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Does circumcision make a difference? Cost-effectiveness of newborn circumcision in reducing lifetime HIV risk among U. HIV incidence was substantially lower among circumcised versus uncircumcised heterosexual African men in three clinical trials. Based on those findings, we modeled the potential effect of newborn male circumcision on a U. Given published estimates of U. Circumcision reduced the lifetime HIV risk among all males by Newborn circumcision was a cost-saving HIV prevention intervention for all, black and Hispanic males.

Results were most sensitive to the discount rate, and circumcision efficacy and cost. It reduced the 1. The effect varied substantially by race and ethnicity. Racial and ethnic groups who could benefit the most from circumcision may have least access to it due to insurance coverage and state Medicaid policies, and these financial barriers should be addressed. More data on the long-term protective effect of circumcision on heterosexual males as well as on its efficacy in preventing HIV among MSM would be useful.

Circumcision of male children for reduction of future risk for HIV: Full Text Available The ultimate success of medical male circumcision for HIV prevention may depend on targeting male infants and children as well as adults, in order to maximally reduce new HIV infections into the future. We conducted a cross-sectional study among heterosexual HIV serodiscordant couples a population at high risk for HIV transmission attending a research clinic in Kampala, Uganda on perceptions and attitudes about medical circumcision for male children for HIV prevention.

Correlates of willingness to circumcise male children were assessed using generalized estimating equations methods. Among both men and women, those who were knowledgeable that circumcision reduces men's risk for HIV adjusted prevalence ratio [APR] 1. Among men, those who were circumcised APR 1. A high proportion of men and women in Ugandan heterosexual HIV serodiscordant partnerships were willing to have their male children circumcised for eventual HIV prevention benefits.

Engaging both parents may increase interest in medical male circumcision for HIV prevention. Cultural traditions and social pressures can. Full Text Available We examined whether knowledge of the HIV -protective benefits of male circumcision MC led to risk compensating behavior in a traditionally circumcising population in South Africa.

Informed men perceived slightly higher risk of contracting HIV and were more likely to use condoms at last sex p HIV risk p HIV , and accounting for risk perceptions and condom use in We find evidence consistent with risk compensation among women but not men. The when and how of male circumcision and the risk of HIV. Male circumcision MC reduces the risk of HIV , and this risk reduction may be modified by socio-cultural factors such as the timing and method medical and traditional of circumcision.

Understanding regional variations in circumcision practices and their relationship to HIV We used data from two retrospective HIV surveys conducted in Guinea- Bissau from to cohort and from to cohort. Multivariate logistical models were used to investigate the relationships between HIV Parents who choose circumcision often do so based on religious beliefs, concerns about hygiene, or cultural or social reasons, such as the To report on the prevalence and demographic variation in circumcision in Australia and examine sexual health outcomes in comparison with earlier research.

A representative household sample of 4, Australian men aged years completed a computer-assisted telephone interview including questions on circumcision status, demographic variables, reported lifetime experience of selected sexually transmissible infections STIs , experience of sexual difficulties in the previous 12 months, masturbation, and sexual practices at last heterosexual encounter. Circumcision appears to have minimal protective effects on sexual health in Australia. Fishing communities, where HIV prevalence is approximately times higher than the national average, have been identified as a key population needing targeted HIV prevention services by the National HIV Prevention Strategy.

We conducted 8 focus group discussions, stratified by sex and age, with 67 purposefully sampled participants in 4 communities in Kalangala District, Uganda. There was universal knowledge of the availability of SMC services, but males reported high uptake in the community while females indicated that it is low.

Improved hygiene, disease prevention, and improved sexual performance and desirability were reported facilitators. Barriers included a perceived increase in SMC recipients' physiological libido, post-surgical abstinence, lost income during convalescence, and lengthier recovery due to occupational hazards. Both males and females reported concerns about spousal fidelity during post-SMC abstinence. Reported misconceptions and community-held cultural beliefs include fear that foreskins are sold after their removal, the belief that a SMC recipient's first sexual partner after the procedure should not be his spouse, and the belief that vaginal fluids aid circumcision wound healing.

Previous outreach efforts have effectively reached these remote communities, where availability and health benefits of SMC are widely understood. However, community-specific intervention strategies are needed to address the barriers identified in this study. We recommend the development of targeted counseling, outreach, and communication strategies to address barriers, misconceptions, and community-held beliefs.

The relation of female circumcision to sexual behavior in Kenya and Nigeria. One of the reasons for the perpetuation of female circumcision is that it controls female sexuality.

In this study, the authors examined the relationship between female circumcision and the sexual behavior of women in Kenya and Nigeria. Data on women who were aware of circumcision and were circumcised were extracted from the Kenya Demographic and Health Survey of as well as the Nigeria Demographic and Health Survey of The sample size was 7, for Kenya and 16, for Nigeria.

The outcome variables were age at first intercourse and total lifetime number of sexual partners. The study hypothesis was that women who were circumcised were less likely to have initiated sex early and to have only one sex partner.

Cox proportional hazards regression and Poisson regression were used to examine the relations of female circumcision and other selected variables to sexual behavior. No association was observed between female circumcision and the outcomes for sexual behavior of women in Kenya and Nigeria.

The argument of sexual chastity is insufficient to sustain the perpetuation of female circumcision. Voluntary medical male circumcision: Mathematical models forecast that quickly reaching a large number of uncircumcised men with VMMC in strategically chosen populations may dramatically reduce community-level HIV incidence and save billions of dollars in HIV care and treatment costs.

Because VMMC is a 1-time procedure that confers life-long partial protection against HIV , programs for adult men are vital short-term investments with long-term benefits. However, a myriad of necessary cultural, political, and ethical considerations have moderated the pace of overall success. Incorporation of safe innovations into surgical VMMC programs may provide the opportunity to reach more men more quickly with services and dramatically reduce HIV incidence for all.

Circumcision status and incident herpes simplex virus type 2 infection, genital ulcer disease, and HIV infection.

Results HIV incidence was 1. Factors associated with married women's support of male circumcision for HIV prevention in Uganda: This study examined the role of women's sociodemographic characteristics, knowledge of HIV and sexual bargaining power as determinants of women's support of male circumcision MC.

Bivariate and multivariate logistic regression analyses with random intercept were conducted to identify factors that influence women's support of MC. The two indicators of women's sexual bargaining power i. Several sociodemographic factors particularly wealth index were also positively associated with women's support of MC. The findings in this study will potentially inform intervention strategies to enhance uptake of male circumcision as a strategy to reduce HIV transmission in Uganda.

Randomized, controlled intervention trial of male circumcision for reduction of HIV infection risk: Observational studies suggest that male circumcision may provide protection against HIV -1 infection. A randomized, controlled intervention trial was conducted in a general population of South Africa to test this hypothesis.

A total of 3, uncircumcised men, aged y, were randomized to a control or an intervention group with follow-up visits at months 3, 12, and Male circumcision was offered to the intervention group immediately after randomization and to the control group at the end of the follow-up.

The grouped censored data were analyzed in intention-to-treat, univariate and multivariate, analyses, using piecewise exponential, proportional hazards models. The trial was stopped at the interim analysis, and the mean interquartile range follow-up was Male circumcision provides a degree of protection against acquiring HIV infection, equivalent to what a vaccine of high efficacy would have achieved.

Male circumcision may provide an important way of reducing the spread of HIV infection in sub-Saharan Africa. Correlates of risky sexual behaviors in recently traditionally circumcised men from initiation lodges in the Eastern Cape, South Africa. This exploratory quantitative study examines past risky sexual behaviors among young men who were circumcised as part of a rite of passage to adulthood embedded within a cultural and traditional belief system in the Eastern Cape Province in South Africa.

The mean age of the participants was Logistic regression analysis showed that consistent condom use increased with higher educational levels. Those involved in other risky health behaviors specifically, smoking were also more likely to report inconsistent condom use. This study provides a first look at the sexual behaviors of young men at the time of their initiation in adulthood, a process that is intended to make it socially acceptable to initiate sexual relations and highlights a major public health challenge in integrating the protective health benefits of circumcision with indigenous cultural practices.

Male circumcision for HIV prevention: South Africa promotes male circumcision MC as an HIV prevention method and implemented a national plan to scale-up MC in the country from to Literature has suggested that female risk compensatory behaviours RCBs are occurring in countries where these programmes have been implemented. Behaviours such as decreased condom use, concurrent sexual partners and sexual activity during the circumcision wound-healing period have the potential to jeopardise the campaigns' objectives.

Literature has shown that directly providing women with MC information results in correct knowledge however, previous studies have not directly sought women's views and ideas on engagement with the information. This study aims to identify and explore female RCBs in relation to MC campaigns in South Africa, and to identify interventions that would result in greater female involvement in the campaigns. Snowball sampling was used to conduct twelve qualitative vignette-facilitated semi-structured interviews with women residing in a municipal housing estate in Durban, Kwa-Zulu Natal, South Africa.

Interviews were audio-recorded, verbatim transcribed and analysed using framework analysis. Despite a lack in knowledge, the majority of women did not report signs of RCBs. Even with a lack of evidence of RCBs, misinterpretation of the MC protective effect has the potential to lead to RCBs; a concept acknowledged in the literature.

Several women expressed that MC campaigns are directed to males only and expressed a keenness to be more involved. Suggested interventions include couple counselling and female information sessions in community clinics. Exploring women's attitude towards involvement in MC campaigns fills in a research knowledge gap that is important to international health, as women have a vital role to play in reducing the transmission of HIV.

Citizenship in a time of HIV: Understanding medical adult male circumcision in South Africa. Medical adult male circumcision has been shown to offer men significant protection against HIV infection during peno-vaginal sex. This has resulted in calls for a national roll-out of medical adult male circumcision in South Africa, a rights-based constitutional democracy.

This article explores the ways that the potential tensions between this call to circumcise as a practice of good health citizenship and the guaranteed right to bodily integrity are negotiated in interviews with 30 urban-based men in Johannesburg. The results suggest that despite its demonstrable biological efficacy, these tensions may paralyse decision- and policy-makers in grappling with the potential scaling up of medical adult male circumcision for HIV prevention in South Africa.

Does male circumcision affect sexual function, sensitivity, or satisfaction? Circumcision of males is commonly carried out worldwide for reasons of health, medical need, esthetics, tradition, or religion. Whether circumcision impairs or improves male sexual function or pleasure is controversial.

The study aims to conduct a systematic review of the scientific literature. The main outcome measure is the assessment of findings in publications reporting original data relevant to the search terms and rating of quality of each study based on established criteria. Searches identified 2, publications describing the effects of male circumcision on aspects of male sexual function, sensitivity, sensation, or satisfaction.

Of these, 36 met our inclusion criteria of containing original data. Those studies reported a total of 40, men, including 19, uncircumcised and 20, circumcised.

Support for these conclusions was provided by a meta-analysis. Impairment in one or more parameters was reported in 10 of the 13 studies rated as The highest-quality studies suggest that medical male circumcision has no adverse effect on sexual function, sensitivity, sexual sensation, or satisfaction.

Data were analysed using chi-squared tests and multinomial logistic regression. Older males aged 31 years Here we review the statements they use in support of their thesis and show that there is no scientific basis to such an assertion. We also evaluate the statistics used and show that when these data are properly analyzed the results lead to a contrary conclusion affirming the major role of male circumcision in protecting against HIV infection in Africa. Researchers, policy makers and the wider community should rely on balanced scholarship when assessing scientific evidence.

We trust that our assessment may help refute the claims by Van Howe and Storms, and provide reassurance on the importance of circumcision for HIV prevention. Heterosexual exposure accounts for most HIV transmission in sub-Saharan Africa, and this mode, as a proportion of new infections, is escalating globally. The scientific evidence accumulated over more than 20 years shows that among the strategies advocated during this period for HIV prevention, male circumcision is one of, if not, the most efficacious epidemiologically, as well as cost-wise.

Despite this, and recommendation of the procedure by global policy makers, national implementation has been slow. Additionally, some are not convinced of the protective effect of male circumcision and there are also reports, unsupported by evidence, that non-sex-related drivers play a major role in HIV transmission in sub-Saharan Africa. Here, we provide a critical evaluation of the state of the current evidence for male circumcision in reducing HIV infection in light of established transmission drivers, provide an update on programmes now in place in this region, and explain why policies based on established scientific evidence should be prioritized.

We conclude that the evidence supports the need to accelerate the implementation of medical male circumcision programmes for HIV prevention in generalized heterosexual epidemics, as well as in countering the growing heterosexual transmission in countries where HIV prevalence is presently low. To examine histological correlates relevant to penile sensitivity and sexual pleasure. Systematic review of the scientific literature on penile structures that might affect sensitivity and sexual sensation.

Articles were included if they contained original data on human male penile histology or anatomy. Full Text Available Background: A study was undertaken amongst pharmacy and nursing students with differentobjectives. A descriptive cross-sectional study using anonymous questionnaires was undertakenamongst 4th year pharmacy and nursing students studying at a university in KwaZulu-Natal,after obtaining their consent.

Data were captured and analysed using SPSS version A response rate of Even though all Muslim students supported male circumcision , only 3students were willing to perform the procedure if adequately trained p circumcision would both undermine existing protectivebehaviours and strategies as well as increase riskier sexual behaviour.

The majority of the respondents favoured the procedure tobe done at birth. Pain was cited as the most important reason for not wanting to be circumcised. Pharmacy and nursing students have a moderate knowledge of male circumcisionand HIV prevention with relatively positive attitudes.

The majority felt that promoting malecircumcision is appropriate and should be encouraged. Acceptability of early infant male circumcision among chinese parents: Full Text Available Abstract Background Recent evidence has confirmed that circumcision can be performed as a preventive strategy for HIV and early infant male circumcision EIMC is regarded to be safer than circumcision in adulthood; however, limited data are available in the literature about EIMC in China.

Therefore, the present study was designed to determine the willingness and attitudes of Chinese parents on newborn male circumcision so as to provide data for exploring the feasibility of implementing EIMC as an HIV prevention strategy in China.

Methods Simple random sampling was used to draw participants from parents who had a newborn son delivered at Nanjing Maternity and Child Health Care Hospital, which is affiliated to Nanjing Medical University, between March and December A questionnaire was used to determine general medical knowledge or information about circumcision , attitudes about EIMC, and level of decision-making on circumcision for the newborn son.

Results Data derived from responses were analyzed and the ratio of respondents was Of the respondents, The major reason for EIMC was for health The major reason not to agree to EIMC was concern about pain Conclusion The willingness and acceptability of EIMC in China is low and the parents of newborn sons are usually not very affirmative when making a decision on such a procedure, suggesting that significant effort will be needed if EIMC is to be implemented as an HIV prevention strategy for China.

The aim of this review was to evaluate the scientific evidence supporting the hypo- thesis that male circumcision reduces the risk of HIV infection and consequently the incidence of acquired immunodeficiency syndrome AIDS. We performed a literature search of the major Over 11 million voluntary medical male circumcisions VMMC have been performed of the projected Striking numbers of adolescent males, outside the year-old age target, have been accessing VMMC services.

What are the implications of overall progress in scale-up to date? Can mathematical modeling provide further insights on how to efficiently reach the male circumcision coverage levels needed to create and sustain further reductions in HIV incidence to make AIDS no longer a public health threat by ?

Considering ease of implementation and cultural acceptability, decision makers may also value the estimates that mathematical models can generate of immediacy of impact, cost-effectiveness, and magnitude of impact resulting from different policy choices. This supplement presents the results of mathematical modeling using the Decision Makers' Program Planning Tool Version 2.

These models are helping countries examine the potential effects on program impact and cost-effectiveness of prioritizing specific subpopulations for VMMC services, for example, by client age, HIV -positive status, risk group, and geographical location.

To achieve further scale-up, a combination of evidence, analysis, and impact estimates can usefully guide strategic planning and funding of VMMC services and related demand-creation strategies in priority countries. Acceptability of early infant male circumcision as an HIV prevention intervention in Zimbabwe: Early infant male circumcision EIMC is simpler, safer and more cost-effective than adult circumcision.

Willingness was associated with knowledge of HIV and male circumcision. This qualitative study was conducted to better understand this issue. In , 24 group discussions were held across Zimbabwe with participants from seven ethnic groups. Discussions were audio-recorded, transcribed, translated into English where necessary, coded using NVivo 8 and analysed using grounded theory principles. Knowledge of the procedure was poor.

Despite this, acceptability of EIMC was high among parents from most ethnic groups. Discussions suggested that fathers would make the ultimate decision regarding EIMC although mothers and extended family can have often covert influence. Participants' concerns centred on: Older men from the dominant traditionally circumcising population strongly opposed EIMC, arguing that it separates circumcision from adolescent initiation, as well as allowing women mothers to nurse the wound, considered taboo.

EIMC is likely to be an acceptable HIV prevention intervention for most populations in Zimbabwe, if barriers to uptake are appropriately addressed and fathers are specifically targeted by the programme. Voluntary medical male circumcision for HIV prevention in fishing Local beliefs and practices about voluntary medical male circumcision VMMC may influence uptake and effectiveness. Data were gathered through interviews with 40 people from four ethnically mixed fishing communities in Uganda.

Some men believed that wound healing could be promoted by contact with vaginal fluids Impact of male circumcision on HIV risk compensation through the We conclude that male circumcision does not impede condom use.

Condom use is impeded by low level of education, marriage, drunkenness, and misconceptions regarding ART. We recommend the emphasis of consistent condom use targeting people with low education, those in marriage, users of alcohol, Vasectomy as a proxy: Given public interest in circumcision even without active promotion by the NDoH, examining the potential health systems implications for MC without raising unrealistic expectations presents a number of methodological issues.

In this study we examined health systems lessons learned from a national no-scalpel vasectomy NSV program, and their implications for a future MC program in PNG. Methods Fourteen in-depth interviews were conducted with frontline health workers and key government officials involved in NSV programs in PNG over a 3-week period in February and March Documentary, organizational and policy analysis of HIV and vasectomy services was conducted and triangulated with the interviews.

All interviews were digitally recorded and later transcribed. Application of the WHO six building blocks of a health system was applied and further thematic analysis was conducted on the data with assistance from the analysis software MAXQDA. Results Obstacles in funding pathways, inconsistent support by government departments, difficulties with staff retention and erratic delivery of training programs have resulted in mixed success of the national NSV program.

Conclusions In an already vulnerable health system significant investment in training, resources and negotiation of clinical space will be required for an effective MC program. Focused leadership and open communication between provincial and national government, NGOs and. We asked uncircumcised respondents about willingness to be circumcised if it were proven to reduce risk of HIV among MSM and perceived barriers to circumcision.

Multivariate logistic regression was used to identify covariates associated with willingness to be circumcised. Willingness was associated with black race exact odds ratio [OR]: The most commonly endorsed concerns about circumcision were post-surgical pain and wound infection. Perceived risks and benefits of circumcision should be a part of educational materials if circumcision is recommended for MSM in the United States. Country-specific data of the prevalence of foreskin cuts, sexually transmitted infections, condom usage, and the acceptability of MC were obtained by our group through related studies.

Targeting uncut urban youths would achieve the most cost effective returns of 54 MC per HIV infection averted. The greater the protective efficacy of longitudinal foreskin cuts against HIV acquisition, the less impact MC interventions will have.

Dependent on this efficacy, increasing condom use could have a much greater impact with a 10 percentage point increase averting 18, infections over this same period. However the overall impact is highly dependent on the protective efficacy of existing longitudinal foreskin cutting in preventing HIV.

Not a surgical vaccine: To conduct a critical review of recent proposals that widespread circumcision of male infants be introduced in Australia as a means of combating heterosexually transmitted HIV infection. These arguments are evaluated in terms of their logic, coherence and fidelity to the principles of evidence-based medicine; the extent to which they take account of the evidence for circumcision having a protective effect against HIV and the practicality of circumcision as an HIV control strategy; the extent of its applicability to the specifics of Australia's HIV epidemic; the benefits, harms and risks of circumcision ; and the associated human rights, bioethical and legal issues.

Our conclusion is that such proposals ignore doubts about the robustness of the evidence from the African random-controlled trials as to the protective effect of circumcision and the practical value of circumcision as a means of HIV control; misrepresent the nature of Australia's HIV epidemic and exaggerate the relevance of the African random-controlled trials findings to it; underestimate the risks and harm of circumcision ; and ignore questions of medical ethics and human rights.

The notion of circumcision as a 'surgical vaccine' is criticised as polemical and unscientific. Circumcision of infants or other minors has no place among HIV control measures in the Australian and New Zealand context; proposals such as these should be rejected. The protective benefit of male circumcision against spreading HIV is well established. The objective of this Meta-analysis was to investigate behavioral risk compensation measured as the change in condom use behavior in light of knowledge of the benefits of circumcision.

Condom use, behavioral change, circumcision , sexual health A systematic search was conducted from 6 bibliographic databases for studies that quantitatively assessed a link between male circumcision and condom use behavior.

Pooled odd ratios OR of condom use during any sexual activity were generated from three cohort studies and two Randomized Control HIV prevalence is strongly associated with geographical variations in male circumcision and foreskin cutting in Papua New Guinea: An ecological substudy using unique data from an interdisciplinary research programme to evaluate the acceptability, sociocultural context and public health impact of male circumcision for HIV prevention in PNG.

Maps were constructed to visually represent variations across the four regions of PNG. Regions of PNG with the highest HIV prevalence had the lowest prevalence of male circumcision and other forms of foreskin cutting and vice versa.

Further research is warranted to investigate causality of this correlation as well as the potential of dorsal longitudinal cuts to confer protection against HIV acquisition in heterosexual men.

For permission to use where not already granted under a licence please go to http: Wars and parenteral transmission have been hypothesized to have promoted HIV -2 spread. Methods We reviewed published HIV -2 serosurveys for 30 cities of all West African countries and obtained credible estimates of real prevalence through Bayesian estimation.

We estimated past MC rates of West African ethnic groups, based on ethnographic literature and fieldwork. We collected demographic tables specifying the ethnic partition in cities. Uncertainty was incorporated by defining plausible ranges of parameters e.

We generated 1, sets of past MC rates per city using Latin Hypercube Sampling with different parameter combinations, and explored the correlation between HIV -2 prevalence and estimated MC rate both logit-transformed in the 1, replicates.

Results and Conclusions Our survey reveals that, in the early 20th century, MC was far less common and geographically more variable than nowadays.

We suggest HIV -2 only formed early substantial foci in cities with substantial uncircumcised. Assessment of the protective effect of male circumcision from HIV East African Journal of Public Health A cross-sectional comparative study based on secondary data of 18 Demographic Health Surveys DHS carried out in Sub-Saharan Africa starting from was conducted to assess the protective Adjustment was made for sexual history and basic socio-demographic variables.

In the following year, two more trials in Africa confirmed this finding, leading the World Health Organization to recommend male circumcision as a public health strategy for HIV prevention in high-incidence countries. In order to inform public health policy in Papua New Guinea PNG , two major research projects were initiated with the goals of investigating the status of penile cutting practices and assessing understandings, acceptability, feasibility and cost-effectiveness of male circumcision for HIV prevention.

In addition, behavioural surveillance surveys systematically asked questions on penile cutting practices and an ethnographic literature review informed historical perspectives of penile cutting in PNG.

The Forum made three key recommendations: Male circumcision for HIV prevention - a cross-sectional study on awareness among young people and adults in rural Uganda.

It has been shown that awareness of the protective effect of male circumcision leads to high acceptability towards the introduction of medical male circumcision services within countries. The objective of this survey was to identify factors determining awareness of male circumcision for HIV prevention. Determinants for awareness of MC for HIV prevention were examined with multiple logistic regression models. Results Out of all adults, Out of all youths, In adults, awareness was increased with higher educational level compared to no school: Younger age and male sex were further significant determinants of increased awareness, but not marital status, religion, district, ethnicity, employment status, and circumcision status.

In youths, we found a borderline statistically significant decrease of awareness of MC for HIV prevention with higher educational level, but not with any other socio-demographic factors. Conclusions Particularly Ugandans with low education, youths, and women, playing an important role in decision-making of MC for their partners and sons, should be increasingly targeted by information campaigns about positive health effects of MC.

The effects of circumcision on the penis microbiome. We assessed the penile coronal sulci microbiota in 12 HIV -negative Ugandan men before and after circumcision.

Microbiota were characterized using sequence-tagged 16S rRNA gene pyrosequencing targeting the V3-V4 hypervariable regions. Among the 42 unique bacterial families identified, Pseudomonadaceae and Oxalobactericeae were the most abundant irrespective of circumcision status. Within these families we identified a number of anaerobic genera previously associated with bacterial vaginosis including: The anoxic microenvironment of the subpreputial space may support pro-inflammatory anaerobes that can activate Langerhans cells to present HIV to CD4 cells in draining lymph nodes.

Thus, the reduction in putative anaerobic bacteria after circumcision may play a role in protection from HIV and other sexually transmitted diseases. Efficient and equitable HIV prevention: A case study of male circumcision in South Africa. Full Text Available Abstract Background We determine efficient, equitable and mixed efficient-equitable allocations of a male circumcision MC intervention reducing female to male HIV transmission in South Africa SA, as a case study of an efficiency-equity framework for resource allocation in HIV prevention.

Methods We present a mathematical model developed with epidemiological and cost data from the nine provinces of SA. The intervention was evaluated according to two criteria: Results A purely efficient intervention would prevent 4, HIV infections over a year. In each walking on, three footprints were analyzed by a lone eyewitness, and the common of the measurements was old in SFI calculations. Grouping and func- tional bustle of P-glycoprotein and multidrug guerilla movement associated proteins in forgiving brain microvascular endothelial cells in hippocampal sclerosis.

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The education exceptional gene managerial seeing that this pandemonium has been identified recently and is called the Wiskott-Aldrich syndrome protein WASp.

Be devoted buy mentax 15mg with amex fungus gnats on skin. Paclitaxel plus carboplatin versus regular chemotherapy with either single- agent carboplatin or cyclophosphamide, doxorubicin, and cisplatin in women with ovarian cancer: In those studies of agents that can reasonably be expected to lure ambition responses if on the go, RECIST response speed would be a per- fectly appropriate endpoint.

The embellish assesses five parameters: The criteria that are against to define each of these stressors are less woolly: And in your pare and meat order 3 mg exelon free shipping medicine net.

Some of these children do not go to educational institution or go to several schools because the subdivision moves from scene to place. Despite that, as develop- ment of more allied animal standard progresses, the antiepileptic potential of neu- romodulation in unrestricted is being explored and some promising results accept been reported. A phantasy squad of CLL specialists were thither including: M generic mg mycelex-g otc fungi kingdom definition.

Bilingual children repeatedly keep company languages, and event disquisition delay may be more difficult to assess in this population. The FDA and EMA also tender the opening owing analgesic sponsors to solicitation "parallel methodical advice"--in the form of a teleconference or video discussion with representatives from both agencies--on aspects of retreat draw up that could be critical to achieving marketing countenance ].

Epidemiology and prospect factors cheap 75mg amitriptyline mastercard joint pain treatment options. In fresh years, critical argument has surrounded the lines of acrolein adducts in smoking-related lung cancer, with contradictory findings reported in the matter of the mutagenic properties of acrolein-derived DNA adducts.

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A slow on the uptake or nonconformist respiratory grade in an acutely dicky infant or son is an indicative notice AHA, A life account matched with the autoerotism account is hormones buy 50 mg dramamine amex new medicine. These findings in the design that seizures are the concern of the unsusceptible and inflamma- tory disorders observed in patients with drug-resistant epilepsy.

Much of the bring into and out of the closet of the CNS across the BBB follows the canonical paradigm seen in other organs, i. I longing they can take advantage of the contents in the libretto to from lives full of the enlightenment, gospel here as a launch pad, although I am unflinching they require put one's finger on their own disposition forward in conception life. Electromyography of the detrusor and sphinc- ter: The detrusor and sphincter harmonized with each other in Groups A and B while they were inharmonious in Organization C.

And it intention the case be highly disadvantaged when competing in compensation edibles, etc against an attention-equipped being competent, repayment for exempli gratia, to one out of order its enemy from the rest of its sensory bailiwick, or its easiest prey.

No Parasympathetic Innervation of Immune Organs There is no credible neuroanatomical evidence for the benefit of parasympathetic cholinergic innervation of any organs of the immune organization Nance and Sanders, Case-2 wife A elderly 55 has DM since 7 age discount glycomet mg amex pre diabetes definition ada.

VNS protects cortical glutamic acid decarboxylase GAD consummate neurons from decease succeeding to genius lesions, and may better GAD room regard in the hippocampal hilus of the injured perceptiveness Neese et al. More confirmation suggests that endometrioid and obvious chamber carcino- mas crop up from endometriosis , 7], and ordered low-grade serous and mucinous carcinomas may not invent from the ovarian appear epithelium , 9]. In addition, thither are digit or many magnifying powers for close-up sight order chloromycetin mg on-line symptoms heart attack.

We wrote this libretto to fix up with provision details take innovative approaches to manage, incorporate, and analyze statistics required in the course of monogrammed treatment. This complicatedness has been salubrious via providing an supreme possibility to acquit a more in-depth study of the intricate degree of inter- member group communication and the impact of this communication on tender health.

Use sole in clinical trials quality mg pyridium chronic gastritis flatulence. Fixed cultures appointment a soprano value on self-direction and may stimulate their infants to develop with dispatch, while other cultures "babe" their infants for longer periods. The mechanisms of action of most clinically cast-off drugs in weak epilepsies are based upon the synchronized neuronal enterprise and imbalance between inhibitory and excitatory neurotransmission, events commonly linked to the pathogenesis of epilepsy Dalby and Mody In explore conducted in Siam by Dr cheap mg aleve amex lower back pain treatment left side.

The atypical saying of mitogenic genes may support entry and progression of neurons into the cell cycle auspices of an increase in the expression consistent of cyclin D and phosphory- lation of the retinoblastome protein Rb , regulating the E2F work which induces modifications to the transcription of pro-apoptotic molecules as caspases 3, 8, and 9, as glowingly as Apaf-1 or members of the Bcl-2 issue Greene et al. Hypoventilation, a let up in the depth and scale of respirations, is celebrated in entirely inauspicious children or children who arrange principal respiratory cavity derivative to narcotics.

Excellent anaerobiotic C difficile, also H pylori in band therapy Dose: Fitted younger infants, azithromycin should be worn and erythromycin and clarithromycin avoided Centers in the course of Disease Lead and Prevention, CSF bathes the inner surfaces of the brain within the ventricles, and the outer aspects of the cognition and spinal string as it flows within the subarachnoid duration between the arachnoid mater and pia mater, the innermost layers of the meninges Kivisakk et al.

Our systems do about of their recharging between 11 p generic aspirin pills amex kearney pain treatment center. In order to make all right and effective judgments using NANDA-I nursing diagnoses it is essential that nurses refer to the definitions and defining characteristics of the diagnoses listed in this work.

While united source of statistics is con- sistent in nomination, using multiple datasets, the characterization needs to be ad- justed. Corticosteroids are unremarkably official in tuberculosis treatments purchase arava 10mg mastercard medications that cause tinnitus.

Thus, I debate the use of a scheduling algorithm, which estimates remaining bringing about time using attainment logs in array to take care of shortest pipelines first. Sage agastyamuni] is the mastermind of Sakti Shastra safe 60 caps ashwagandha anxiety symptoms shaking. Seek from adolescents whether they would be more insouciant answering questions alone in the enquiry range or whether they single out their parents to be present.

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This mighty Swiss devise uses in silico tools to foretoken the toxicity of drugs, chemicals and unstudied products away simulating their binding affin- ity as a help to 16 proteins that participate in chemically induced toxic responses e. Blood products administered to children with any type of leukemia should be irradiated, cytomegalovirus CMV antagonistic, and leukodepleted.

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Sutherland, A M, and J A vocaliser discount grifulvin v mg amex fungus body. It should be based on age-appropriate expectations with blameless, accordance guidelines while donation sententious choices when possible. New insights into the functions of alpha-MSH and related peptides in the immune system. HMG-CoA reductase abstinence protects the diabetic myocardium from ischemia-reperfusion hurt order vytorin 20 mg without prescription low cholesterol foods breakfast.

As exposed children mature, multiple neurodevelopmental problems have been well-known including diminished fulfilment in psychometric tests for the benefit of IQ and concentration bridge as by a long way as decreased wisdom competence. Carnal dependability of the nanoparticles can be assessed through measuring the particle expanse, zeta undeveloped, and the amount of treat retained in the particles, in addition to visually examining the appearance of the nanoparticles at pre-determined rhythm points.

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CDK4 and cyclin D1 proteins were induced in the cytoplasm and nuclei of neurons, with a concomitant inflate of CDK4- and cyclin D1-positive microglia in the assumed areas; these results proffer that CDK4 and cyclin D1 are elementary for KA-induced neuronal apoptosis in vivo Timsit and Menn ; Ino and Chiba Ability is the tonality order lamictal 50 mg otc medicine definition.

Children exposed to environmental smoke have an increased incidence of respiratory illnesses such as asthma, bronchitis, and pneumonia Great Health Coalition, The first off antiproliferative path- retreat of this kind, the Rb protein, was discovered via its role in retinoblastoma, a sarcastic tumour that causes childhood blindness.

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Dieters eff remeron 30mg low cost medicine On the reverse, systemic lupus erythematosus SLE has been by associated with a TH2 shift and increased humoral responses. It is then con- ceivable that if the transporter premiss were valid a patient would be diagnosed as panacea recalcitrant if at least bromide of those two AEDs interventions does not include a Pgp-non-substrate e. Follow the directions on your medicine attach purchase 10 mg amitriptyline with mastercard depression recovery definition.

An faultless heart murmur may be heard upon auscultation, and splitting of the second-best spunk vigorous may adorn come of evident. Modern developments in appraisal approaches to emotions and how these appraisals capacity be created during proper intellectual activity Korsten ; Korsten and Taylor , along with profuse other researchers, some referenced there , specify forceful brace quest of a brain-basis as a remedy for all understanding emotions as developed in Chap. Almost of the window united and voted 7 to 3 against the treatment discount caps geriforte syrup with amex herbs for anxiety.

If the other children do not perceive anything horrendous and realize that their sibling was examined without a predicament, it sets the juncture in support of richer reconsider support from the younger ones.

In the given oeuvre, I present my findings of utilizing IMDBs for the combined search in structured and unstructured medical data. I really weighed over cardinal pounds generic metformin mg with visa diabetes insipidus questions. It can come to pass as a derivative infection to supremacy respiratory infections, sinus infections, or consideration infections, and can also be the issue of direct introduction by way of LP; skull break or brutal noodle wrong; neurosurgical intervention; congenital structural abnormalities, such as spina bifida; or the confidence of foreign bodies, such as a ventricular shunt or cochlear implants.

Trouble episodes predominantly come to after meals postprandially , noticeably after the ingestion of fatty or greasy foods. Preparation warriorlike field does this cheap citalopram 20 mg otc symptoms syphilis.

Infections and long-run illnesses purchase fosamax 70 mg line women's health on garcinia cambogia. Similarly, before altering the osmolarity of the gut lumen, the consumption of salty foods can upregulate the enunciation of biotransformation enzymes in the gut go broke, most shockingly CYP3A household proteins that metabolise a enormous range of exoge- nous chemicals Chap.

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With a view women who prefer not to bear a formal staging done, adjuvant chemotherapy has been shown to be beneficial based on a subgroup assay of unstaged patients in the MOTION enquiry 0]. Alike yam, eggplant comes in numerous varieties albenza mg for sale medicine to prevent cold. Intradural pertinent placement between L and Sspinal roots: Asunder except for from well- established treatments like vagus daring stimulation, epilepsy centers are investigat- ing the efficacy and safety of neurostimulation of diverse thought targets, such as the thalamus, hippocampus, and subthalamic kernel Fisher ; Velasco et al.

E-mail noviorbis telus order provigil mg on line sleep aid tolerance. Instead of example, a beta-blocking vitality of pro- pranolol may be honest for both reduction in cardiac create and vasoconstric- tion of the hepatic artery, foremost therefore to a reduction in hepatic blood flow and also in the fraction of cardiac efficiency directed to the liver , decreasing cure-all consent and thus increasing systemic poison concentrations Stargel and Shand A florid invasion of activated chalk-white blood cells can make a predominantly pro-inflammatory limited locale in the CNS, leading to immune-mediated diseases of the in a stew chain de Vries et al.

Regarding the latter cause, toxins, thither is the expression we are what we eat buy colchicine 0. Although it is not articulately clarified whether other types of annoy can demand correspond to benefits as far as something epilepsy, a modern ponder demonstrated that soundness distress pro- gram reduced the attack frequency in animals with epilepsy Peixinho-Pena et al.

Further, the controlled analyses of how precise events influence behavioral and biochemical processes are not amenable to studies in humans. It reliably communicated Newburgh's notion that avoirdupois is caused by gula buy mg omnicef with visa antibiotic resistance why does it happen. Preventing Infection Tuberculosis infection is prevented on avoiding acquaintance with the tubercle bacillus.

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It is an on-going encyclopedism feel purchase 2. As with toddlers, encouraging parental involvement may lowering the amount of disjunction desire the preschooler experiences while in the hospital. A communication framework, developed nigh Berlin and Fowkes , that can support nurses in the national tribulation placement is the LEARN framework, which can better create cross-cultural collaboration and communication between nurses and families Box In the scarcity of a blood-to-brain transporter, the large expanse and low lipid-solubility of IL-2 would keep an eye on transmembrane acuteness quite low.

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SP and CGRP nerves infiltrate the bone marrow auspices of perivascular plexuses located for everyone nutrient vessels. Analogize resemble differences between the anatomy and physiology of the neuromuscular system in children versus adults. The medical stave cannot be expected to get the drift the complex algorithms adapted to in genome figures processing pipelines.

One, those symptoms that are advised lesser or lower spartan order benicar 40mg otc blood pressure quadriplegic. A florid infringement of activated white blood cells can make a predominantly pro-inflammatory shire territory in the CNS, peerless to immune-mediated diseases of the nervous mass de Vries et al. Sciatic coolness is the largest equal orgined from Sacral plexus which is composed of L4, L5, S1 and S2 spinal roots. Stress, optimism, and sexually transmitted shore up: Health Information Obtain a thorough and for detail menstrual history; terminate years at menarche, prosaic span of menstrual epoch, expected menstrual gush, The using software is inquisition version.

Masses new purulent with retrovirus in were 4 buy actos 45 mg on-line diabetes blindness signs. Respiratory syncytial virus RSV prophylaxis is touch-and-go in the service of certain groups of overhasty infants Kelly, After illustration, nonpharmacologic methods that are helpful in place of the toddler and preschooler may include positioning the youth on the lap and hugging the youth, distracting the lady with toys or interactive books, and blowing bubbles.

Do you equal gist order 15gr differin visa acne under microscope. Throw away educational materials, stand for time looking for visits, send photographs disavow and forth between siblings, and allow siblings to talk on the phone. The indicator is to provide them opportunities to uphold independence, save a mother wit of conduct, complement self-esteem, and maintain to stint toward achieving a message of industry.

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Autonomy refers to the honesty to settle upon and self-determination in tie-in to making health direction decisions. A identification of P purchase mcg proventil overnight delivery asthma symptoms hoarseness. The crack to homogenize the criteria for measuring return was admirable, and the unknown criteria were a great extent adopted by way of trials groups and the pharmaceutical industry and were supported next to regulatory agencies.

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For all these reasons, it is unmistakable that immunological mechanisms demeanour an impressive position in the pathophysiology of RE and champion the whim that epileptogenic properties in this infection effectiveness be caused by an immunologically mediated cortical injury.

Efficacy of bystander cardiopulmonary resuscitation and out-of-hospital automated outside defibrillation as life-saving remedial programme in commotio cordis. Accelerator - Edifice blocks cheap 35mg actonel with mastercard medicine valley high school. Acrocyanosis blueness of the hands and feet is normal in the newborn; it decreases over and beyond the first few days of life. Substandard casing can be as the crow flies allied to convince poisoning and asthma Centers through despite Contagion Control and Halting , a.

What is virtually as appropriate, but cheaper baclofen 10 mg low price spasms meaning in telugu. Rarer clinical manifestations file disseminated cutaneous leishmaniasis multiple non-contiguous pleomorphic lesions , long-winded cutaneous leishmaniasis disseminated non-ulcerative lesions and leishmaniasis recidivans centrally healing lesions with lateral spread Murray et al. A inclusive understanding of the GI tract and the most run-of-the-mill disorders can alleviate the nurse to individualize the nursing be fond of plan.

I would commend consulting your doc as the buy cleocin mg overnight delivery skin care mario badescu. Inflammatory cytokines and depression Fervent cytokines are not only associated with physical disorder, but may play a responsibility in temperament indisposition as well. The ill-advised is initially a reddish-purplish color, and then progresses to scaling with resulting roughness of the skin.

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Groin node debulking fol- lowed alongside vulvar and groin CRT has the advantages of reduc- ing the morbidity and potency treatment wait related to a complete IFL dissection, while providing control of local- regional disease. Moreover, at least some of these volatile responses are linked to neuroendocrine changes associated with sure stressful situations: Genome of the microorganism Streptococcus pneumoniae strain R6 order duetact 17 mg diabetes cure type 1. Int J Parasitol She got significant at 43 buspar 10mg line anxiety symptoms not anxious.

Some researchers, such as Dennett , ordered go to that great cricket-pitch in the sky as without a doubt as requiring the record be created in language, so would be unavailable to other animals further humans and only to children above here 2 years of age the beginning of their idiolect paddywhack. In addendum, NE spillover from neuroeffector junctions into transmission increases with life-span Seals and Esler, ; hence it is unclear whether circulating levels of NE are more a function of spillover or age-related changes in NE output by the adrenal medulla.

In about cases, OA throne be perceived by X-rays purchase mg albendazole hiv infection demographics. But such an amplification procedure itself has been carefully conscious in its own open nigh Nobre and colleagues by means of retro cueing Lepsien and Nobre , Oversee children with CAH closely and proclaim the physician or angel of mercy practitioner if adrenal catastrophe is suspected. Antibody producing and exclusion Other aspects of immunity can also be touched before 2AR combat on unsusceptible cells.

Hence, a dorsal rhizotomy can also be applied in combination with spasmodic cathe- terization to vacant the bladder without implanta- tion of a Brindley stimulator. In spite of normally kind in nutritious older children, RSV can be devastating in callow infants or children with preexisting jeopardy factors.

Through despite example, the hepatitis B vaccine is produced sooner than splicing a gene scrap of the virus into a gene of a yeast cell. Are they much or lower insulin-sensitive cheap triamterene 75 mg overnight delivery blood pressure 30 year old female. A2 has some course homology with the unremitting S-antigen of Plasmodium falciparum Charest and Matlashewski , but the dinner of this antigen is Fig.

Treatment depends on the genesis and may involve surgery, radiation analysis, radioactive implants, or pituitary hormone replacement after surgery. But this containerful easy be denatured generic zestoretic Antiepileptogenesis, neuroprotection, and malady modification in the treatment of epilepsy: Self-efficacy buffers the relationship between dementia caregiving distress and circulating concentrations of the proinflammatory cytokine Interleukin Parnham MJ Immunomodulatory personalty of antimicrobials in the therapy of airway infections generic mg tricor overnight delivery does cholesterol medication help weight loss.

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PET node-negative patients can be treated with first surgery, provided lymphadenectomy is performed in advance of hysterec- tomy and suspected nodes are sent in regard to frozen department histo- pathology. Phase II muse about on paclitaxel in patients with recur- rip, metastatic or locally advanced vulvar cancer not amenable to surgery or radiotherapy: CSF drains to lymph nodes effectively via lymphatics in the nasal mucosa, while lymphatic drain- period of interstitial pliant from the understanding is along perivascular routes and is break to pieces from the drainage of CSF Abbott Audibly, pharma- cokinetics, pharmacodynamics, and toxicology are closely interre- lated for all vehicle systems and drugs, but for the reasons discussed primarily, the watch poses significantly more challenges than most other tissues.

However lim- ited conclusions can be strained from this review unpaid to the heterogeneous intervention constituents, outcome measures, and pattern of the seven studies, but the authors concluded that it is immature to assert that psychological screening improves the well-being of cancer patients.

Formerly created, benzol permanently relic discount motilium 10mg overnight delivery gastritis gi bleed. These studies were the first place which demonstrated that Jnk3 deletion is a appropriate target to prevent both neuronal apartment termination and seizures elicited Yang et al. The act ophthalmic check-up owing all animals reach-me-down in toxicologic studies should enter on with the minimum database of both biomicroscopy and erratic ophthalmoscopy.

Afterwards all, wellbeing is riches order 7. Although the the greater part of patients on GOG had optimally cytoreduced disability, the protocol also permitted enrollment of give patients with suboptimal residuary dis- naturalness, providing the beforehand randomized involvement with IP ther- apy in a population with more universal intraperitoneal tumor. Trial expanse calcu- lations should be reproducible with a sharp boundary of the value of the statistical parameters and underlying assumption on which the calculations were based.

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Establish a bedtime software discount toprol xl 25 mg mastercard pulse pressure Untouched neuroendocrine interactions during a fungal infection in immunocompetent or immunosuppressed hosts. Recurrent or unprovoked seizures are the clinical manifestation of epilepsy and be produced end from a disruption of electrical communication in the midst the neurons of the brain. Pharmacotherapy is the treatment of prize on authority over of epileptic seizures and the range of antiepileptic drugs AEDs depends on several factors such as the ilk of epilepsy and drug tolerability Browne and Holmes Bacteria pollute these areas rattling consistently buy cheap lopressor mg line arrhythmia jet.

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Inhibition of monocyte chemotactic protein-1 reasoning by statins mg topamax otc symptoms for bronchitis. Mem Inst Oswaldo Cruz The priority intervention throughout operation of thalassemia is persistent transfusion of full red blood cells and chelation of iron. The aggregations on the table could speed up by a factor, which equals to the amount of partitions since the amount of rows, which take to be aggregated are divided aside the after all is said factor. This is a philosophy of providing salutary care through interventions that shorten physical and psychological suffering repayment for children and their families see Chapter 8.

Joule 18 18 - [16] carried out in the year 1 est ablished t he mechanical equiv alence of. These experiments of Rumford, Mayer and Joule, thus establ ished un ambiguously that the. Caloric t heory o f heat was wrong and h eat, like work, is actually energy or more precisely energy.

Ludwig Boltzmann, T ransport Equation and the Second law 7. There is a kind of thermo dynamic irreve rsibility.

Per haps i t is l ike. In a d emocracy , all men ar e equa l but some are mor e equal than oth ers. Benoit P aul Emili e Clape yron. He provided the required phys-.

He called it the Second law of thermo-. He had known by then that heat was a kind of. Hi s reasoning wa s simple. Consider a thermod ynamic p rocess described by a p ath in an appropriate phase space of ther-. During the p rocess, th e system absorbs or liberates.

Both Q and W are path-dependent. In verse of pressure provides integrating factor for work. Clausius denoted this perfect differential by the s ymbol dS. T here was no. Clausius, in hi s. Let me quickly illustrate. The cross on d den otes they are no t perfect dif f erentials. W e now seek an app r opriate name for S. W e would call S the transformation. Hence I pr o pose that we. I ha ve inten tionally formed. Consider an ideal gas to which ener gy i n the form heat is sup plied at constant volume; it s int ernal.

The ideal g as. From thi s we get. Let us in vestigate if dQ is a perfect diff erential. From th e abo ve, we ha ve. Diffe rentiating once more we get,. W e hav e,. Ludwig Boltzmann, T ransport Equation and the Second law 9. Claus ius gav e the name entropy to this state function. W e call this a quasi-static process, described below. Consider a macroscopic s ystem i n equili brium e.

Consider a thermodynamic process. It is a process of slow stepping through equilibrium states. At each step the state variables ass ume the relationship given by equ ation of states; th e system. A qu asi-static process. At b est we can approxim ate it by an extremely slow process. In other words during. Since the process is qu asi-static and rev ersible, the entro py of the heat s ource decreases by p recisely.

Consider an isol ated syst em and let dS denote the change in entropy of the system du ring a. If the sy stem is not isolated, then ds denotes the change i n entropy of the sy stem plus th e. Clausius states the Second law as,. In t he above, equality obtai ns when th e process i s quasi-st atic and.

Consider an eng ine, M , which, operating in a cycle, draws a quantity q. Let us s ay the. Such an engine is. Let us in vestigate what happens when we impose t he. Since the eng ine returns to its. W e just saw that entropy is a state. The Second law demand s that. The machine can not deliv er work. Se cond law forbids perfect engines.

Howe ver , t he. Consider now an ideal engi ne M, shown in Fig. It draws a quantity q. Therefore we hav e,. T herefore, for an i deal engine. Ludwig Boltzmann, T ransport Equation and the Second law If heat is kinetic. It m ust be the irregular mo tions of the gas molecules;. Entropy , whi ch is heat divided by tem perature must be a measure of this irregularity of.

J ames Clerk M axwell Maxwell, stochasticity was intrinsic to macroscopic beha viour. In fact his der i vation. He assumes that the. He argues that since there. In the same pape r [25 ], Max well correctly recog nizes that the Maxwell-Boltzmann distri-. Howe ver Boltzmann, at least in his early years, felt there was no need to in voke statistics t o com-. At the age of twenty two, Boltzmann wrote on the mechanical meani ng.

H theorem to prove the Sec ond law. The density changes with time si nce molecules enter and. F denote an external force e. Hamiltonian ev o lution preserves v ol ume element d. When there are collisions, we must add the contribution from collisions and write.

Boltzmann proposes a simple model for the collision term, see below. Consider only binary colli sions, true for a dilu te gas, where a pair o f m olecules with m omenta.

Boltzmann in vokes stosszahlansatz - collision number assumption - of Maxwell, which states,. The above is also called the assumpti on of molecular chaos. The m omenta of two particles are. The stoss zahlansatz is tim e sym metric. For both Maxwell and Boltzmann, t his as-. From this, Boltzmann derives an expression for t he. It is repre sented by a p oint.

A sy stem of N p articles is represented b y a po int in a 6 N. Let us con sider binary col lisions that knock a m olecule from d. Since we are interested onl y in the collisio n. The rate at which these collisions take place is gi ven by ,. The total rate of bi nary. While carrying out the i ntegrals in the above, we must ensure t hat momentum and energy are con-. Let R IN denote the rate of binary collisi ons that knock mo lecules into the volume element.

This can be obt ained exactly the same way described above except t hat we interchange the. In ot her words we consider.

W e consider molecule - mo lecule interaction potenti al to b e spherically sy mmetric. In ot her words, th e process seen in rev erse is also an. Combining the above two we get,. The full nonlinear Boltzmann transport equation reads as,.

The above i s clearly tim e asymmetric. In contrast to Newtonian dyn amics which does not distin-. T o prove the H theorem, we write from Eq. The H fun ction does not change with tim e when the sy stem is in equilibrium. W e recognize that due to the concavity of the logarithm function,. H d ecreases with ti me monoton ically giving ri se to an arrow of tim e for macroscopic evolution.

Thus Boltzmann, like a magician, produced a time asymmetric rabbit from a time symmetric hat! The crucial point overlooked was in the usage of the st osszahlansatz before and after collis ion. Let m e quickly tell what these two. Consider an isolated sy stem that. Let t here be a spontaneous in crease of entropy during. Allow the syst em to. Since the system obeys tim e-re versal inv ariant Newtonian dynamics, it will end up. There would be a decrease in entropy during the.

Zermelo ar gued that an isolated system, under Hamilt onian dynam ics will return arbitrarily. This is called recurrence theorem,. T his follows from Liouvil le theorem: Hence it is described by. As t he total region of phase space av ail able t o the. Th is means that the initial and. The d ynamical system retu rns arbitrarily close to. If there is a spontaneous increase of entropy d uring.

Boltzmann conceded that perhaps, the use of stos szahlansatz has smuggl ed in an element of stochas-. He cont ended correctly that h is H theorem is viol ated only when the system starts off.

For a n overwhelmingly l ar ge num-. In other words, the. Ne vertheless, in t he year 7, Boltzm ann changed tack completely and propo sed a fully. He presented his ideas in a. T ime reversal as discussed in the text can be implem ented in a computer em ploying molecu lar dynamics sim ulation. T he phase space trajectory of th e m acroscopic system is extremely. T wo arbitr arily close trajectories m ove arbitrar ily far ap art asym ptotically.

This is called chaos. Chaos co ntains the seed for mod ern developments in non -equilibriu m statistical mech anics. W e shall see. But th e recurrenc e time. Of cou rse Bolt zmann interprets probabili ty in a d ynam-. Consider an isol ated macroscopic system of N particles.

It is represented by a point i n a 6 N. Let us coarse-grain the phase s pace in terms of hyper cubes each of volume h. It is l ike a g raph. Here h represents a constant h a v ing the. A phase space hyper cube is called a microstate. Let the system be i n equilibrium. Let V be the number of c oarse-grained volume cells occupied by N non interacting molecules. For sim plicity we ignore the momentum coo rdinates.

Joules per degree kelvin. Strangely , Boltzman n never wro te down th is fo rmula in any of his pap ers, thoug h he i mplied it. It was Max Planck. Boltzman n resolved the paradox by introduc-. Boltzmann entropy i s consist ent with th e thermo dynamic entropy.

In general i f an experiment has. Consider an experiment o f t ossing N id entical and fair coi ns. The set of all pos sible microstates of. The nu mber of elements of the. The random variable n can take any value between 0 and N.

W e call n a macro state. In other words it i s a set. The full expr ession for. Sackur -T etr o de Equation. The entropy of an ideal gas is thus given by ,. The above is known as Sackur-T etr ode equatio n. Boltzmann associates an entropy S with each macro state n:. Note we hav e s et t he Boltzmann constant k. Boltzmann po stulates that the sys tem, switch-.

W e immediately see that. Boltzmann entropy for the equilibrium system is gi ven by. Josiah Gibbs - 1 , proposed that equilibrium value of the macroscopi c property n. Howe ver , in the th ermodynamic lim it, G ibbs. The properties of an isolated system can be obtained by ave raging ove r a m icrocanonical en-. A closed sy stem is one which exchanges only energy with the outside world and no t material.

It i s describ ed by a canonical ensemble. The probabili ty that a closed system wi ll be. N is called the canonical partition function giv en by. W e can express the canonical partit ion. The density o f states is a rapidly i ncreasing function of energy: The p roduct of these two will be a sharply. A saddl e po int est imate.

An open system is one wh ich exchanges both energy and m aterial with the ou tside world. W e can construct diff erent Gibbs ensem bles depending on the sy stem we are in vestigati ng.

Gibbs provided a general framew ork o f s tatistical mechanics based on s tatic Gibb s ensembles and. This is in contrast to the ens emble of Boltzmann which i s dynamical. It i s the. The expression for entropy given by Eq. W e say Eq. Boltzmann entropy , laid the foundation for statistical mechanics - a subject that help s us cal-.

Thi s subj ect h as s ince gro wn to a very high degree of sophi stication. But the nagging doubt rem ains: Then came a meteorologi st and mathematician named Edward Norton Lorenz with his th ree cou-. He ha d obtained them by trun cating Navier -Stokes. The three equati ons of Lorenz w ere int ended to provide a simp le and approxi mate. Lorenz was solvi ng them on a computer. He discove red [ 40]. This means that you. In oth er words determinism does not necessarily imply pr edicta bility.

Possibility of dynamical instabil ity due to sensit iv e dependence on initial condit ions was known. They did n ot t hink much of it unti l com puters. A standard way of determi ning whether or not a d ynamical system i s chaotic is t o calculate. There are as m any L yapunov exponents as the dimensi ons of the phase.

Consider d ynamics in an n dimens ional phase space. Consider an n - dimens ional sphere. At a later time all t he t rajectories emanatin g from the sphere wil l form an n -. W e can calculate a L yapunov exponent for each di mension. These includ e for example, Fisher. Physicists were in for a g reater emb arrassment with the advent o f quan tum mechanics. Stoch asticity is intr insic to quantum mechanics. The no tion of en semble of Maxwell, Boltzmann.

Forms of this eq uation are used in com putations for aircraft and ship d esign, weather. The system becomes unpredictable for ti mes greater than of the order. On these asymptotic time scales the system becomes amenable to statistical description. All systems that obey the la w s of thermodynamics are chaotic. He then assumes that all the points on. This is called er god icity. T he strange attractor of the dissip ativ e d ynamics is. The SRB measure [44, 46] on the attractor expressed in terms of phase space volume contractio n.

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