Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions

The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions. Applying these equations, we give new proofs for some standard identities for the Bernstein basis functions, including formulas for sums, alternating sums, recursion, subdivision, degree raising, differentiation and a formula for the monomials in terms of the Bernstein basis functions. We also derive many new identities for the Bernstein basis functions based on this approach. Moreover, by applying the Laplace transform to the generating functions for the Bernstein basis functions, we obtain some interesting series representations for the Bernstein basis functions.Comment: 1

Three-Dimensional Radiofrequency Tissue Tightening: A Proposed Mechanism and Applications for Body Contouring

The use of radiofrequency energy to produce collagen matrix contraction is presented. Controlling the depth of energy delivery, the power applied, the target skin temperature, and the duration of application of energy at various soft tissue levels produces soft tissue contraction, which is measurable. This technology allows precise soft tissue modeling at multiple levels to enhance the result achieved over traditional suction-assisted lipectomy as well as other forms of energy such as ultrasonic and laser-generated lipolysis

SPECULOOS exoplanet search and its prototype on TRAPPIST

One of the most significant goals of modern science is establishing whether life exists around other suns. The most direct path towards its achievement is the detection and atmospheric characterization of terrestrial exoplanets with potentially habitable surface conditions. The nearest ultracool dwarfs (UCDs), i.e. very-low-mass stars and brown dwarfs with effective temperatures lower than 2700 K, represent a unique opportunity to reach this goal within the next decade. The potential of the transit method for detecting potentially habitable Earth-sized planets around these objects is drastically increased compared to Earth-Sun analogs. Furthermore, only a terrestrial planet transiting a nearby UCD would be amenable for a thorough atmospheric characterization, including the search for possible biosignatures, with near-future facilities such as the James Webb Space Telescope. In this chapter, we first describe the physical properties of UCDs as well as the unique potential they offer for the detection of potentially habitable Earth-sized planets suitable for atmospheric characterization. Then, we present the SPECULOOS ground-based transit survey, that will search for Earth-sized planets transiting the nearest UCDs, as well as its prototype survey on the TRAPPIST telescopes. We conclude by discussing the prospects offered by the recent detection by this prototype survey of a system of seven temperate Earth-sized planets transiting a nearby UCD, TRAPPIST-1.Comment: Submitted as a chapter in the "Handbook of Exoplanets" (editors: H. Deeg & J.A. Belmonte; Section Editor: N. Narita). 16 pages, 4 figure

Genome Sizes and the Benford Distribution

BACKGROUND: Data on the number of Open Reading Frames (ORFs) coded by genomes from the 3 domains of Life show the presence of some notable general features. These include essential differences between the Prokaryotes and Eukaryotes, with the number of ORFs growing linearly with total genome size for the former, but only logarithmically for the latter. RESULTS: Simply by assuming that the (protein) coding and non-coding fractions of the genome must have different dynamics and that the non-coding fraction must be particularly versatile and therefore be controlled by a variety of (unspecified) probability distribution functions (pdf's), we are able to predict that the number of ORFs for Eukaryotes follows a Benford distribution and must therefore have a specific logarithmic form. Using the data for the 1000+ genomes available to us in early 2010, we find that the Benford distribution provides excellent fits to the data over several orders of magnitude. CONCLUSIONS: In its linear regime the Benford distribution produces excellent fits to the Prokaryote data, while the full non-linear form of the distribution similarly provides an excellent fit to the Eukaryote data. Furthermore, in their region of overlap the salient features are statistically congruent. This allows us to interpret the difference between Prokaryotes and Eukaryotes as the manifestation of the increased demand in the biological functions required for the larger Eukaryotes, to estimate some minimal genome sizes, and to predict a maximal Prokaryote genome size on the order of 8-12 megabasepairs. These results naturally allow a mathematical interpretation in terms of maximal entropy and, therefore, most efficient information transmission

The Functional DRD3 Ser9Gly Polymorphism (rs6280) Is Pleiotropic, Affecting Reward as Well as Movement

Abnormalities of motivation and behavior in the context of reward are a fundamental component of addiction and mood disorders. Here we test the effect of a functional missense mutation in the dopamine 3 receptor (DRD3) gene (ser9gly, rs6280) on reward-associated dopamine (DA) release in the striatum. Twenty-six healthy controls (HCs) and 10 unmedicated subjects with major depressive disorder (MDD) completed two positron emission tomography (PET) scans with [11C]raclopride using the bolus plus constant infusion method. On one occasion subjects completed a sensorimotor task (control condition) and on another occasion subjects completed a gambling task (reward condition). A linear regression analysis controlling for age, sex, diagnosis, and self-reported anhedonia indicated that during receipt of unpredictable monetary reward the glycine allele was associated with a greater reduction in D2/3 receptor binding (i.e., increased reward-related DA release) in the middle (anterior) caudate (p<0.01) and the ventral striatum (p<0.05). The possible functional effect of the ser9gly polymorphism on DA release is consistent with previous work demonstrating that the glycine allele yields D3 autoreceptors that have a higher affinity for DA and display more robust intracellular signaling. Preclinical evidence indicates that chronic stress and aversive stimulation induce activation of the DA system, raising the possibility that the glycine allele, by virtue of its facilitatory effect on striatal DA release, increases susceptibility to hyperdopaminergic responses that have previously been associated with stress, addiction, and psychosis

A new implicit review instrument for measuring quality of care delivered to pediatric patients in the emergency department

BackgroundThere are few outcomes experienced by children receiving care in the Emergency Department (ED) that are amenable to measuring for the purposes of assessing of quality of care. The purpose of this study was to develop, test, and validate a new implicit review instrument that measures quality of care delivered to children in EDs.MethodsWe developed a 7-point structured implicit review instrument that encompasses four aspects of care, including the physician's initial data gathering, integration of information and development of appropriate diagnoses; initial treatment plan and orders; and plan for disposition and follow-up. Two pediatric emergency medicine physicians applied the 5-item instrument to children presenting in the highest triage category to four rural EDs, and we assessed the reliability of the average summary scores (possible range of 5-35) across the two reviewers using standard measures. We also validated the instrument by comparing this mean summary score between those with and without medication errors (ascertained independently by two pharmacists) using a two-sample t-test.ResultsWe reviewed the medical records of 178 pediatric patients for the study. The mean and median summary score for this cohort of patients were 27.4 and 28.5, respectively. Internal consistency was high (Cronbach's alpha of 0.92 and 0.89). All items showed a significant (p &lt; 0.005) positive correlation between reviewers using the Spearman rank correlation (range 0.24 to 0.39). Exact agreement on individual items between reviewers ranged from 70.2% to 85.4%. The Intra-class Correlation Coefficient for the mean of the total summary score across the two reviewers was 0.65. The validity of the instrument was supported by the finding of a higher score for children without medication errors compared to those with medication errors which trended toward significance (mean score = 28.5 vs. 26.0, p = 0.076).ConclusionThe instrument we developed to measure quality of care provided to children in the ED has high internal consistency, fair to good inter-rater reliability and inter-rater correlation, and high content validity. The validity of the instrument is supported by the fact that the instrument's average summary score was lower in the presence of medication errors, which trended towards statistical significance

Quantitative estimation of tissue blood flow rate

The rate of blood flow through a tissue (F) is a critical parameter for assessing the functional efficiency of a blood vessel network following angiogenesis. This chapter aims to provide the principles behind the estimation of F, how F relates to other commonly used measures of tissue perfusion, and a practical approach for estimating F in laboratory animals, using small readily diffusible and metabolically inert radio-tracers. The methods described require relatively nonspecialized equipment. However, the analytical descriptions apply equally to complementary techniques involving more sophisticated noninvasive imaging. Two techniques are described for the quantitative estimation of F based on measuring the rate of tissue uptake following intravenous administration of radioactive iodo-antipyrine (or other suitable tracer). The Tissue Equilibration Technique is the classical approach and the Indicator Fractionation Technique, which is simpler to perform, is a practical alternative in many cases. The experimental procedures and analytical methods for both techniques are given, as well as guidelines for choosing the most appropriate method

Rhesus macaques as a tractable physiological model of human ageing

This is the author accepted manuscript. The final version is available from the Royal Society via the DOI in this recordResearch in the basic biology of ageing is increasingly identifying mechanisms and modifiers of ageing in short-lived organisms such as worms and mice. The ultimate goal of such work is to improve human health, particularly in the growing segment of the population surviving into old age. Thus far, few interventions have robustly transcended species boundaries in the laboratory, suggesting that changes in approach are needed to avoid costly failures in translational human research. In this review, we discuss both well-established and alternative model organisms for ageing research and outline how research in nonhuman primates is sorely needed, first, to translate findings from shorter-lived organisms to humans, and second, to understand key aspects of ageing that are unique to primate biology. We focus on rhesus macaques as a particularly promising model organism for ageing research due to their social and physiological similarity to humans as well as the existence of key resources that have been developed for this species. As a case study, we compare gene regulatory signatures of ageing in the peripheral immune system between humans and rhesus macaques from a free-ranging study population in Cayo Santiago. We show that both mRNA expression and DNA methylation signatures of immune ageing are broadly shared between macaques and humans, indicating strong conservation of the trajectory of ageing in the immune system. We conclude with a review of key issues in the biology of ageing for which macaques and other nonhuman primates may uniquely contribute valuable insights, including the effects of social gradients on health and ageing. We anticipate that continuing research in rhesus macaques and other nonhuman primates will play a critical role in conjunction with model organism and human biodemographic research in ultimately improving translational outcomes and extending health and longevity in our ageing population.National Institutes of Health (NIH

Measuring macroscopic brain connections in vivo

Decades of detailed anatomical tracer studies in non-human animals point to a rich and complex organization of long-range white matter connections in the brain. State-of-the art in vivo imaging techniques are striving to achieve a similar level of detail in humans, but multiple technical factors can limit their sensitivity and fidelity. In this review, we mostly focus on magnetic resonance imaging of the brain. We highlight some of the key challenges in analyzing and interpreting in vivo connectomics data, particularly in relation to what is known from classical neuroanatomy in laboratory animals. We further illustrate that, despite the challenges, in vivo imaging methods can be very powerful and provide information on connections that is not available by any other means