The exact sample complexity of PAC-learning problems with unit VC dimension

The Vapnik-Chervonenkis (VC) dimension is a combinatorial measure of a certain class of machine learning problems, which may be used to obtain upper and lower bounds on the number of training examples needed to learn to prescribed levels of accuracy. Most of the known bounds apply to the Probably Approximately Correct (PAC) framework, which is the framework within which we work in this paper. For a learning problem with some known VC dimension, much is known about the order of growth of the sample-size requirement of the problem, as a function of the PAC parameters. The exact value of sample-size requirement is however less well-known, and depends heavily on the particular learning algorithm being used. This is a major obstacle to the practical application of the VC dimension. Hence it is important to know exactly how the sample-size requirement depends on VC dimension, and with that in mind, we describe a general algorithm for learning problems having VC dimension 1. Its sample-size requirement is minimal (as a function of the PAC parameters), and turns out to be the same for all non-trivial learning problems having VC dimension 1. While the method used cannot be naively generalised to higher VC dimension, it suggests that optimal algorithm-dependent bounds may improve substantially on current upper bounds.

Quid pro quo:reflections on the value of problem structuring workshops

Attracting clients who are willing to invest in using a problem structuring method (PSM) can be particularly difficult for the emerging generation of modellers. There are many reasons for this, not least that the benefits of a problem structuring intervention are vague and evidence of benefits are often anecdotal for example, claims of constructing a deeper understanding of the problem or building the commitment of a group to implementing an outcome. This paper contributes to the evaluation of problem structuring methods by reflecting on the quid pro quo that a client and problem structuring modeller can enjoy from collaboration. The paper reflects on 21 cases, where Journey Making (a problem structuring method) was used with 16 organizations to help managers agree a suite of actions to tackle a complex strategic issue. The reflections are clustered around those benefits that pertain to: PSMs in general; PSMs that use computer-supported workshops; the Journey Making methodology.

Building user commitment to implementing a knowledge management strategy

In the IS literature, commitment is typically considered to involve organizational or managerial support for a system and not that of its users. This paper however reports on a field study involving 16 organizations that attempted to build user involvement in developing a knowledge management strategy by having them design it. Twenty-two IT-supported group workshops (involving 183 users) were run to develop action plans for better knowledge management that users would like to see implemented. Each workshop adopted the same problem structuring technique to assist group members develop a politically feasible action plan to which they were psychologically and emotionally dedicated. In addition to reviewing the problem structuring method, this paper provides qualitative insight into the factors a knowledge management strategy should have to encourage user commitment. © 2004 Elsevier B.V. All rights reserved.

Problem structuring methods for large group interventions

Problem structuring methods (PSMs) aim to build shared understanding in a group of decision makers. This shared understanding is used as a basis for them to negotiate an agreed action plan that they are prepared to help implement. Engaging in a social process of negotiation with a large number of people is difficult, and so PSMs have typically focused on small groups of less than 20. This paper explores the legitimacy of deploying PSMs in large groups of people (50–1000), where the aim is to negotiate action and build commitment to its implementation. We review the difficulties of facilitating large groups with PSMs, drawing heavily on our experience of working with over 25 large groups. We offer a range of lessons learned and suggest concrete approaches to facilitating large groups to achieve the objectives of PSMs. This paper contributes to the evaluation and development of PSMs.

Sales manager problem resolution styles:measure development and an examination of their salesperson-related consequences

Personal selling and sales management play a critical role in the short and long term success of the firm, and have thus received substantial academic interest since the 1970s. Sales research has examined the role of the sales manager in some depth, defining a number of key technical and interpersonal roles which sales managers have in influencing sales force effectiveness. However, one aspect of sales management which appears to remain unexplored is that of their resolution of salesperson-related problems. This study represents the first attempt to address this gap by reporting on the conceptual and empirical development of an instrument designed to measure sales managers' problem resolution styles. A comprehensive literature review and qualitative research study identified three key constructs relating to sales managers' problem resolution styles. The three constructs identified were termed; sales manager willingness to respond, sales manager caring, and sales manager aggressiveness. Building on this, existing literature was used to develop a conceptual model of salesperson-specific consequences of the three problem resolution style constructs. The quantitative phase of the study consisted of a mail survey of UK salespeople, achieving a total sample of 140 fully usable responses. Rigorous statistical assessment of the sales manager problem resolution style measures was undertaken, and construct validity examined. Following this, the conceptual model was tested using latent variable path analysis. The results for the model were encouraging overall, and also with regard to the individual hypotheses. Sales manager problem resolution styles were found individually to have significant impacts on the salesperson-specific variables of role ambiguity, emotional exhaustion, job satisfaction, organisational commitment and organisational citizenship behaviours. The findings, theoretical and managerial implications, limitations and directions for future research are discussed.

An evaluation of motivations for studying pharmacy, career commitment and future career plans

It has been predicted that there will be a full time pharmacist workforce shortage of over 15,000 by 2013. It is therefore necessary to recruit more students of a suitable calibre to undergraduate pharmacy degree courses. This study was designed to investigate the motivations of pre-university and MPharm students for studying pharmacy. A series of focus groups was conducted with Year 12 students and a national survey of Year 13, 1st year MPharm and 4th year MPharm students was undertaken. The study found that amongst Year 12 students, pharmacy is perceived as a background profession and was also perceived as being of a lower status than medicine and dentistry. It was concluded that there was a need for greater promotion of pharmacy as a career amongst pre-university students, including the provision of structured work experience placements. Analysis of UCAS applicant data for pharmacy shows that the applicant pool is buoyant and that the majority of applicants are female. Female respondents to the surveys were significantly more likely than males to wish to work part time if they had a family. This could lead to further shortages in the full time workforce. The largest ethnic group of applicants to pharmacy degree courses were Asian. Business ownership and self-employment were motivations for entering the procession of pharmacy and career aims for significantly more Asian than White respondents. Ownership of independent pharmacies is declining and this could be a barrier to future recruitment to pharmacy degree courses. A high degree of interest in locum working may present a problem for continuity in commissioned services within community pharmacy practice. Further work is needed to examine the motivations for working as a locum pharmacist.

Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations.

Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations. © 2005 Springer Science+Business Media, Inc.

Investigating the role of capacitive coupling between the operating table and the return electrode of an electrosurgery unit in the modification of the current density distribution within the patients’ body

Background: Electrosurgery units are widely employed in modern surgery. Advances in technology have enhanced the safety of these devices, nevertheless, accidental burns are still regularly reported. This study focuses on possible causes of sacral burns as complication of the use of electrosurgery. Burns are caused by local densifications of the current, but the actual pathway of current within patient's body is unknown. Numerical electromagnetic analysis can help in understanding the issue. Methods: To this aim, an accurate heterogeneous model of human body (including seventy-seven different tissues), electrosurgery electrodes, operating table and mattress was build to resemble a typical surgery condition. The patient lays supine on the mattress with the active electrode placed onto the thorax and the return electrode on his back. Common operating frequencies of electrosurgery units were considered. Finite Difference Time Domain electromagnetic analysis was carried out to compute the spatial distribution of current density within the patient's body. A differential analysis by changing the electrical properties of the operating table from a conductor to an insulator was also performed. Results: Results revealed that distributed capacitive coupling between patient body and the conductive operating table offers an alternative path to the electrosurgery current. The patient's anatomy, the positioning and the different electromagnetic properties of tissues promote a densification of the current at the head and sacral region. In particular, high values of current density were located behind the sacral bone and beneath the skin. This did not occur in the case of non-conductive operating table. Conclusion: Results of the simulation highlight the role played from capacitive couplings between the return electrode and the conductive operating table. The concentration of current density may result in an undesired rise in temperature, originating burns in body region far from the electrodes. This outcome is concordant with the type of surgery-related sacral burns reported in literature. Such burns cannot be immediately detected after surgery, but appear later and can be confused with bedsores. In addition, the dosimetric analysis suggests that reducing the capacity coupling between the return electrode and the operating table can decrease or avoid this problem. © 2013 Bifulco et al.; licensee BioMed Central Ltd.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

Learning to live with Parkinson’s disease in the family unit:an interpretative phenomenological analysis of well-being

We investigated family members’ lived experience of Parkinson’s disease (PD) aiming to investigate opportunities for well-being. A lifeworld-led approach to healthcare was adopted. Interpretative phenomenological analysis was used to explore in-depth interviews with people living with PD and their partners. The analysis generated four themes: It’s more than just an illness revealed the existential challenge of diagnosis; Like a bird with a broken wing emphasizing the need to adapt to increasing immobility through embodied agency; Being together with PD exploring the kinship within couples and belonging experienced through support groups; and Carpe diem! illuminated the significance of time and fractured future orientation created by diagnosis. Findings were interpreted using an existential-phenomenological theory of well-being. We highlighted how partners shared the impact of PD in their own ontological challenges. Further research with different types of families and in different situations is required to identify services required to facilitate the process of learning to live with PD. Care and support for the family unit needs to provide emotional support to manage threats to identity and agency alongside problem-solving for bodily changes. Adopting a lifeworld-led healthcare approach would increase opportunities for well-being within the PD illness journey.

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.