Solution of differential equations by application of transformation groups

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations

Application of group and transformation theory to the solution of ordinary and partial differential equations Final report, 17 Jan. 1967 - 16 Jan. 1968

Application of transformation groups to solution of partial differential equation

Application of group and transformation theory to the solution of ordinary and partial differential equations Final report

Lie transformation group for solution of partial differential equation

Active Vision during Action Execution, Observation and Imagery: Evidence for Shared Motor Representations

The concept of shared motor representations between action execution and various covert conditions has been demonstrated through a number of psychophysiological modalities over the past two decades. Rarely, however, have researchers considered the congruence of physical, imaginary and observed movement markers in a single paradigm and never in a design where eye movement metrics are the markers. In this study, participants were required to perform a forward reach and point Fitts’ Task on a digitizing tablet whilst wearing an eye movement system. Gaze metrics were used to compare behaviour congruence between action execution, action observation, and guided and unguided movement imagery conditions. The data showed that participants attended the same task-related visual cues between conditions but the strategy was different. Specifically, the number of fixations was significantly different between action execution and all covert conditions. In addition, fixation duration was congruent between action execution and action observation only, and both conditions displayed an indirect Fitts’ Law effect. We therefore extend the understanding of the common motor representation by demonstrating, for the first time, common spatial eye movement metrics across simulation conditions and some specific temporal congruence for action execution and action observation. Our findings suggest that action observation may be an effective technique in supporting motor processes. The use of video as an adjunct to physical techniques may be beneficial in supporting motor planning in both performance and clinical rehabilitation environments

Roles of Dynein and Dynactin in Early Endosome Dynamics Revealed Using Automated Tracking and Global Analysis

Microtubule-dependent movement is crucial for the spatial organization of endosomes in most eukaryotes, but as yet there has been no systematic analysis of how a particular microtubule motor contributes to early endosome dynamics. Here we tracked early endosomes labeled with GFP-Rab5 on the nanometer scale, and combined this with global, first passage probability (FPP) analysis to provide an unbiased description of how the minus-end microtubule motor, cytoplasmic dynein, supports endosome motility. Dynein contributes to short-range endosome movement, but in particular drives 85–98% of long, inward translocations. For these, it requires an intact dynactin complex to allow membrane-bound p150Glued to activate dynein, since p50 over-expression, which disrupts the dynactin complex, inhibits inward movement even though dynein and p150Glued remain membrane-bound. Long dynein-dependent movements occur via bursts at up to ∼8 µms−1 that are linked by changes in rate or pauses. These peak speeds during rapid inward endosome movement are still seen when cellular dynein levels are 50-fold reduced by RNAi knock-down of dynein heavy chain, while the number of movements is reduced 5-fold. Altogether, these findings identify how dynein helps define the dynamics of early endosomes

Developments in cell biology for quantitative immunoelectron microscopy based on thin sections: a review

Quantitative immunoelectron microscopy uses ultrathin sections and gold particle labelling to determine distributions of molecules across cell compartments. Here, we review a portfolio of new methods for comparing labelling distributions between different compartments in one study group (method 1) and between the same compartments in two or more groups (method 2). Specimen samples are selected unbiasedly and then observed and expected distributions of gold particles are estimated and compared by appropriate statistical procedures. The methods can be used to analyse gold label distributed between volume-occupying (organelle) and surface-occupying (membrane) compartments, but in method 1, membranes must be treated as organelles. With method 1, gold counts are combined with stereological estimators of compartment size to determine labelling density (LD). For volume-occupiers, LD can be expressed simply as golds per test point and, for surface-occupiers, as golds per test line intersection. Expected distributions are generated by randomly assigning gold particles to compartments and expressing observed/expected counts as a relative labelling index (RLI). Preferentially-labelled compartments are identified from their RLI values and by Chi-squared analysis of observed and expected distributions. For method 2, the raw gold particle counts distributed between compartments are simply compared across groups by contingency table and Chi-squared analysis. This identifies the main compartments responsible for the differences between group distributions. Finally, we discuss labelling efficiency (the number of gold particles per target molecule) and describe how it can be estimated for volume- or surface-occupiers by combining stereological data with biochemical determinations

Motor imagery and action observation: cognitive tools for rehabilitation

Rehabilitation, for a large part may be seen as a learning process where old skills have to be re-acquired and new ones have to be learned on the basis of practice. Active exercising creates a flow of sensory (afferent) information. It is known that motor recovery and motor learning have many aspects in common. Both are largely based on response-produced sensory information. In the present article it is asked whether active physical exercise is always necessary for creating this sensory flow. Numerous studies have indicated that motor imagery may result in the same plastic changes in the motor system as actual physical practice. Motor imagery is the mental execution of a movement without any overt movement or without any peripheral (muscle) activation. It has been shown that motor imagery leads to the activation of the same brain areas as actual movement. The present article discusses the role that motor imagery may play in neurological rehabilitation. Furthermore, it will be discussed to what extent the observation of a movement performed by another subject may play a similar role in learning. It is concluded that, although the clinical evidence is still meager, the use of motor imagery in neurological rehabilitation may be defended on theoretical grounds and on the basis of the results of experimental studies with healthy subjects

Best practice for motor imagery: a systematic literature review on motor imagery training elements in five different disciplines

<p>Abstract</p> <p>Background</p> <p>The literature suggests a beneficial effect of motor imagery (MI) if combined with physical practice, but detailed descriptions of MI training session (MITS) elements and temporal parameters are lacking. The aim of this review was to identify the characteristics of a successful MITS and compare these for different disciplines, MI session types, task focus, age, gender and MI modification during intervention.</p> <p>Methods</p> <p>An extended systematic literature search using 24 databases was performed for five disciplines: Education, Medicine, Music, Psychology and Sports. References that described an MI intervention that focused on motor skills, performance or strength improvement were included. Information describing 17 MITS elements was extracted based on the PETTLEP (physical, environment, timing, task, learning, emotion, perspective) approach. Seven elements describing the MITS temporal parameters were calculated: study duration, intervention duration, MITS duration, total MITS count, MITS per week, MI trials per MITS and total MI training time.</p> <p>Results</p> <p>Both independent reviewers found 96% congruity, which was tested on a random sample of 20% of all references. After selection, 133 studies reporting 141 MI interventions were included. The locations of the MITS and position of the participants during MI were task-specific. Participants received acoustic detailed MI instructions, which were mostly standardised and live. During MI practice, participants kept their eyes closed. MI training was performed from an internal perspective with a kinaesthetic mode. Changes in MI content, duration and dosage were reported in 31 MI interventions. Familiarisation sessions before the start of the MI intervention were mentioned in 17 reports. MI interventions focused with decreasing relevance on motor-, cognitive- and strength-focused tasks. Average study intervention lasted 34 days, with participants practicing MI on average three times per week for 17 minutes, with 34 MI trials. Average total MI time was 178 minutes including 13 MITS. Reporting rate varied between 25.5% and 95.5%.</p> <p>Conclusions</p> <p>MITS elements of successful interventions were individual, supervised and non-directed sessions, added after physical practice. Successful design characteristics were dominant in the Psychology literature, in interventions focusing on motor and strength-related tasks, in interventions with participants aged 20 to 29 years old, and in MI interventions including participants of both genders. Systematic searching of the MI literature was constrained by the lack of a defined MeSH term.</p