million–8.6 million) YLLs from cancer were attributable to alcohol consumption, 20.8 million (17.0 million–24.6 million) YLLs to tobacco smoking, 3.1 million (2.4 million–3.8 million) YLLs to excess body weight, and 4.0 million (3.9 million–4.2 million) YLLs to HPV infection. The ASYR from cancer due to alcohol consumption was highest in China (351.4 YLLs per 100,000 population [95% CI 194.5–519.2]) and lowest in the US (113.5 [69.6–157.1]) and India (115.4 [49.7–172.7). For tobacco smoking, China (1159.9 [950.6–1361.8]) had the highest ASYR followed by Russia (996.8 [831.0–1154.5). For excess body weight, Russia and the US had the highest ASYRs (385.1 [280.6–481.2] and 369.4 [299.6–433.6], respectively). The highest ASYR due to HPV infection was in South Africa (457.1 [453.3–462.6]). ASYRs for alcohol consumption and tobacco smoking were higher among men than women, whereas women had higher ASYRs for excess body weight and HPV infection. Interpretation: Our findings demonstrate the importance of cancer control efforts to reduce the burden of cancer death and YLLs due to modifiable cancer risk factors and promote the use of YLLs to summarise disease burden. Funding: Cancer Research UK

The culture and economic attributes of pusostreet food industry: Basis for a contextualized framework of pusoteaching model

Recognizing the cultural and economic attributes of pusois an essential part of Cebuanostreet food culture and industry that serves as the basis for a contextualized framework of pusoteaching model. The study used a grounded theorydesign with interviews among 18 key research participants. The attributes of pusomirror a social identity in Cebu’s street food industry and culture. Its orientation as a ritual object has shifted to a pragmatic orientation reflecting Cebu city’s fast paced-life. Its new identification creates a changing perspective; its characteristics remain integral to the Cebuano cultural identity; its rapid changes serve as one of the basesfor local government units to regulate the industry’s management operations; and serve as a framework in the creation and dissemination of a contextualizedteaching framework known as the Contextualized PUSO Teaching Model (CPTM). This innovative and culture-based teaching model addresses all teachers in academia to develop a sufficient grounding of cultural orientation and traditions that may warrant best learning opportunities

Tobacco smoking changes during the first pre-vaccination phases of the COVID-19 pandemic: A systematic review and meta-analysis

Background: Globally, tobacco smoking remains the largest preventable cause of premature death. The COVID-19 pandemic has forced nations to take unprecedented measures, including ‘lockdowns’ that might impact tobacco smoking behaviour. We performed a systematic review and meta-analyses to assess smoking behaviour changes during the early pre-vaccination phases of the COVID-19 pandemic in 2020. Methods: We searched Medline/Embase/PsycINFO/BioRxiv/MedRxiv/SSRN databases (January–November 2020) for published and pre-print articles that reported specific smoking behaviour changes or intentions after the onset of the COVID-19 pandemic. We used random-effects models to pool prevalence ratios comparing the prevalence of smoking during and before the pandemic, and the prevalence of smoking behaviour changes during the pandemic. The PROSPERO registration number for this systematic review was CRD42020206383. Findings: 31 studies were included in meta-analyses, with smoking data for 269,164 participants across 24 countries. The proportion of people smoking during the pandemic was lower than that before, with a pooled prevalence ratio of 0·87 (95%CI:0·79–0·97). Among people who smoke, 21% (95%CI:14–30%) smoked less, 27% (95%CI:22–32%) smoked more, 50% (95%CI:41%-58%) had unchanged smoking and 4% (95%CI:1–9%) reported quitting smoking. Among people who did not smoke, 2% (95%CI:1–3%) started smoking during the pandemic. Heterogeneity was high in all meta-analyses and so the pooled estimates should be interpreted with caution (I2\u3e91% and p-heterogeneity\u3c0·001). Almost all studies were at high risk of bias due to use of non-representative samples, non-response bias, and utilisation of non-validated questions. Interpretation: Smoking behaviour changes during the first phases of the COVID-19 pandemic in 2020 were highly mixed. Meta-analyses indicated that there was a relative reduction in overall smoking prevalence during the pandemic, while similar proportions of people who smoke smoked more or smoked less, although heterogeneity was high. Implementation of evidence-based tobacco control policies and programs, including tobacco cessation services, have an important role in ensuring that the COVID-19 pandemic does not exacerbate the smoking pandemic and associated adverse health outcomes

Joint IARC/NCI International Cancer Seminar Series Report: Expert consensus on future directions for ovarian carcinoma research

Recently, ovarian cancer research has evolved considerably because of the emerging recognition that rather than a single disease, ovarian carcinomas comprise several different histotypes that vary by etiologic origin, risk factors, molecular profiles, therapeutic approaches, and clinical outcome. Despite significant progress in our understanding of the etiologic heterogeneity of ovarian cancer, as well as important clinical advances, it remains the eighth most frequently diagnosed cancer in women worldwide and the most fatal gynecologic cancer. The International Agency for Research on Cancer (IARC) and the US National Cancer Institute (NCI) jointly convened an expert panel on ovarian carcinoma to develop consensus research priorities based on evolving scientific discoveries. Expertise ranged from etiology, prevention, early detection, pathology, model systems, molecular characterization, and treatment/clinical management. This report summarizes the current state of knowledge and highlights expert consensus on future directions to continue advancing etiologic, epidemiologic, and prognostic research on ovarian carcinoma

Cancer Risks in Shipyard Workers Exposed to Asbestos and Welding Fumes

The association between asbestos exposure and lung cancer, as well as between asbestos exposure and mesothelioma, had long since been established, while the relationship between asbestos exposure and other types of malignancies remains unclear. Aside from asbestos, numerous other potential exposures are present in the shipyard. Several occupations are exposed to substances such as welding fumes. The purpose of this dissertation is to examine the association between occupational agents in the Long Beach Naval shipyard and the health outcomes experienced by the workers employed in the shipyard. The study will assess the relationship between asbestos exposure and colorectal cancer by asbestos exposures levels, as well as, the incidence and mortality rates of lung cancer in relation to the exposure to welding fumes. The leading causes of deaths and the incidence of cancers was evaluated in 13,924 shipyard workers employed in the Long Beach Naval shipyard employed between 1978 and 1985. Mortality data (1978-2013) was ascertained through the California Deaths Statistical Master files. The incidence of cancer (1988-2011) was ascertained through the California cancer registry. Workers were classified into low, intermediate, and high asbestos exposure groups. Workers were also separated into exposed versus non-exposed to examine the effects of welding fumes exposure. Age-specific standardized mortality ratio and age-specific standardized incidence ratio for cancer were calculated using the general population of the state of California as the standard population. The Kaplan-Meier method was used to determine the time until occurrence of disease for colorectal cancer and lung cancer among workers exposed to asbestos and workers exposed to welding fumes. The leading causes of deaths in the Long Beach Naval shipyard included diseases of the circulatory and neoplasms. There was excess mortality and incidence of cancer in the study cohort including excess mesothelioma, lung, and colorectal cancer. Excess incidence of mesothelioma were observed in all three asbestos exposure groups. The study found no statistical difference in the time to disease occurrence between exposure groups for colorectal and lung cancer outcomes. This study showed that employment in the Long Beach Naval shipyard increased workers’ risk to a wide variety of cancers including asbestos-related malignancies