Structured Linearization of Discrete Mechanical Systems for Analysis and Optimal Control

Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they are not energy-preserving they do exhibit long-time stable energy behavior. However, variational integrators often simulate mechanical system dynamics by solving an implicit difference equation at each time step, one that is moreover expressed purely in terms of configurations at different time steps. This paper formulates the first- and second-order linearizations of a variational integrator in a manner that is amenable to control analysis and synthesis, creating a bridge between existing analysis and optimal control tools for discrete dynamic systems and variational integrators for mechanical systems in generalized coordinates with forcing and holonomic constraints. The forced pendulum is used to illustrate the technique. A second example solves the discrete LQR problem to find a locally stabilizing controller for a 40 DOF system with 6 constraints.Comment: 13 page

Neuronal gain modulability is determined by dendritic morphology: a computational optogenetic study

The mechanisms by which the gain of the neuronal input-output function may be modulated have been the subject of much investigation. However, little is known of the role of dendrites in neuronal gain control. New optogenetic experimental paradigms based on spatial profiles or patterns of light stimulation offer the prospect of elucidating many aspects of single cell function, including the role of dendrites in gain control. We thus developed a model to investigate how competing excitatory and inhibitory input within the dendritic arbor alters neuronal gain, incorporating kinetic models of opsins into our modeling to ensure it is experimentally testable. To investigate how different topologies of the neuronal dendritic tree affect the neuron’s input-output characteristics we generate branching geometries which replicate morphological features of most common neurons, but keep the number of branches and overall area of dendrites approximately constant. We found a relationship between a neuron’s gain modulability and its dendritic morphology, with neurons with bipolar dendrites with a moderate degree of branching being most receptive to control of the gain of their input-output relationship. The theory was then tested and confirmed on two examples of realistic neurons: 1) layer V pyramidal cells—confirming their role in neural circuits as a regulator of the gain in the circuit in addition to acting as the primary excitatory neurons, and 2) stellate cells. In addition to providing testable predictions and a novel application of dual-opsins, our model suggests that innervation of all dendritic subdomains is required for full gain modulation, revealing the importance of dendritic targeting in the generation of neuronal gain control and the functions that it subserves. Finally, our study also demonstrates that neurophysiological investigations which use direct current injection into the soma and bypass the dendrites may miss some important neuronal functions, such as gain modulation

A Groundwater Sampler\u27s Handbook for Pollution Control Department of SIU-C

My honor\u27s project began as an essay on hazardous waste disposal problems, but ended with a radically different product. This Groundwater Sampler\u27s Handbook is a compilation of information that was either disjunctly found throughout Pollution Control\u27s landfill project, non-existent, or unthought of

Mapping the ratio of agricultural inputs to yields reveals areas with potentially less sustainable farming

Fertilisers and pesticides are major sources of the environmental harm that results from farming, yet it remains difficult to target reductions in their impacts without compromising food production. We suggest that calculating the ratio of agrochemical inputs to yield can provide an indication of the potential sustainability of farmland, with those areas that have high input relative to yield being considered as less sustainable. Here we design an approach to characterise such Input to Yield Ratios (IYR) for four inputs that can be plausibly linked to environmental impacts: the cumulative risk resulting from pesticide exposure for honeybees and for earthworms, and the amount of nitrogen or phosphorus fertiliser applied per unit area. We capitalise on novel national-scale data to assess IYR for wheat farming across all of England. High-resolution spatial patterns of IYR differed among the four inputs, but hotspots, where all four IYRs were high, were in key agricultural regions not usually characterised as having low suitability for cropping. By scaling the magnitude of each input against crop yield, the IYR does not penalise areas of high yield with higher inputs (important for food production), or areas with low yields but which are achieved with low inputs (important as low impact areas). Instead, the IYR provides a globally applicable framework for evaluating the broad patterns of trade-offs between production and environmental risk, as an indicator of the potential for harm, over large scales. Its use can thus inform targeting to improve agricultural sustainability, or where one might switch to other land uses such as ecosystem restoration

The effectiveness, acceptability and cost-effectiveness of psychosocial interventions for maltreated children and adolescents: an evidence synthesis.

BACKGROUND: Child maltreatment is a substantial social problem that affects large numbers of children and young people in the UK, resulting in a range of significant short- and long-term psychosocial problems. OBJECTIVES: To synthesise evidence of the effectiveness, cost-effectiveness and acceptability of interventions addressing the adverse consequences of child maltreatment. STUDY DESIGN: For effectiveness, we included any controlled study. Other study designs were considered for economic decision modelling. For acceptability, we included any study that asked participants for their views. PARTICIPANTS: Children and young people up to 24 years 11 months, who had experienced maltreatment before the age of 17 years 11 months. INTERVENTIONS: Any psychosocial intervention provided in any setting aiming to address the consequences of maltreatment. MAIN OUTCOME MEASURES: Psychological distress [particularly post-traumatic stress disorder (PTSD), depression and anxiety, and self-harm], behaviour, social functioning, quality of life and acceptability. METHODS: Young Persons and Professional Advisory Groups guided the project, which was conducted in accordance with Cochrane Collaboration and NHS Centre for Reviews and Dissemination guidance. Departures from the published protocol were recorded and explained. Meta-analyses and cost-effectiveness analyses of available data were undertaken where possible. RESULTS: We identified 198 effectiveness studies (including 62 randomised trials); six economic evaluations (five using trial data and one decision-analytic model); and 73 studies investigating treatment acceptability. Pooled data on cognitive-behavioural therapy (CBT) for sexual abuse suggested post-treatment reductions in PTSD [standardised mean difference (SMD) -0.44 (95% CI -4.43 to -1.53)], depression [mean difference -2.83 (95% CI -4.53 to -1.13)] and anxiety [SMD -0.23 (95% CI -0.03 to -0.42)]. No differences were observed for post-treatment sexualised behaviour, externalising behaviour, behaviour management skills of parents, or parental support to the child. Findings from attachment-focused interventions suggested improvements in secure attachment [odds ratio 0.14 (95% CI 0.03 to 0.70)] and reductions in disorganised behaviour [SMD 0.23 (95% CI 0.13 to 0.42)], but no differences in avoidant attachment or externalising behaviour. Few studies addressed the role of caregivers, or the impact of the therapist-child relationship. Economic evaluations suffered methodological limitations and provided conflicting results. As a result, decision-analytic modelling was not possible, but cost-effectiveness analysis using effectiveness data from meta-analyses was undertaken for the most promising intervention: CBT for sexual abuse. Analyses of the cost-effectiveness of CBT were limited by the lack of cost data beyond the cost of CBT itself. CONCLUSIONS: It is not possible to draw firm conclusions about which interventions are effective for children with different maltreatment profiles, which are of no benefit or are harmful, and which factors encourage people to seek therapy, accept the offer of therapy and actively engage with therapy. Little is known about the cost-effectiveness of alternative interventions. LIMITATIONS: Studies were largely conducted outside the UK. The heterogeneity of outcomes and measures seriously impacted on the ability to conduct meta-analyses. FUTURE WORK: Studies are needed that assess the effectiveness of interventions within a UK context, which address the wider effects of maltreatment, as well as specific clinical outcomes. STUDY REGISTRATION: This study is registered as PROSPERO CRD42013003889. FUNDING: The National Institute for Health Research Health Technology Assessment programme