Towards a mathematical system for extension education

A system of equations describing the relationship of change agent in extension education and client (e.g. a leader of a local community) is presented. The main task of the former is to ensure that he is able to transfer information to the latter, also learning difficulties involved and passing them into institutions of higher learning.

Towards a mathematical system for extension education - II

A brief description is given of a mathematical model for use in extension education regarding fisheries in developing countries.

Explosion pressure prediction via polynomial mathematical correlation based on advanced CFD Modelling

Computational Fluid Dynamics CFD can be used as a powerful tool supporting engineers throughout the steps of the design. The combination of CFD with response surface methodology can play an important role in such cases. During the conceptual engineering design phase, a quick response is always a matter of urgency. During this phase even a sketch of the geometrical model is rare. Therefore, the utilisation of typical response surface developed for congested and confined environment rather than CFD can be an important tool to help the decision making process, when the geometrical model is not available, provided that similarities can be considered when taking into account the characteristic of the geometry in which the response surface was developed. The present work investigates how three different types of response surfaces behave when predicting overpressure in accidental scenarios based on CFD input. First order, partial second order and complete second order polynomial expressions are investigated. The predicted results are compared with CFD findings for a classical offshore experiment conducted by British Gas on behalf of Mobil and good agreement is observed for higher order response surfaces. The higher order response surface calculations are also compared with CFD calculations for a typical offshore module and good agreement is also observed. © 2011 Elsevier Ltd.

Augmented attribute representations

We propose a new learning method to infer a mid-level feature representation that combines the advantage of semantic attribute representations with the higher expressive power of non-semantic features. The idea lies in augmenting an existing attribute-based representation with additional dimensions for which an autoencoder model is coupled with a large-margin principle. This construction allows a smooth transition between the zero-shot regime with no training example, the unsupervised regime with training examples but without class labels, and the supervised regime with training examples and with class labels. The resulting optimization problem can be solved efficiently, because several of the necessity steps have closed-form solutions. Through extensive experiments we show that the augmented representation achieves better results in terms of object categorization accuracy than the semantic representation alone. © 2012 Springer-Verlag.

Representations and algorithms for finite-state bisimulations of linear discrete-time control systems

While a large amount of research over the past two decades has focused on discrete abstractions of infinite-state dynamical systems, many structural and algorithmic details of these abstractions remain unknown. To clarify the computational resources needed to perform discrete abstractions, this paper examines the algorithmic properties of an existing method for deriving finite-state systems that are bisimilar to linear discrete-time control systems. We explicitly find the structure of the finite-state system, show that it can be enormous compared to the original linear system, and give conditions to guarantee that the finite-state system is reasonably sized and efficiently computable. Though constructing the finite-state system is generally impractical, we see that special cases could be amenable to satisfiability based verification techniques. ©2009 IEEE.

Internal representations of temporal statistics and feedback calibrate motor-sensory interval timing.

Humans have been shown to adapt to the temporal statistics of timing tasks so as to optimize the accuracy of their responses, in agreement with the predictions of Bayesian integration. This suggests that they build an internal representation of both the experimentally imposed distribution of time intervals (the prior) and of the error (the loss function). The responses of a Bayesian ideal observer depend crucially on these internal representations, which have only been previously studied for simple distributions. To study the nature of these representations we asked subjects to reproduce time intervals drawn from underlying temporal distributions of varying complexity, from uniform to highly skewed or bimodal while also varying the error mapping that determined the performance feedback. Interval reproduction times were affected by both the distribution and feedback, in good agreement with a performance-optimizing Bayesian observer and actor model. Bayesian model comparison highlighted that subjects were integrating the provided feedback and represented the experimental distribution with a smoothed approximation. A nonparametric reconstruction of the subjective priors from the data shows that they are generally in agreement with the true distributions up to third-order moments, but with systematically heavier tails. In particular, higher-order statistical features (kurtosis, multimodality) seem much harder to acquire. Our findings suggest that humans have only minor constraints on learning lower-order statistical properties of unimodal (including peaked and skewed) distributions of time intervals under the guidance of corrective feedback, and that their behavior is well explained by Bayesian decision theory.

Neural representations of courtship song in the Drosophila brain.

Acoustic communication in drosophilid flies is based on the production and perception of courtship songs, which facilitate mating. Despite decades of research on courtship songs and behavior in Drosophila, central auditory responses have remained uncharacterized. In this study, we report on intracellular recordings from central neurons that innervate the Drosophila antennal mechanosensory and motor center (AMMC), the first relay for auditory information in the fly brain. These neurons produce graded-potential (nonspiking) responses to sound; we compare recordings from AMMC neurons to extracellular recordings of the receptor neuron population [Johnston's organ neurons (JONs)]. We discover that, while steady-state response profiles for tonal and broadband stimuli are significantly transformed between the JON population in the antenna and AMMC neurons in the brain, transient responses to pulses present in natural stimuli (courtship song) are not. For pulse stimuli in particular, AMMC neurons simply low-pass filter the receptor population response, thus preserving low-frequency temporal features (such as the spacing of song pulses) for analysis by postsynaptic neurons. We also compare responses in two closely related Drosophila species, Drosophila melanogaster and Drosophila simulans, and find that pulse song responses are largely similar, despite differences in the spectral content of their songs. Our recordings inform how downstream circuits may read out behaviorally relevant information from central neurons in the AMMC.

Long range exhaustion-a mathematical model for the axisymmetric air flow of a local exhaust ventilation hood assisted by a turbulent radial jet

Abstract-Mathematical modelling techniques are used to predict the axisymmetric air flow pattern developed by a state-of-the-art Banged exhaust hood which is reinforced by a turbulent radial jet flow. The high Reynolds number modelling techniques adopted allow the complexity of determining the hood's air Bow to be reduced and provide a means of identifying and assessing the various parameters that control the air Bow. The mathematical model is formulated in terms of the Stokes steam function, ψ, and the governing equations of fluid motion are solved using finite-difference techniques. The injection flow of the exhaust hood is modelled as a turbulent radial jet and the entrained Bow is assumed to be an inviscid potential flow. Comparisons made between contours of constant air speed and centre-line air speeds deduced from the model and all the available experimental data show good agreement over a wide range of typical operating conditions. | Mathematical modelling techniques are used to predict the axisymmetric air flow pattern developed by a state-of-the-art flanged exhaust hood which is reinforced by a turbulent radial jet flow. The high Reynolds number modelling techniques adopted allow the complexity of determining the hood's air flow to be reduced and provide a means of identifying and assessing the various parameters that control the air flow. The mathematical model is formulated in terms of the Stokes steam function, Ψ, and the governing equations of fluid motion are solved using finite-difference techniques. The injection flow of the exhaust hood is modelled as a turbulent radial jet and the entrained flow is assumed to be an inviscid potential flow. Comparisons made between contours of constant air speed and centre-line air speeds deduced from the model and all the available experimental data show good agreement over a wide range of typical operating conditions.

Cognitive Tomography Reveals Complex, Task-Independent Mental Representations

Humans develop rich mental representations that guide their behavior in a variety of everyday tasks. However, it is unknown whether these representations, often formalized as priors in Bayesian inference, are specific for each task or subserve multiple tasks. Current approaches cannot distinguish between these two possibilities because they cannot extract comparable representations across different tasks [1-10]. Here, we develop a novel method, termed cognitive tomography, that can extract complex, multidimensional priors across tasks. We apply this method to human judgments in two qualitatively different tasks, "familiarity" and "odd one out," involving an ecologically relevant set of stimuli, human faces. We show that priors over faces are structurally complex and vary dramatically across subjects, but are invariant across the tasks within each subject. The priors we extract from each task allow us to predict with high precision the behavior of subjects for novel stimuli both in the same task as well as in the other task. Our results provide the first evidence for a single high-dimensional structured representation of a naturalistic stimulus set that guides behavior in multiple tasks. Moreover, the representations estimated by cognitive tomography can provide independent, behavior-based regressors for elucidating the neural correlates of complex naturalistic priors. © 2013 The Authors.

A simplified mathematical approach for modelling stack ventilation in multi-compartment buildings

A simple mathematical model of stack ventilation flows in multi-compartment buildings is developed with a view to providing an intuitive understanding of the physical processes governing the movement of air and heat through naturally ventilated buildings. Rules of thumb for preliminary design can be ascertained from a qualitative examination of the governing equations of flow, which elucidate the relationships between 'core' variables - flow rates, air temperatures, heat inputs and building geometry. The model is applied to an example three-storey office building with an inlet plenum and atrium. An examination of the governing equations of flow is used to predict the behaviour of steady flows and to provide a number of preliminary design suggestions. It is shown that control of ventilation flows must be shared between all ventilation openings within the building in order to minimise the disparity in flow rates between storeys, and ensure adequate fresh air supply rates for all occupants. © 2013 Elsevier Ltd.