Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds

∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria. ∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.

Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

An online study combining the constructs from the theory of planned behaviour and protection motivation theory in predicting intention to test for chlamydia in two testing contexts

Chlamydia is a common sexually transmitted infection that has potentially serious consequences unless detected and treated early. The health service in the UK offers clinic-based testing for chlamydia but uptake is low. Identifying the predictors of testing behaviours may inform interventions to increase uptake. Self-tests for chlamydia may facilitate testing and treatment in people who avoid clinic-based testing. Self-testing and being tested by a health care professional (HCP) involve two contrasting contexts that may influence testing behaviour. However, little is known about how predictors of behaviour differ as a function of context. In this study, theoretical models of behaviour were used to assess factors that may predict intention to test in two different contexts: self-testing and being tested by a HCP. Individuals searching for or reading about chlamydia testing online were recruited using Google Adwords. Participants completed an online questionnaire that addressed previous testing behaviour and measured constructs of the Theory of Planned Behaviour and Protection Motivation Theory, which propose a total of eight possible predictors of intention. The questionnaire was completed by 310 participants. Sufficient data for multiple regression were provided by 102 and 118 respondents for self-testing and testing by a HCP respectively. Intention to self-test was predicted by vulnerability and self-efficacy, with a trend-level effect for response efficacy. Intention to be tested by a HCP was predicted by vulnerability, attitude and subjective norm. Thus, intentions to carry out two testing behaviours with very similar goals can have different predictors depending on test context. We conclude that interventions to increase self-testing should be based on evidence specifically related to test context.

Sensitivity and Bias within the Binary Signal Detection Theory, BSDT

Similar to classic Signal Detection Theory (SDT), recent optimal Binary Signal Detection Theory (BSDT) and based on it Neural Network Assembly Memory Model (NNAMM) can successfully reproduce Receiver Operating Characteristic (ROC) curves although BSDT/NNAMM parameters (intensity of cue and neuron threshold) and classic SDT parameters (perception distance and response bias) are essentially different. In present work BSDT/NNAMM optimal likelihood and posterior probabilities are analytically analyzed and used to generate ROCs and modified (posterior) mROCs, optimal overall likelihood and posterior. It is shown that for the description of basic discrimination experiments in psychophysics within the BSDT a ‘neural space’ can be introduced where sensory stimuli as neural codes are represented and decision processes are defined, the BSDT’s isobias curves can simultaneously be interpreted as universal psychometric functions satisfying the Neyman-Pearson objective, the just noticeable difference (jnd) can be defined and interpreted as an atom of experience, and near-neutral values of biases are observers’ natural choice. The uniformity or no-priming hypotheses, concerning the ‘in-mind’ distribution of false-alarm probabilities during ROC or overall probability estimations, is introduced. The BSDT’s and classic SDT’s sensitivity, bias, their ROC and decision spaces are compared.

The human hippocampus:structure, function and its significance in neuropsychology and disease

This article discusses the structure, anatomical connections, and functions of the hippocampus (HC) of the human brain and its significance in neuropsychology and disease. The HC is concerned with the analysis of highly abstract data derived from all sensory systems but its specific role remains controversial. Hence, there have been three major theories concerning its function, viz., the memory theory, the spatial theory, and the behavioral inhibition system (BIS) theory. The memory theory has its origin in the surgical destruction of the HC, which results in severe anterograde and partial retrograde amnesia. The spatial theory has its origin in the observation that neurons in the HC of animals show activity related to their location within the environment. By contrast, the behavioral inhibition theory suggests that the HC acts as a 'comparator', i.e., it compares current sensory events with expected or predicted events. If a set of expectations continues to be verified then no alteration of behavior occurs. If, however, a 'mismatch' is detected then the HC intervenes by initiating appropriate action by active inhibition of current motor programs and initiation of new data gathering. Understanding the anatomical connections of the hippocampus may lead to a greater understanding of memory, spatial orientation, and states of anxiety in humans. In addition, HC damage is a feature of neurodegenerative diseases such as Alzheimer's disease (AD), dementia with Lewy bodies (DLB), Pick's disease (PiD), and Creutzfeldt-Jakob disease (CJD) and understanding HC function may help to explain the development of clinical dementia in these disorders.

The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12

Discrete Generalization of Gronwall-Bellman Inequality with Maxima and Application

Снежана Христова, Кремена Стефанова, Лиляна Ванкова - В работата са решени няколко нови видове линейни дискретни неравенства, които съдържат максимума на неизвестната функция в отминал интервал от време. Някои от тези неравенства са приложени за изучаване непрекъснатата зависимост от смущения при дискретни уравнения с максимуми.

Probabilistic Models in Cryptography, Coding Theory and Tests for PRNG

2000 Mathematics Subject Classification: 94A29, 94B70

Encouraging the intellectual craft of living research:tattoos, theory and time

This chapter contributes to the anthology on learning to research - researching to learn because it emphases a need to design curricula that enables living research, and on-going researcher development, rather than one that restricts student and staff activities, within a marketised approach towards time. In recent decades higher education (HE) has come to be valued for its contribution to the global economy. Referred to as the neo-liberal university, a strong prioritisation has been placed on meeting the needs of industry by providing a better workforce. This perspective emphasises the role of a degree in HE to secure future material affluence, rather than to study as an on-going investment in the self (Molesworth , Nixon & Scullion, 2009: 280). Students are treated primarily as consumers in this model, where through their tuition fees they purchase a product, rather than benefit from the transformative potential university education offers for the whole of life.Given that HE is now measured by the numbers of students it attracts, and later places into well-paid jobs, there is an intense pressure on time, which has led to a method where the learning experiences of students are broken down into discrete modules. Whilst this provides consistency, students can come to view research processes in a fragmented way within the modular system. Topics are presented chronologically, week-by-week and students simply complete a set of tasks to ‘have a degree’, rather than to ‘be learners’ (Molesworth , Nixon & Scullion, 2009: 277) who are living their research, in relation to their own past, present and future. The idea of living research in this context is my own adaptation of an approach suggested by C. Wright Mills (1959) in The Sociological Imagination. Mills advises that successful scholars do not split their work from the rest of their lives, but treat scholarship as a choice of how to live, as well as a choice of career. The marketised slant in HE thus creates a tension firstly, for students who are learning to research. Mills would encourage them to be creative, not instrumental, in their use of time, yet they are journeying through a system that is structured for a swift progression towards a high paid job, rather than crafted for reflexive inquiry, that transforms their understanding throughout life. Many universities are placing a strong focus on discrete skills for student employability, but I suggest that embedding the transformative skills emphasised by Mills empowers students and builds their confidence to help them make connections that aid their employability. Secondly, the marketised approach creates a problem for staff designing the curriculum, if students do not easily make links across time over their years of study and whole programmes. By researching to learn, staff can discover new methods to apply in their design of the curriculum, to help students make important and creative connections across their programmes of study.

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.

Green's function for paraxial equation

The theory and experimental applications of optical Airy beams are in active development recently. The Airy beams are characterised by very special properties: they are non-diffractive and propagate along parabolic trajectories. Among the striking applications of the optical Airy beams are optical micro-manipulation implemented as the transport of small particles along the parabolic trajectory, Airy-Bessel linear light bullets, electron acceleration by the Airy beams, plasmonic energy routing. The detailed analysis of the mathematical aspects as well as physical interpretation of the electromagnetic Airy beams was done by considering the wave as a function of spatial coordinates only, related by the parabolic dependence between the transverse and the longitudinal coordinates. Their time dependence is assumed to be harmonic. Only a few papers consider a more general temporal dependence where such a relationship exists between the temporal and the spatial variables. This relationship is derived mostly by applying the Fourier transform to the expressions obtained for the harmonic time dependence or by a Fourier synthesis using the specific modulated spectrum near some central frequency. Spatial-temporal Airy pulses in the form of contour integrals is analysed near the caustic and the numerical solution of the nonlinear paraxial equation in time domain shows soliton shedding from the Airy pulse in Kerr medium. In this paper the explicitly time dependent solutions of the electromagnetic problem in the form of time-spatial pulses are derived in paraxial approximation through the Green's function for the paraxial equation. It is shown that a Gaussian and an Airy pulse can be obtained by applying the Green's function to a proper source current. We emphasize that the processes in time domain are directional, which leads to unexpected conclusions especially for the paraxial approximation.

Conceptualizing leadership perceptions as attitudes:using attitude theory to further the understanding of the relation between leadership and outcomes

Leadership is one of the most examined factors in relation to understanding employee wellbeing and performance. While there are disparate approaches to studying leadership, they share a common assumption that perceptions of a leader's behavior determine reactions to the leader. The concept of leadership perception is poorly understood in most theoretical approaches. To address this, we propose that there are many benefits from examining leadership perceptions as an attitude towards the leader. In this review, we show how research examining a number of aspects of attitudes (content, structure and function) can advance understanding of leadership perceptions and how these affect work-related outcomes. Such a perspective provides a more multi-faceted understanding of leadership perceptions than previously envisaged and this can provide a more detailed understanding of how such perceptions affect outcomes. In addition, we examine some of the main theoretical and methodological implications of viewing leadership perceptions as attitudes to the wider leadership area. The cross-fertilization of research from the attitudes literature to understanding leadership perceptions provides new insights into leadership processes and potential avenues for further research. (C) 2015 Elsevier Inc. All rights reserved

Implementing an agent-based model with a spatial visual display in discrete-event simulation software

There has been an increasing interest in the use of agent-based simulation and some discussion of the relative merits of this approach as compared to discrete-event simulation. There are differing views on whether an agent-based simulation offers capabilities that discrete-event cannot provide or whether all agent-based applications can at least in theory be undertaken using a discrete-event approach. This paper presents a simple agent-based NetLogo model and corresponding discrete-event versions implemented in the widely used ARENA software. The two versions of the discrete-event model presented use a traditional process flow approach normally adopted in discrete-event simulation software and also an agent-based approach to the model build. In addition a real-time spatial visual display facility is provided using a spreadsheet platform controlled by VBA code embedded within the ARENA model. Initial findings from this investigation are that discrete-event simulation can indeed be used to implement agent-based models and with suitable integration elements such as VBA provide the spatial displays associated with agent-based software.

Information theory analysis of regenerative channels

In this paper we summarize our recently proposed work on the information theory analysis of regenerative channels. We discuss how the design and the transfer function properties of the regenerator affect the noise statistics and enable Shannon capacities higher than that of the corresponding linear channels (in the absence of regeneration).

Engineering education research - the UK perspective at a time of change

Engineering education in the United Kingdom is at the point of embarking upon an interesting journey into uncharted waters. At no point in the past have there been so many drivers for change and so many opportunities for the development of engineering pedagogy. This paper will look at how Engineering Education Research (EER) has developed within the UK and what differentiates it from the many small scale practitioner interventions, perhaps without a clear research question or with little evaluation, which are presented at numerous staff development sessions, workshops and conferences. From this position some examples of current projects will be described, outcomes of funding opportunities will be summarised and the benefits of collaboration with other disciplines illustrated. In this study, I will account for how the design of task structure according to variation theory, as well as the probe-ware technology, make the laws of force and motion visible and learnable and, especially, in the lab studied make Newton's third law visible and learnable. I will also, as a comparison, include data from a mechanics lab that use the same probe-ware technology and deal with the same topics in mechanics, but uses a differently designed task structure. I will argue that the lower achievements on the FMCE-test in this latter case can be attributed to these differences in task structure in the lab instructions. According to my analysis, the necessary pattern of variation is not included in the design. I will also present a microanalysis of 15 hours collected from engineering students' activities in a lab about impulse and collisions based on video recordings of student's activities in a lab about impulse and collisions. The important object of learning in this lab is the development of an understanding of Newton's third law. The approach analysing students interaction using video data is inspired by ethnomethodology and conversation analysis, i.e. I will focus on students practical, contingent and embodied inquiry in the setting of the lab. I argue that my result corroborates variation theory and show this theory can be used as a 'tool' for designing labs as well as for analysing labs and lab instructions. Thus my results have implications outside the domain of this study and have implications for understanding critical features for student learning in labs. Engineering higher education is well used to change. As technology develops the abilities expected by employers of graduates expand, yet our understanding of how to make informed decisions about learning and teaching strategies does not without a conscious effort to do so. With the numerous demands of academic life, we often fail to acknowledge our incomplete understanding of how our students learn within our discipline. The journey facing engineering education in the UK is being driven by two classes of driver. Firstly there are those which we have been working to expand our understanding of, such as retention and employability, and secondly the new challenges such as substantial changes to funding systems allied with an increase in student expectations. Only through continued research can priorities be identified, addressed and a coherent and strong voice for informed change be heard within the wider engineering education community. This new position makes it even more important that through EER we acquire the knowledge and understanding needed to make informed decisions regarding approaches to teaching, curriculum design and measures to promote effective student learning. This then raises the question 'how does EER function within a diverse academic community?' Within an existing community of academics interested in taking meaningful steps towards understanding the ongoing challenges of engineering education a Special Interest Group (SIG) has formed in the UK. The formation of this group has itself been part of the rapidly changing environment through its facilitation by the Higher Education Academy's Engineering Subject Centre, an entity which through the Academy's current restructuring will no longer exist as a discrete Centre dedicated to supporting engineering academics. The aims of this group, the activities it is currently undertaking and how it expects to network and collaborate with the global EER community will be reported in this paper. This will include explanation of how the group has identified barriers to the progress of EER and how it is seeking, through a series of activities, to facilitate recognition and growth of EER both within the UK and with our valued international colleagues.