Convergence for PDEs with an arbitrary odd order spatial derivative term

We compute the rate of convergence of forward, backward and central finite difference $\theta$-schemes for linear PDEs with an arbitrary odd order spatial derivative term. We prove convergence of the first or second order for smooth and less smooth initial data

Is the Helmholtz equation really sign-indefinite?

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique at wavenumbers that correspond to eigenvalues of the Laplacian, and thus the variational problem cannot be sign-definite. However, even in cases where the solution is unique for all wavenumbers, the standard variational formulations of the Helmholtz equation are still indefinite when the wavenumber is large. This indefiniteness has implications for both the analysis and the practical implementation of finite element methods. In this paper we introduce new sign-definite (also called coercive or elliptic) formulations of the Helmholtz equation posed in either the interior of a star-shaped domain with impedance boundary conditions, or the exterior of a star-shaped domain with Dirichlet boundary conditions. Like the standard variational formulations, these new formulations arise just by multiplying the Helmholtz equation by particular test functions and integrating by parts

Probabilistic analysis of the upwind scheme for transport

We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we prove that the scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all a>0, for a Lipschitz continuous initial datum. Our analysis provides a new interpretation of the numerical diffusion phenomenon

Sugar-sweetened beverages, obesity, type 2 diabetes mellitus, and cardiovascular disease risk

Obesity has recently emerged as a major global health problem. According to World Health Organization estimates, ≈1.6 billion adults worldwide were overweight (body mass index [BMI] ≥25 kg/m2) and at least 400 million were obese (BMI ≥30 kg/m2) in 2005, numbers that are expected to reach 2.3 billion and 700 million, respectively, by 2015. In the United States, the percentage of overweight and obese adults increased markedly from 47% and 15% in 1976 to 1980 to >66% and 33% in 2005 to 2006, with the greatest proportion of increase seen among non-Hispanic black and Mexican American women.1,2 The implications of excess body weight are far-reaching. Epidemiological studies indicate that overweight and obesity are important risk factors for type 2 diabetes mellitus (T2DM), cardiovascular disease, cancer, and premature death.3 In the United States, healthcare expenditures attributable to overweight and obesity are estimated to be $147 billion or 9.1% of total healthcare costs per year.4 Such excess costs could have serious repercussions for resource-poor countries, which must manage the dual burdens of chronic and infectious disease. In the setting of a pandemic of obesity and related chronic diseases, the American Heart Association recently released a scientific statement recommending reductions in added-sugar intake to no more than 100 to 150 kcal/d for most Americans.5 The statement identified sugar-sweetened beverages (SSBs) as the primary source of added sugars in the American diet.6 Although it has long been suspected that SSBs contribute at least in part to the obesity epidemic, only in recent years have large epidemiological studies been able to substantiate the relationship between SSB consumption and long-term weight gain, T2DM, and cardiovascular risk. It is thought that SSBs contribute to weight gain because of their high added-sugar content, low satiety, and potential incomplete compensation for total energy, leading to increased energy intake.7,8 In addition, because of their high amounts of rapidly absorbable carbohydrates such as various forms of sugar and high-fructose corn syrup (HFCS) and the large quantities consumed, SSBs may increase T2DM and cardiovascular risk independently of obesity as a contributor to a high dietary glycemic load (GL), leading to inflammation, insulin resistance, and impaired β-cell function.9 Fructose from any sugar or HFCS may also increase blood pressure and promote the accumulation of visceral adiposity, dyslipidemia, and ectopic fat deposition because of increased hepatic de novo lipogenesis.10 Here, we review temporal patterns in SSB consumption and clinically relevant effects on obesity, T2DM, and cardiovascular disease risk, emphasizing potential underlying biological mechanisms, clinical implications, and consideration of methodological issues inherent in the literature

Drugs Associated with More Suicidal Ideations Are also Associated with More Suicide Attempts

In randomized controlled trials (RCTs), some drugs, including CB1 antagonists for obesity treatment, have been shown to cause increased suicidal ideation. A key question is whether drugs that increase or are associated with increased suicidal ideations are also associated with suicidal behavior, or whether drug-induced suicidal ideations are unlinked epiphenomena that do not presage the more troubling and potentially irrevocable outcome of suicidal behavior. This is difficult to determine in RCTs because of the rarity of suicidal attempts and completions.To determine whether drugs associated with more suicidal ideations are also associated with more suicide attempts in large spontaneous adverse event (AE) report databases.Generalized linear models with negative binomial distribution were fitted to Food and Drug Administration (FDA) Adverse Event (AE) Reporting System (AERS) data from 2004 to 2008. A total of 1,404,470 AEs from 832 drugs were analyzed as a function of reports of suicidal ideations; other non-suicidal adverse reactions; drug class; proportion of reports from males; and average age of subject for which AE was filed. Drug was treated as the unit of analysis, thus the statistical models effectively had 832 observations.Reported suicide attempts and completed suicides per drug.832 drugs, ranging from abacavir to zopiclone, were evaluated. The 832 drugs, as primary suspect drugs in a given adverse event, accounted for over 99.9% of recorded AERS. Suicidal ideations had a significant positive association with suicide attempts (p<.0001) and had an approximately 131-fold stronger magnitude of association than non-suicidal AERs, after adjusting for drug class, gender, and age.In AE reports, drugs that are associated with increased suicidal ideations are also associated with increased suicidal attempts or completions. This association suggests that drug-induced suicidal ideations observed in RCTs plausibly represent harbingers that presage the more serious suicide attempts and completions and should be a cause for concern

The endocanabinnoid system and diabetes - critical analyses of studies conducted with rimonabant

Rimonabant is the first CB1 receptor inhibitor available in the Brazilian market. This new drug has been approved for the treatment of obese or overweight patients associated with cardiovascular risk factors. In this article it is compared the effects of rimonabant treatment in obese patients with cardiovascular risk factors to usual obesity pharmacological treatment

Impact of a non-restrictive satiating diet on anthropometrics, satiety responsiveness and eating behaviour traits in obese men displaying a high or a low satiety phenotype

The aim of this study was to evaluate the impact of a non-restrictive satiating diet in men displaying various degrees of satiety efficiency. In all, sixty-nine obese men aged 41·5 (sd 5·7) years were randomly assigned to a control (10–15, 55–60 and 30 % energy as protein, carbohydrate and lipid, respectively; n 34) or satiating (20–25, 45–50 and 30–35 % energy as protein, carbohydrate and lipid, respectively; n 35) diet for 16 weeks, and were classified as having a low (LSP) or high (HSP) satiety phenotype. Both diets were consumed ad libitum. Changes in body weight, BMI, percent fat mass, waist circumference, satiety responsiveness and eating behaviour traits were assessed following the intervention. Dropout rates were higher in the control diet (44·1 %) compared with the satiating diet (8·6 %). Decreases in body weight, BMI and waist circumference were significant in both groups, yet HSP individuals lost more body weight than LSP individuals (P=0·048). Decreases in % fat mass were greater in the satiating diet (LSP: −2·1 (sd 2·1) %; P<0·01 and HSP: −3·0 (sd 2·5) %; P<0·001) compared with the control diet (LSP: −1·1 (sd 2·5) % and HSP: −1·3 (sd 2·6) %) (P=0·034). Satiety responsiveness was markedly improved in the satiating diet, whereas no significant changes were observed in the control group. Changes in dietary restraint (+3·3 (sd 2·9) to +7·2 (sd 5·5)), flexible control (+0·9 (sd 1·4) to +2·3 (sd 2·7)), rigid control (+2·2 (sd 1·5) to +2·5 (sd 2·8)), disinhibition (−2·8 (sd 3·7) to −3·2 (sd 2·6)) and susceptibility to hunger (−2·7 (sd 4·1) to −4·6 (sd 3·9)) were similar between the diets. Compared with the control diet, the satiating diet favoured adherence, decreased % fat mass and improved satiety responsiveness in both HSP and LSP individuals

Chimpanzee identification and social network construction through an online citizen science platform

Abstract Citizen science has grown rapidly in popularity in recent years due to its potential to educate and engage the public while providing a means to address a myriad of scientific questions. However, the rise in popularity of citizen science has also been accompanied by concerns about the quality of data emerging from citizen science research projects. We assessed data quality in the online citizen scientist platform Chimp&See, which hosts camera trap videos of chimpanzees (Pan troglodytes) and other species across Equatorial Africa. In particular, we compared detection and identification of individual chimpanzees by citizen scientists with that of experts with years of experience studying those chimpanzees. We found that citizen scientists typically detected the same number of individual chimpanzees as experts, but assigned far fewer identifications (IDs) to those individuals. Those IDs assigned, however, were nearly always in agreement with the IDs provided by experts. We applied the data sets of citizen scientists and experts by constructing social networks from each. We found that both social networks were relatively robust and shared a similar structure, as well as having positively correlated individual network positions. Our findings demonstrate that, although citizen scientists produced a smaller data set based on fewer confirmed IDs, the data strongly reflect expert classifications and can be used for meaningful assessments of group structure and dynamics. This approach expands opportunities for social research and conservation monitoring in great apes and many other individually identifiable species

Optimized schwarz methods for Maxwell equations with discontinuous coefficients

We study non-overlapping Schwarz methods for solving time-harmonic Maxwell’s equations in heterogeneous media. We show that the classical Schwarz algorithm is always divergent when coefficient jumps are present along the interface. In the case of transverse magnetic or transverse electric two dimensional formulations, convergence can be achieved in specific configurations only. We then develop optimized Schwarz methods which can take coefficient jumps into account in their transmission conditions. These methods exhibit rapid convergence, and sometimes converge independently of the mesh parameter, even without overlap. We illustrate our analysis with numerical experiments