Correspondence between geometrical and differential definitions of the sine and cosine functions and connection with kinematics

In classical physics, the familiar sine and cosine functions appear in two forms: (1) geometrical, in the treatment of vectors such as forces and velocities, and (2) differential, as solutions of oscillation and wave equations. These two forms correspond to two different definitions of trigonometric functions, one geometrical using right triangles and unit circles, and the other employing differential equations. Although the two definitions must be equivalent, this equivalence is not demonstrated in textbooks. In this manuscript, the equivalence between the geometrical and the differential definition is presented assuming no a priori knowledge of the properties of sine and cosine functions. We start with the usual length projections on the unit circle and use elementary geometry and elementary calculus to arrive to harmonic differential equations. This more general and abstract treatment not only reveals the equivalence of the two definitions but also provides an instructive perspective on circular and harmonic motion as studied in kinematics. This exercise can help develop an appreciation of abstract thinking in physics.Comment: 6 pages including 1 figur

‘Back to Life’—Using knowledge exchange processes to enhance lifestyle interventions for liver transplant recipients: A qualitative study

Interventions to prevent excessive weight gain after liver transplant are needed. The purpose of the present study was to enhance a specialist post-transplant well-being program through knowledge exchange with end-users.The study used an interactive process of knowledge exchange between researchers, clinicians and health system users. Data were collected as focus groups or telephone interviews and underwent applied thematic analysis.There were 28 participants (age 24-68 years; 64% male). The results identified experiences that may influence decisions around health behaviours during the course of transplant recovery. Three over-arching themes were identified that impact on liver transplant recipients post-transplant health behaviours. These include (i) Finding a coping mechanism which highlighted the need to acknowledge the significant emotional burden of transplant prior to addressing long-term physical wellness; (ii) Back to Life encompassing the desire to return to employment and prioritise family, while co-ordinating the burden of ongoing medical monitoring and self-management and (iii) Tailored, Personalised Care with a preference for health care delivery by transplant specialists via a range of flexible eHealth modalities.This person-centred process of knowledge exchange incorporated experiences of recipients into service design and identified life priorities most likely to influence health behaviours post-transplant. Patient co-creation of services has the potential to improve the integration of knowledge into health systems and future directions will require evaluation of effectiveness and sustainability of patient-centred multidisciplinary service development

Detecting respiratory bacterial communities of wild dolphins: Implications for animal health

Infectious diseases contribute to the vulnerable status of marine mammals, including respiratory illnesses. This study aimed to capture exhaled breath condensate (blow) for microbial identification from wild Indo-Pacific bottlenose dolphins Tursiops aduncus. Individual dolphins were sampled by holding a funnel connected to a 50 ml centrifuge tube over the blowhole of the animal near shore in Shark Bay (SB), Western Australia. Four individuals were sampled on 2 occasions along with seawater samples. Comparative blow and pool water samples were collected from 4 individual common bottlenose dolphins Tursiops truncatus housed in the National Aquarium (NA), Baltimore, Maryland, USA. Bacteria were identified using the V4 region of the 16S rRNA gene from extracted DNA. We identified bacteria independent of seawater in SB dolphins, which included the classes Alphaproteobacteria (26.1%) and Gammaproteobacteria (25.8%); the phyla Bacteroidetes (15.6%) and Fusobacteria (7.2%); and the genera Pseudomonas (11.5%), Pedomicrobium (4.5%), Streptobacillus (3.7%), Phenylobacterium (2.2%) and Sphingomonas (2.1%). There were broad similarities in phyla between SB and NA dolphins yet there were differences between lower taxonomic groups. A number of operational taxonomic units (OTUs) were shared between dolphin individuals, which may be a result of their genetic lineage (siblings or parentage), shared living and social interactions. A number of genera were observed in SB dolphins which have species known to be infectious in marine mammals such as Pseudomonas, Mycoplasma and Streptococcus. This study successfully characterised bacteria from DNA captured in blow from wild dolphins. The ability to capture these communities from individuals in the wild provides a novel health indicator

Genomics reveals historic and contemporary transmission dynamics of a bacterial disease among wildlife and livestock

Whole-genome sequencing has provided fundamental insights into infectious disease epidemiology, but has rarely been used for examining transmission dynamics of a bacterial pathogen in wildlife. In the Greater Yellowstone Ecosystem (GYE), outbreaks of brucellosis have increased in cattle along with rising seroprevalence in elk. Here we use a genomic approach to examine Brucella abortus evolution, cross-species transmission and spatial spread in the GYE. We find that brucellosis was introduced into wildlife in this region at least five times. The diffusion rate varies among Brucella lineages (∼3 to 8 km per year) and over time. We also estimate 12 host transitions from bison to elk, and 5 from elk to bison. Our results support the notion that free-ranging elk are currently a self-sustaining brucellosis reservoir and the source of livestock infections, and that control measures in bison are unlikely to affect the dynamics of unrelated strains circulating in nearby elk populations

Sigma-2 receptors as a biomarker of proliferation in solid tumours

Over the past several years, our group has provided considerable evidence that the expression of sigma-2 (σ2) receptors may serve as a biomarker of tumour cell proliferation. In these in vitro studies, σ2receptors were expressed 8–10 times more in proliferative (P) tumour cells than in quiescent (Q) tumour cells, and the extent and kinetics of their expression were independent of a number of biological, physiological and environmental factors often found in solid tumours. Moreover, the expression of σ2receptors followed both the population growth kinetics when Q-cells were recruited into the P-cell compartment and the proliferative status of human breast tumour cells treated with cytostatic concentrations of tamoxifen. However, these in vitro studies may or may not be indicative of what might occur in solid tumours. In the present study, the σ2receptor P:Q ratio was determined for the cells from subcutaneous 66 (diploid) and 67 (aneuploid) tumours grown in female nude mice. The σ2receptor P:Q ratio of the 66 tumours was 10.6 compared to the σ2receptor P:Q ratio of 9.5 measured for the 66 tissue culture model. The σ2receptor P:Q ratio of the 67 tumours was 4.5 compared to the σ2receptor P:Q ratio of ≈ 8 measured for the 67 tissue culture model. The agreement between the solid tumour and tissue culture data indicates that: (1) the expression of σ2receptors may be a reliable biomarker of the proliferative status of solid tumours and (2) radioligands with both high affinity and high selectivity for σ2receptors may have the potential to non-invasively assess the proliferative status of human solid tumours using imaging techniques such as positron emission tomography or single-photon emission computerized tomography. © 2000 Cancer Research Campaig

Conversion of the Mycotoxin Patulin to the Less Toxic Desoxypatulinic Acid by the Biocontrol Yeast Rhodosporidium kratochvilovae Strain LS11

Se describe en este artículo el descubrimiento de la degradación de la micotoxina patulina por una levaduraThe infection of stored apples by the fungus Penicillium expansum causes the contamination of fruits and fruit-derived products with the mycotoxin patulin, which is a major issue in food safety. Fungal attack can be prevented by beneficial microorganisms, so-called biocontrol agents. Previous time-course thin layer chromatography analyses showed that the aerobic incubation of patulin with the biocontrol yeast Rhodosporidium kratochvilovae strain LS11 leads to the disappearance of the mycotoxin spot and the parallel emergence of two new spots, one of which disappears over time. In this work, we analyzed the biodegradation of patulin effected by LS11 through HPLC. The more stable of the two compounds was purified and characterized by nuclear magnetic resonance as desoxypatulinic acid, whose formation was also quantitated in patulin degradation experiments. After R. kratochvilovae LS11 had been incubated in the presence of 13C-labeled patulin, label was traced to desoxypatulinic acid, thus proving that this compound derives from the metabolization of patulin by the yeast. Desoxypatulinic acid was much less toxic than patulin to human lymphocytes and, in contrast to patulin, did not react in vitro with the thiol-bearing tripeptide glutathione. The lower toxicity of desoxypatulinic acid is proposed to be a consequence of the hydrolysis of the lactone ring and the loss of functional groups that react with thiol groups. The formation of desoxypatulinic acid from patulin represents a novel biodegradation pathway that is also a detoxification process

Genomics of Brucellosis in Wildlife and Livestock of the Greater Yellowstone Ecosystem

Brucellosis, a disease caused by the bacterium Brucella abortus, has recently been expanding its distribution in the Greater Yellowstone Ecosystem (GYE), with increased outbreaks in cattle and rising seroprevalence in elk (Cervus elaphus) over the past decade. Genetic studies suggest elk are a primary source of recent transmission to cattle. However, these studies are based on Variable Number Tandem Repeat (VNTR) data, which are limited in assessing and quantifying transmission among species. The goal of this study was to (i) investigate the introduction history of B. abortus in the GYE, (ii) identify B. abortus lineages associated with host species and/or geographic localities, and (iii) quantify transmission across wildlife and livestock host species and populations. We sequenced B. abortus whole genomes (n= 207) derived from isolates collected from three host species (bison, elk, cattle) over the past 30 years, throughout the GYE. We identified genetic variation among isolates, and applied a spatial diffusion phylogeographic modeling approach that incorporated temporal information from sampling. Based on these data, our results suggest four divergent Brucella lineages, with a time to most recent common ancestor of ~130 years ago, possibly representing a minimum of four brucellosis introductions into the GYE. Two Brucella lineages were generally clustered by geography. Evidence for cross-species transmission was detected among all species, though most events occur within species and herds. Understanding transmission dynamics is imperative for implementing effective control measures and may assist in identifying source populations responsible for past and future brucellosis infections in wildlife and outbreaks in livestock

Interactive molecular dynamics in virtual reality from quantum chemistry to drug binding: An open-source multi-person framework

© 2019 Author(s). As molecular scientists have made progress in their ability to engineer nanoscale molecular structure, we face new challenges in our ability to engineer molecular dynamics (MD) and flexibility. Dynamics at the molecular scale differs from the familiar mechanics of everyday objects because it involves a complicated, highly correlated, and three-dimensional many-body dynamical choreography which is often nonintuitive even for highly trained researchers. We recently described how interactive molecular dynamics in virtual reality (iMD-VR) can help to meet this challenge, enabling researchers to manipulate real-time MD simulations of flexible structures in 3D. In this article, we outline various efforts to extend immersive technologies to the molecular sciences, and we introduce "Narupa," a flexible, open-source, multiperson iMD-VR software framework which enables groups of researchers to simultaneously cohabit real-time simulation environments to interactively visualize and manipulate the dynamics of molecular structures with atomic-level precision. We outline several application domains where iMD-VR is facilitating research, communication, and creative approaches within the molecular sciences, including training machines to learn potential energy functions, biomolecular conformational sampling, protein-ligand binding, reaction discovery using "on-the-fly" quantum chemistry, and transport dynamics in materials. We touch on iMD-VR's various cognitive and perceptual affordances and outline how these provide research insight for molecular systems. By synergistically combining human spatial reasoning and design insight with computational automation, technologies such as iMD-VR have the potential to improve our ability to understand, engineer, and communicate microscopic dynamical behavior, offering the potential to usher in a new paradigm for engineering molecules and nano-architectures