An optimization problem concerning multiplicative functions

In this paper we study the problem of maximizing a quadratic form 〈Ax,x〉 subject to ‖x‖q=1, where A has matrix entries View the MathML source with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that 0

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

Using problem-based learning in a chemistry practical class for pharmacy students and engaging them with feedback

Objective: To introduce a new approach to problem based learning (PBL) used in the context of medicinal chemistry practical class teaching pharmacy students. Design: The described chemistry practical is based on independent studies by small groups of undergraduate students (4-5), who design their own practical work taking relevant professional standards into account. Students are carefully guided by feedback and acquire a set of skills important to their future profession as healthcare professionals. This model has been tailored to the application of PBL in a chemistry practical class setting for a large student cohort (150 students). Assessment: The achievement of learning outcomes is based on the submission of relevant documentation including a certificate of analysis, in addition to peer assessment. Some of the learning outcomes are also assessed in the final written examination at the end of the academic year. Conclusion: The described design of a novel PBL chemistry laboratory course for pharmacy students has been found to be successful. Self-reflective learning and engagement with feedback were encouraged, and students enjoyed the challenging learning experience. Skills that are highly essential for the students’ future careers as healthcare professionals are promoted.

The housing market channel of monetary policy transmission in the Euro area

Purpose – The purpose of this paper is to explore the role of the housing market in the monetary policy transmission to consumption among euro area member states. It has been argued that the housing market in one country is then important when its mortgage market is well developed. The countries in the euro area follow unitary monetary policy, however, their housing and mortgage markets show some heterogeneity, which may lead to different policy effects on aggregate consumption through the housing market. Design/methodology/approach – The housing market can act as a channel of monetary policy shocks to household consumption through changes in house prices and residential investment – the housing market channel. We estimate vector autoregressive models for each country and conduct a counterfactual analysis in order to disentangle the housing market channel and assess its importance across the euro area member states. Findings – We find little evidence for heterogeneity of the monetary policy transmission through house prices across the euro area countries. Housing market variations in the euro area seem to be better captured by changes in residential investment rather than by changes in house prices. As a result we do not find significantly large house price channels. For some of the countries however, we observe a monetary policy channel through residential investment. The existence of a housing channel may depend on institutional features of both the labour market or with institutional factors capturing the degree of household debt as is the LTV ratio. Originality/value – The study contributes to the existing literature by assessing whether a unitary monetary policy has a different impact on consumption across the euro area countries through their housing and mortgage markets. We disentangle monetary-policy-induced effects on consumption associated with variations on the housing markets due to either house price variations or residential investment changes. We show that the housing market can play a role in the monetary transmission mechanism even in countries with less developed mortgage markets through variations in residential investment.

Housing provision in 21st century Europe

European housing markets exhibited considerable volatility so far in the 21st century while affordability worsened for many. Boom-bust has had greater housing impacts than any specific housing policy, which illustrates the difficulty in policy terms of seeing housing in isolation and the central significance of interlinked relationships between housing, the economy and financial markets. Europe historically invented a powerful set of interventionist tools to alter housing circumstances but, as the overview of rental markets here indicates, today they have mixed success. Examples of what to avoid in policy are at least as common as exemplars.

Spatial housing economics: a survey

This introduction to the Virtual Special Issue surveys the development of spatial housing economics from its roots in neo-classical theory, through more recent developments in social interactions modelling, and touching on the role of institutions, path dependence and economic history. The survey also points to some of the more promising future directions for the subject that are beginning to appear in the literature. The survey covers elements hedonic models, spatial econometrics, neighbourhood models, housing market areas, housing supply, models of segregation, migration, housing tenure, sub-national house price modelling including the so-called ripple effect, and agent-based models. Possible future directions are set in the context of a selection of recent papers that have appeared in Urban Studies. Nevertheless, there are still important gaps in the literature that merit further attention, arising at least partly from emerging policy problems. These include more research on housing and biodiversity, the relationship between housing and civil unrest, the effects of changing age distributions - notably housing for the elderly - and the impact of different international institutional structures. Methodologically, developments in Big Data provide an exciting framework for future work.

Reducing defects through organizational learning within a Housing Association environment

Housing Associations (HAs) contribute circa 20% of the UK’s housing supply. HAs are however under increasing pressure as a result of funding cuts and rent reductions. Due to the increased pressure, a number of processes are currently being reviewed by HAs, especially how they manage and learn from defects. Learning from defects is considered a useful approach to achieving defect reduction within the UK housebuilding industry. This paper contributes to our understanding of how HAs learn from defects by undertaking an initial round table discussion with key HA stakeholders as part of an ongoing collaborative research project with the National House Building Council (NHBC) to better understand how house builders and HAs learn from defects to reduce their prevalence. The initial discussion shows that defect information runs through a number of groups, both internal and external of a HA during both the defects management process and organizational learning (OL) process. Furthermore, HAs are reliant on capturing and recording defect data as the foundation for the OL process. During the OL process defect data analysis is the primary enabler to recognizing a need for a change to organizational routines. When a need for change has been recognized, new options are typically pursued to design out defects via updates to a HAs Employer’s Requirements. Proposed solutions are selected by a review board and committed to organizational routine. After implementing a change, both structured and unstructured feedback is sought to establish the change’s success. The findings from the HA discussion demonstrates that OL can achieve defect reduction within the house building sector in the UK. The paper concludes by outlining a potential ‘learning from defects model’ for the housebuilding industry as well as describing future work.

Are mortgage lenders guilty of the housing bubble? A UK perspective

Existing theoretical models of house prices and credit rely on continuous rationality of consumers, an assumption that has been frequently questioned in recent years. Meanwhile, empirical investigations of the relationship between prices and credit are often based on national-level data, which is then tested for structural breaks and asymmetric responses, usually with subsamples. Earlier author argues that local markets are structurally different from one another and so the coefficients of any estimated housing market model should vary from region to region. We investigate differences in the price–credit relationship for 12 regions of the UK. Markov-switching is introduced to capture asymmetric market behaviours and turning points. Results show that credit abundance had a large impact on house prices in Greater London and nearby regions alongside a strong positive feedback effect from past house price movements. This impact is even larger in Greater London and the South East of England when house prices are falling, which are the only instances where the credit effect is more prominent than the positive feedback effect. A strong positive feedback effect from past lending activity is also present in the loan dynamics. Furthermore, bubble probabilities extracted using a discrete Kalman filter neatly capture market turning points.

The multiple team formation problem using sociometry

The Team Formation problem (TFP) has become a well-known problem in the OR literature over the last few years. In this problem, the allocation of multiple individuals that match a required set of skills as a group must be chosen to maximise one or several social positive attributes. Speci�cally, the aim of the current research is two-fold. First, two new dimensions of the TFP are added by considering multiple projects and fractions of people's dedication. This new problem is named the Multiple Team Formation Problem (MTFP). Second, an optimization model consisting in a quadratic objective function, linear constraints and integer variables is proposed for the problem. The optimization model is solved by three algorithms: a Constraint Programming approach provided by a commercial solver, a Local Search heuristic and a Variable Neighbourhood Search metaheuristic. These three algorithms constitute the first attempt to solve the MTFP, being a variable neighbourhood local search metaheuristic the most effi�cient in almost all cases. Applications of this problem commonly appear in real-life situations, particularly with the current and ongoing development of social network analysis. Therefore, this work opens multiple paths for future research.