Search

The binary Goldbach conjecture asserts that every even integer greater than 2 can be expressed as the sum of two primes. In addition, the ternary Goldbach conjecture states that every odd integer greater than 5 is the sum of three primes. Both conjectures originated in an exchange of letters between Leonhard Euler and Christian Goldbach in 1742. We claim that both Goldbach problems are valid with multiple partitions for every integer greater than 12. We approached the binary Goldbach problem by the second principle of mathematical induction. Based on the inductive hypothesis, we found that every even integer within a finite interval can be expressed as the difference between two primes. This fact allowed us to tackle the inductive step advantageously. Once both Goldbach problems were proved, we were empowered to claim that every even integer can be written infinitely many ways, as the difference between two primes, where the twin-prime conjecture is a particular case. MSC Classification: 11P32 , 11N05

Background: Sexually transmitted infections (STIs) are increasing among adolescents and young adults (AYA) across the United States. However, data are scarce on trends in condom use, number of partners, and other STI risk factors among AYA. The present study evaluated associations between sexual behaviors and STI diagnoses over time among AYA. Methods: We evaluated linked encounters of AYA aged 13–26 attending an urban Northeast public STI clinic from 2013–2017. Demographics, risk behaviors, self-reported past year and lifetime STI, and STI diagnosis during clinic encounter (positive test for urine, oral, or anal chlamydia; urine, oral, or anal gonorrhea; urine trichomonas; HIV; and syphilis) were extracted from electronic health records. We estimated prevalence and performed trend analyses of the repeated cross-sectional data. Cochran–Armitage and Kruskal–Wallis trend test were conducted for categorical and continuous variables, respectively. Results: Among 3822 encounters, clinical STIs demonstrated statistically significant increases including chlamydia (+9%, p = 0.001), gonorrhea (+5%, p = 0.008), and syphilis (+3%, p = 0.006) all of which significantly increased over time, as did any STI (+10%, p < 0.001). HIV and trichomonas rates remained low and unchanged. Self-reported STI increased as well, both past year (+9%) and lifetime (+14%). Greater proportions of AYA reported multiple partners (+9%, p < 0.001), and condomless oral (+12%, p = 0.001) and vaginal/anal (+7%, p = 0.001) sex. Conclusion: Among AYA presenting to a STI clinic, the proportion who engaged in condomless sex and had multiple partners increased over a 5 year period, which corresponded to increased STI prevalence during this period. Preventions efforts for AYA should continue to emphasize the importance of condoms and partner selection.

Many studies have described the detrimental effect of lack of health insurance on trauma-related outcomes. It is unclear, though, whether these effects are related to pre-injury health status, access to trauma centers, or differences in quality of care after presentation. The aim of this study was to determine if patient and insurance type affect outcomes after trauma surgery.We conducted a retrospective chart review of prospectively collected data at the American College of Surgeons level 1 trauma registry in Rhode Island. All blunt trauma patients aged 18-45 observed from 2004 to 2014 were included. Patients were divided into one of four groups on the basis of their type of insurance: Private/commercial, Medicare, Medicaid, and uninsured. Co-morbidities and infections were recorded. Analysis of variance or the Mann-Whitney U test, as appropriate, was used to analyze the data.A total of 8,018 patients were included. Uninsured patients were more likely to be male and younger, whereas the Medicare patient group had significantly fewer male patients. Rates of co-morbidities were highest in the Medicare group (28.1%) versus the private insurance (16.7%), Medicaid (19.9%), and uninsured (12.9%) groups (p 0.05). However, among patients with any co-morbidity, there was no difference in the average number of co-morbidities between insurance groups. The rate of infection was highest in Medicaid patients (7.7%) versus private (5.6%), Medicare (6.3%), and uninsured (4.3%) patients (p 0.05). Only Medicaid was associated with a significantly greater risk of developing a post-injury infection (odds ratio 1.6; 95% confidence interval 1.1-2.3).The presence of insurance, namely Medicaid, does not equate to diagnosis and management of conditions that affect trauma outcomes. Medicaid is associated with worse pre-trauma health maintenance and a greater risk of infection.

Recent studies have linked postoperative serum troponin elevation to mortality in a range of different clinical scenarios. To date, there has been no investigation into the significance of preoperative troponin elevation in emergency general surgery (EGS) patients. We define this as preoperative myocardial injury (PMI). We hypothesize that PMI seen in EGS patients may predict postoperative morbidity and mortality.Using the American College of Surgeons (ACS) National Surgical Quality Improvement Program (NSQIP) database, we performed a retrospective review of all EGS cases between 2008 and 2014. Patients with preoperative troponin I drawn were compared.There were 464 EGS patients who had troponin I measurements preoperatively. Eighty-two (18%) had preoperative troponin elevations. Patients with PMI were more likely to have the following preoperative physiologic derangements: acute renal failure (18% vs 4%; p = 0.002) and septic shock (40% vs 13%; p0.001). Patient comorbidities associated with PMI included congestive heart failure (13% vs 3%; p = 0.007), dialysis dependence (16% vs 3%; p = 0.002), and American Society of Anesthesiologists (ASA) class ≥ 4 (52% vs 29%; p0.001). Compared with controls, patients with PMI had higher rates of postoperative events (77% vs 52%; p0.001) and mortality (34% vs 13%; p = 0.009). Univariate analysis showed that patients with PMI had an increased risk of postoperative events (odds ratio [OR] 3.02; 95% CI 1.74 to 5.25) and mortality (OR 3.53; 95% CI 1.66 to 7.47). Multivariate analysis revealed preoperative troponin I elevation was an independent predictor of mortality (OR 3.03; 95% CI 1.19 to 7.72, p = 0.020).Emergency general surgery patients with PMI are at increased risk for postoperative events and death. Preoperative myocardial injury is an independent predictor of mortality and has prognostic utility that can prepare surgical teams for adverse events so that they can be recognized, evaluated, and treated earlier.

Trauma remains a leading cause of death and long term-morbidity. We have shown that patients who sustain traumatic injuries are at increased risk for the development of infectious complications. Psychiatric illnesses (PIs) are also noted to occur frequently among the general population. The presence of a PI has been shown to be a risk factor for the development of infections. Despite the prevalence of both traumatic injuries and psychiatric diseases, there are little data relating the impact of PI on the outcome of patients with trauma. We hypothesize that the presence of a PI will be associated with an increased risk of an infection developing after injury.This is a five year retrospective chart review of all admitted patients with trauma age 18 years and older. Patients with and without a major psychiatric illness were compared. Demographic data, mechanism of injury and Injury Severity Score (ISS) were reviewed. Co-morbidities included diabetes mellitus, obesity, pre-injury steroid use, and International Classification of Diseases, 9th edition, based psychiatric illness. All infections were diagnosed by microbiologic criteria (urinary tract infection [UTI], ventilator-associated pneumonia) or Centers for Disease Control and Prevention criteria for clinically evident infections (surgical site infection).Of the 11,147 admitted trauma patients, 14.5% had a pre-injury PI diagnosis. The PI patients were older (61.5 ± 0.5 vs. 54.3; p 0.001), more often female (56% vs. 39.1%; p 0.001), and had no difference in blunt mechanism rates (88.4% vs. 89.9%; p = 0.06) or median ISS (9 vs. 9; p = 0.06). There was no difference between PI and non-PI patients in pre-injury diabetes mellitus (13.4% vs. 12.7%; p = 0.4), steroid use (2.5% vs. 1.9%; p = 0.1), but patients with PI were more likely to be obese (15.7% vs. 13.6%; p = 0.03). Patients with PI were more likely to have an infection develop (10.4% vs. 7.5%; p 0.001). The most common infection in both groups was UTI (6.9% vs. 4.2%; p 0.001). Compared with non-PI patients, adjusting for age, gender, ISS, diabetes mellitus, and obesity, patients with PI were more likely to have an infection develop (odds ratio 1.3, 95% confidence interval = 1.1-1.5) Conclusions: Patients with an underlying PI are at increased risk of having a UTI after traumatic injury. This study identifies a previously unknown independent risk factor for UTIs in patients with trauma. This stresses the need for increased awareness and attention to this vulnerable population.

A proportion of trauma patients present for evaluation in a delayed fashion after injury, likely due to a variety of medical and nonmedical reasons. There has been little investigation into the characteristics and outcomes of trauma patients who present delayed. We hypothesize that trauma patients who present in a delayed fashion are a unique population at risk of increased trauma-related complications.This was a retrospective review from 2010-2015 at a Level I trauma center. Patients were termed delayed if they presented24 hours after injury. Patients admitted within 24 hours of their injury were the comparison group. Charts were reviewed for demographics, mechanism, comorbidities, complications and outcomes. A subgroup analysis was done on patients who suffered falls.During the 5-y period, 11,705 patients were admitted. A total of 588 patients (5%) presented24 h after their injury. Patients in the delayed group were older (65 versus 55 y, P 0.001) and more likely to have psychiatric comorbidities (33% vs. 24%, P = 0.0001) than the control group. They were also more likely to suffer substance withdrawal (8.9% vs. 4.1%, P 0.001) but had toxicology testing for drugs and alcohol done at significantly lower rates. Patients that presented delayed after falls were similar in age and injury severity score (ISS) but more likely to suffer substance withdrawal when compared to those with falls that presented within 24 hours. Patients with falls that presented delayed had toxicology testing at significantly lower rates than the comparison group.Trauma patients that present to the hospital in a delayed fashion have unique characteristics and are more likely to suffer negative outcomes including substance withdrawal. Future goals will include exploring strategies for early intervention, such as automatic withdrawal monitoring and social work referral for all patients who present in a delayed fashion.

Participatory evaluation is a process in which evaluation experts and members of a community who are not experts in evaluation evaluate community actions or projects jointly and on the same level. Participatory evaluation is a community development strategy. In this paper, we analyse the relationship between participatory evaluation and community development processes via three case studies in which participatory evaluation processes are instigated within community development plans. The results show that participatory evaluation is a useful working methodology not only for evaluating community development processes in a participatory way but also in generating learning that can contribute to empowering the people and communities involved in it

Brazil has pursued a mix of policy interventions in the fuel sector to achieve multiple objectives of economic and social development, promoting biofuels and reducing dependence on oil. We develop a welfare economic framework to analyze the rationale the fuel policy choices in Brazil and to analyze the trade-offs they have engendered in the fuel and sugar sectors. We also examine their distributional impacts on producers and consumers in the sugar, oil and biofuel sectors and on government revenues. Additionally, we undertake a normative analysis for the purpose of comparing the welfare and environmental impacts of existing policies with those justified by the goal of maximizing social welfare and addressing market failure. The ex-post analysis of the outcomes for different stakeholders in the fuel and sugar sectors provides insights on the likely political-economic factors guiding policy choices. We find that the status quo policies are likely to have been motivated by the objectives of exporting oil, raising government revenue and promoting rural development through the sugarcane sector and have had a significant adverse effect on fuel and sugar consumers and aggregate social welfare in Brazil.

We evaluated the accuracy of real-time 3D-TEE (RT3DTEE) by measuring mitral (MV) and aortic (AV) prosthetic sewing ring diameter and comparing to known prosthesis size. We also compared RT3DTEE accuracy to standard 2DTEE. RT3DTEE and 2DTEE were performed simultaneously in 30 consecutive patients