When is a symmetric pin-jointed framework isostatic?

Maxwell's rule from 1864 gives a necessary condition for a framework to be isostatic in 2D or in 3D. Given a framework with point group symmetry, group representation theory is exploited to provide further necessary conditions. This paper shows how, for an isostatic framework, these conditions imply very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. In particular, it turns out that an isostatic framework in 2D can belong to one of only six point groups. Some conjectures and initial results are presented that would give sufficient conditions (in both 2D and 3D) for a framework that is realized generically for a given symmetry group to be an isostatic framework.Comment: 24 pages, 10 figures; added references, minor changes, revised last paragrap

Maintaining natural spawning timing in Acropora corals following long distance inter-continental transportation.

The majority of research focusing on coral reproductive biology (e.g. spawning timing and synchrony) is carried out in facilities adjacent to reefs that the corals originated from. This is in part because transporting corals for long distances by air leads to sub-lethal stress that may confound the results of any experimental study. However, these constraints often mean research associated with coral reproductive timing is restricted to relatively few locations. To assess the potential for studying environmental drivers of spawning timing in corals in captivity (defined here as ex situ closed aquaria), we aimed to transport 14 large (16-37 cm) Acropora hyacinthus colonies from reefs in Singapore to a closed aquarium system in London (a journey time of ~34 hours). Collection was purposefully timed to occur just before the predicted annual mass spawning event and on the day of transportation it was noted that 12 of the 14 corals contained large visible oocytes. The ‘inverted submersion method’ was applied and the water used for transport was buffered to ensure the colonies remained healthy throughout their travel time. At the end location all colonies were placed into a purpose built aquarium research system which allowed for the approximation of the environmental conditions found on the fringing reefs south of Singapore (the original location). While three colonies appeared partially bleached (visibly pale) and one colony suffered from partial tissue loss, all colonies (i.e. 100% of those collected) were still alive at the time of writing (28 months post collection). More importantly, all corals that were gravid at the time of collection spawned ex situ within the same lunar month as those in the wild (within 3-4 nights of each other). This paper describes the procedures for carrying out long distance transportation of large gravid broadcast spawning coral colonies from reef sites to public aquariums or research facilities around the world for the purpose of ex situ spawning research.N

Brazil Basin Tracer Release Experiment

The purpose of the Brazil Basin Tracer Release Experiment is to measure diapycnal (across isopycnal) mixing and epipycnal (along-isopycnal) mixing and stirring in the deep ocean. This cruise is the fourth in the overall experiment. In the first cruise in early 1996, 110 kg of sulfur hexafluoride (SF6) were released on an isopycnal surface near 4000 meters depth in the eastern part of the basin on the flanks of the Mid-Atlantic Ridge (MAR). The location of the release was near 21.7 S, 18.4 W. The release site was over a zonal valley that leads to the MAR and is about 5000 m deep. The isopycnal surface of the release was defined as the surface on which the potential density anomaly, referenced to 4000 dbar pressure, was 45.9408 kg/m3. The release streaks and results of initial sampling in 1996 are described in Polzin et al. [1997]

Latitudinal variation in monthly-scale reproductive synchrony among Acropora coral assemblages in the Indo-Pacific

Early research into coral reproductive biology suggested that spawning synchrony was driven by variations in the amplitude of environmental variables that are correlated with latitude, with synchrony predicted to break down at lower latitudes. More recent research has revealed that synchronous spawning, both within and among species, is a feature of all speciose coral assemblages, including equatorial reefs. Nonetheless, considerable variation in reproductive synchrony exists among locations and the hypothesis that the extent of spawning synchrony is correlated with latitude has not been formally tested on a large scale. Here, we use data from 90 sites throughout the Indo-Pacific and a quantitative index of reproductive synchrony applied at a monthly scale to demonstrate that, despite considerable spatial and temporal variation, there is no correlation between latitude and reproductive synchrony. Considering the critical role that successful reproduction plays in the persistence and recovery of coral reefs, research is urgently needed to understand the drivers underpinning variation in reproductive synchrony

Latitudinal variation in monthly-scale reproductive synchrony among Acropora coral assemblages in the Indo-Pacific

Early research into coral reproductive biology suggested that spawning synchrony was driven by variations in the amplitude of environmental variables that are correlated with latitude, with synchrony predicted to break down at lower latitudes. More recent research has revealed that synchronous spawning, both within and among species, is a feature of all speciose coral assemblages, including equatorial reefs. Nonetheless, considerable variation in reproductive synchrony exists among locations and the hypothesis that the extent of spawning synchrony is correlated with latitude has not been formally tested on a large scale. Here, we use data from 90 sites throughout the Indo-Pacific and a quantitative index of reproductive synchrony applied at a monthly scale to demonstrate that, despite considerable spatial and temporal variation, there is no correlation between latitude and reproductive synchrony. Considering the critical role that successful reproduction plays in the persistence and recovery of coral reefs, research is urgently needed to understand the drivers underpinning variation in reproductive synchrony

Experimental Treatments for Spinal Cord Injury: What you Should Know

Experiencing a spinal cord injury (SCI) is extremely distressing, both physically and psychologically, and throws people into a complex, unfamiliar world of medical procedures, terminology, and decision making. You may have already had surgery to stabilize the spinal column and reduce the possibility of further damage. You are understandably distressed about the functions you may have lost below the level of spinal injury. You wish to recover any lost abilities as soon as possible. You, your family, or friends may have searched the Internet for treatments and cures

The conceptual and practical ethical dilemmas of using health discussion board posts as research data.

Increasing numbers of people living with a long-term health condition are putting personal health information online, including on discussion boards. Many discussion boards contain material of potential use to researchers; however, it is unclear how this information can and should be used by researchers. To date there has been no evaluation of the views of those individuals sharing health information online regarding the use of their shared information for research purposes

GG-Strands

A $G$-strand is a map $g(t,{s}):\,\mathbb{R}\times\mathbb{R}\to G$ for a Lie group $G$ that follows from Hamilton's principle for a certain class of $G$-invariant Lagrangians. The SO(3)-strand is the $G$-strand version of the rigid body equation and it may be regarded physically as a continuous spin chain. Here, $SO(3)_K$-strand dynamics for ellipsoidal rotations is derived as an Euler-Poincar\'e system for a certain class of variations and recast as a Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as for a perfect complex fluid. For a special Hamiltonian, the $SO(3)_K$-strand is mapped into a completely integrable generalization of the classical chiral model for the SO(3)-strand. Analogous results are obtained for the $Sp(2)$-strand. The $Sp(2)$-strand is the $G$-strand version of the $Sp(2)$ Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical sorting. Numerical solutions show nonlinear interactions of coherent wave-like solutions in both cases. ${\rm Diff}(\mathbb{R})$-strand equations on the diffeomorphism group $G={\rm Diff}(\mathbb{R})$ are also introduced and shown to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc

A clinical prediction model for long-term functional outcome after traumatic spinal cord injury based on acute clinical and imaging factors.

To improve clinicians\u27 ability to predict outcome after spinal cord injury (SCI) and to help classify patients within clinical trials, we have created a novel prediction model relating acute clinical and imaging information to functional outcome at 1 year. Data were obtained from two large prospective SCI datasets. Functional independence measure (FIM) motor score at 1 year follow-up was the primary outcome, and functional independence (score ≥ 6 for each FIM motor item) was the secondary outcome. A linear regression model was created with the primary outcome modeled relative to clinical and imaging predictors obtained within 3 days of injury. A logistic model was then created using the dichotomized secondary outcome and the same predictor variables. Model validation was performed using a bootstrap resampling procedure. Of 729 patients, 376 met the inclusion criteria. The mean FIM motor score at 1 year was 62.9 (±28.6). Better functional status was predicted by less severe initial American Spinal Injury Association (ASIA) Impairment Scale grade, and by an ASIA motor score \u3e50 at admission. In contrast, older age and magnetic resonance imaging (MRI) signal characteristics consistent with spinal cord edema or hemorrhage predicted worse functional outcome. The linear model predicting FIM motor score demonstrated an R-square of 0.52 in the original dataset, and 0.52 (95% CI 0.52,0.53) across the 200 bootstraps. Functional independence was achieved by 148 patients (39.4%). For the logistic model, the area under the curve was 0.93 in the original dataset, and 0.92 (95% CI 0.92,0.93) across the bootstraps, indicating excellent predictive discrimination. These models will have important clinical impact to guide decision making and to counsel patients and families

Developing Peri-Operative Rehabilitation in Degenerative Cervical Myelopathy [AO Spine RECODE-DCM Research Priority Number 6]: An Unexplored Opportunity?

Study Design Narrative review. Objective Degenerative cervical myelopathy is one of the most frequent impairments of the spinal cord encountered internationally in adults. Currently, surgical decompression is the recommended treatment for people with DCM (PwCM) presenting with moderate to severe symptoms or neurological deficits. However, despite surgical intervention, not all patients make a complete recovery due to the irreversible tissue damage within the spinal cord. The objective of this review is to describe the state and gaps in the current literature on rehabilitation for PwCM and possible innovative rehabilitation strategies. Methods Literature search. Results In other neurological disorders such as stroke and acute traumatic spinal cord injury (SCI), timely and strategic rehabilitation has been shown to be indispensable for maximizing functional outcomes, and it is imperative that appropriate perioperative rehabilitative interventions accompany surgical approaches in order to enable the best outcomes. In this review, the current state of knowledge regarding rehabilitation for PwCM is described. Additionally, various therapies that have shown to improve outcomes in comparable neurological conditions such as stroke and SCI which may be translated to DCM will be reviewed. Conclusions We conclude that locomotor training and arm/hand therapy may benefit PwCM. Further, we conclude that body weight support, robotic assistance, and virtual/augmented reality therapies may be beneficial therapeutic analogs to locomotor and hand therapies